Chapter 12
Discussion Questions
12-1.
What are the important administrative considerations in the capital budgeting process?
Important administrative considerations relate to,the search for and discovery of investment opportunities,the collection of data,the evaluation of projects,and the reevaluation of prior decisions.
12-2.
Why does capital budgeting rely on analysis of cash flows rather than on net income?
Cash flow rather than net income is used in capital budgeting analysis because the primary concern is with the amount of actual dollars generated,For example,depreciation is subtracted out in arriving at net income,but this noncash deduction should be added back in to determine cash flow or actual dollars generated.
12-3.
What are the weaknesses of the payback method?
The weaknesses of the payback method are:
There is no consideration of inflows after the cutoff period.
The concept fails to consider the time value of money.
12-4.
What is normally used as the discount rate in the net present value method?
The cost of capital as determined in Chapter 11.
12-5.
What does the term mutually exclusive investments mean?
The selection of one investment precludes the selection of other alternative investments.
12-6.
How does the modified internal rate of return include concepts from both the traditional internal rate and the net present value methods?
The modified internal ratio of return calls for the determination of the interest rate that equates future inflows to the investment as does the traditional internal rate or return,However,it incorporates the reinvestment rate assumption of the net present value method,That is that inflows are reinvested at the cost of capital.
12-7.
If a corporation has projects that will earn more than the cost of capital,should it ration capital?
From a purely economic viewpoint,a firm should not ration capital,The firm should be able to find additional funds and increases its overall profitability and wealth through accepting investments to the point where marginal return equals marginal cost.
12-8.
What is the net present value profile? What three points should be determined to graph the profile?
The net present value profile allows for the graphic portrayal of the net present value of a project at different discount rates,Net present values are shown along the vertical axis and discount rates are shown along the horizontal axis.
The points that must be determined to graph the profile are:
The net present value at zero discount rate.
The net present value as determined by a normal discount rate.
The internal rate of return for the investment.
12-9.
How does an asset's ADR (asset depreciation range) relate to its MACRS category?
The ADR represents the asset depreciation range or the expected physical life of the asset,Generally,the midpoint of the range or life is utilized,The longer the ADR midpoint,the longer the MACRS category in which the asset is placed,However,most assets can still be written off more rapidly than the midpoint of the ADR,For example,assets with ADR midpoints of 10 years to 15 years can be placed in the 7-year MACRS category for depreciation purposes.
Problems
12-1.
Assume a corporation has earnings before depreciation and taxes of $90,000,and depreciation of $40,000,and that it has a 30 percent tax bracket,Compute its cash flow using the format below.
Earnings before depreciation and taxes
Depreciation
Earnings before taxes
Taxes @ 30%
Earnings after taxes
Depreciation
Cash flow
Solution:
Earnings before depreciation and taxes $90,000
Depreciation –40,000
Earnings before taxes 50,000
Taxes @ 30% –15,000
Earnings after taxes $35,000
Depreciation +40,000
Cash flow $75,000
12-2.
a. In problem 1,how much would cash flow be if there were only $10,000 in depreciation? All other factors are the same.
b. How much cash flow is lost due to the reduced depreciation between problems 1 and 2a?
Solution:
a. Earnings before depreciation and taxes $90,000
Depreciation –10,000
Earnings before taxes $80,000
Taxes @ 30% –24,000
Earnings after taxes $56,000
Depreciation +10,000
Cash flow $66,000
b. Cash flow (problem 1) $75,000
Cash flow (problem 2) 66,000
Difference in cash flow $ 9,000
12-3.
Assume a firm has earnings before depreciation and taxes of $200,000 and no depreciation,It is in a 40 percent tax bracket.
a. Compute its cash flow.
b. Assume it has $200,000 in depreciation,Recompute its cash flow.
c. How large a cash flow benefit did the depreciation provide?
d. Would the president of a firm on the New York Stock Exchange likely be satisfied with the earnings after taxes results in part c?
Solution:
a. Earnings before depreciation and taxes $200,000
Depreciation – 0
Earnings before taxes 200,000
Taxes @ 40% – 80,000
Earnings after taxes 120,000
Depreciation – 0
Cash flow $120,000
b. Earnings before depreciation and taxes $200,000
Depreciation –200,000
Earnings before taxes 0
Taxes @ 40% 0
Earnings after taxes 0
Depreciation 200,000
Cash flow $200,000
12-3,Continued
c. The $200,000 in depreciation provided a cash flow benefit of $80,000.
Cash flow (b) $200,000
Cash flow (a) 120,000
Cash flow benefit $ 80,000
d. The president of a New York Stock Exchange firm might not be satisfied by the results provided by depreciation,Although depreciation increased cash flow by $80,000,it decreased earnings after taxes by $120,000 down to zero,CEOs tend to be very sensitive to earnings performance,Although this is not necessarily rational,it is likely to be true.
12-4.
Assume a $40,000 investment and the following cash flows for two alternatives.
Year
Investment X
Investment Y
1
$ 6,000
$15,000
2
8,000
20,000
3
9,000
10,000
4
17,000
5
20,000
Which of the alternatives would you select under the payback method?
Solution:
Payback for Investment X
Payback for Investment Y
$40,000 – $ 6,000 1 year
$40,000 – $15,000 1 year
34,000 – 8,000 2 years
25,000 – 20,000 2 years
26,000 – 9,000 3 years
5,000/10,000 ,5 years
17,000 – 17,000 4 years
Payback Investment X = 4.00 years
Payback Investment Y = 2.50 years
Investment Y would be selected because of the faster payback.
12-5.
Referring back to problem 4,if the inflow in the fifth year for investment X were $20,000,000 instead of $20,000,would your answer change under the payback method?
Solution,
The $20,000,000 inflow would still leave the payback period for Investment X at 4 years,It would remain inferior to Investment Y under the payback method.
12-6.
The Short-Line Railroad is considering a $100,000 investment in either of two companies,The cash flows are as follows:
Year
Electric Co.
Water Works
1
$70,000
$15,000
2
15,000
15,000
3
15,000
70,000
4-10
10,000
10,000
a. Using the payback method,what will the decision be?
b. Explain why the answer in part a can be misleading.
Solution:
Short-Line Railroad
a.
Payback for Electric Co.
Payback for Water Works
$100,000 – $70,000 1 year
$100,000 – $15,000 1 year
30,000 – 15,000 2 years
85,000 – 15,000 2 years
15,000 – 15,000 3 years
70,000 – 70,000 3 years
Payback (Electric Co.) = 3 years
Payback (Water Works) = 3 years
12-6,Continued
b. The answer in part a is misleading because the two investments seem to be equal with the same payback period of three year,Nevertheless,the Electric Co,is a superior investment because it recovers large cash flows in the first year,while the large recovery for Water Works is not until the third year,The problem is that the payback method does not consider the time value of money.
12-7.
X-treme Vitamin Company is considering two investments,both of which cost $10,000,The cash flows are as follows:
Year
Project A
Project B
1
$12,000
$10,000
2
8,000
6,000
3
6,000
16,000
a. Which of the two projects should be chosen based on the payback method?
b. Which of the two projects should be chosen based on the net present value method? Assume a cost of capital of 10 percent.
c. Should a firm normally have more confidence in answer a or answer b?
Solution:
X-treme Vitamin Company
a. Payback Method
Payback for Project A
Payback for Project B
Under the Payback Method,you should select Project A because of the shorter payback period.
12-7,Continued
b. Net Present Value Method
Project A
Year
Cash Flow
PVIF at 10%
Present Value
1
$12,000
.909
$10,908
2
$ 8,000
.826
$ 6,608
3
$ 6,000
.751
$ 4,506
Present Value of Inflows
$22,022
Present Value of Outflows
10,000
Net Present Value
$12,022
Project B
Year
Cash Flow
PVIF at 10%
Present Value
1
$10,000
.909
$ 9,090
2
$ 6,000
.826
$ 4,956
3
$16,000
.751
$12,016
Present Value of Inflows
$26,062
Present Value of Outflows
10,000
Net Present Value
$16,062
Under the net present value method,you should select Project B because of the higher net present value.
c. A company should normally have more confidence in answer b because the net present value considers all inflows as well as the time value of money,The heavy late inflow for Project B was partially ignored under the payback method.
12-8.
You buy a new piece of equipment for $16,980,and you receive a cash inflow of $3,000 per year for 12 years,What is the internal rate of return?
Solution:
Appendix D
PVIFA =
IRR = 14%
For n = 12,we find 5.660 under the 14% column.
12-9.
Warner Business Products is considering the purchase of a new machine at a cost of $11,070,The machine will provide $2,000 per year in cash flow for eight years,Warner’s cost of capital is 13 percent,Using the internal rate of return method,evaluate this project and indicate whether it should be undertaken.
Solution:
Warner Business Products
Appendix D
PVIFA = $11,070/$2,000 = 5.535
IRR = 9%
For n = 8,we find 5.353 under the 9% column.
The machine should not be purchased since its return is under 13 percent.
12-10.
Elgin Restaurant Supplies is analyzing the purchase of manufacturing equipment that will cost $20,000,The annual cash inflows for the next three years will be:
Year Cash Flow
1 $10,000
2 9,000
3 6,500
a. Determine the internal rate of return using interpolation.
b. With a cost of capital of 12 percent,should the machine be purchased?
Solution:
Elgin Restaurant Supplies
a. Step 1 Average the inflows.
$10,000
9,000
6,500
$25,500 ÷ 3 = $8,500
Step 2 Divide the inflows by the assumed annuity in Step 1.
Step 3 Go to Appendix D for the 1st approximation,The value in Step 2 (for n = 3) falls between 13% and 14%.
Step 4 Try a first approximation of discounting back the inflows,Because the inflows are biased toward the early years,we will use the higher rate of 14%.
12-10,Continued
Year
Cash Flow
PVIF at 14%
Present Value
1
$10,000
.877
$ 8,770
2
9,000
.769
6,921
3
6,500
.675
4,388
$20,079
Step 5 Since the NPV is slightly over $20,000,we need to try a higher rate,We will try 15%.
Year
Cash Flow
PVIF at 15%
Present Value
1
$10,000
.870
$ 8,700
2
9,000
.756
6,804
3
6,500
.658
4,277
$19,781
Because the NPV is now below $20,000,we know the IRR is between 14% and 15%,We will interpolate.
$20,079 PV @ 14%
–19,781 PV @ 15%
$ 298
$20,079 PV @ 14%
–20,000 Cost
$ 79
14% + ($79/$298) (1%) =,265
14% +,265 (1%) = 14.265% IRR
The IRR is 14.265%
12-10,Continued
If the student skipped from 14% to 16%,the calculations to find the IRR would be as follows:
Year
Cash Flow
PVIF at 16%
Present Value
1
$10,000
.862
$ 8,620
2
9,000
.743
6,687
3
6,500
.641
4,167
$19,474
$20,079 PV @ 14%
–19,474 PV @ 16%
$ 605
$20,079 PV @ 14%
–20,000 Cost
$ 79
14% + ($79/$605) (2%) =,131 (2%)
14% + (.131) (2%) = 14.262%
This answer is very close to the previous answer,the difference is due to rounding.
b. Since the IRR of 14.265% (or 14.262%) is greater than the cost of capital of 12%,the project should be accepted.
12-11.
Aerospace Dynamics will invest $110,000 in a project that will produce the following cash flows,The cost of capital is 11 percent,Should the project be undertaken? (Note that the fourth year's cash flow is negative.)
Year Cash Flow
1 $36,000
2 44,000
3 38,000
4 (44,000)
5 81,000
Solution:
Aerospace Dynamics
Year
Cash Flow
PVIF at 11%
Present Value
1
$36,000
.901
$ 32,436
2
44,000
.812
35,728
3
38,000
.731
27,778
4
(44,000)
.659
(28,996)
5
81,000
.593
48,033
Present value of inflows
$114,979
Present value of outflows
110,000
Net present value
$ 4,979
The net present value is positive and the project should be undertaken
12-12.
The Horizon Company will invest $60,000 in a temporary project that will generate the following cash inflows for the next three years.
Year Cash Flow
1 $15,000
2 25,000
3 40,000
The firm will be required to spend $10,000 to close down the project at the end of the three years,If the cost of capital is 10 percent,should the investment be undertaken?
Solution:
Horizon Company
Present Value of Inflows
Year
Cash Flow
x PVIF at 10%
Present Value
1
$15,000
.909
$13,635
2
25,000
.826
20,650
3
40,000
.751
30,040
$64,325
Present Value of Outflows
0
$60,000
1.000
$60,000
3
10,000
.751
7,510
$67,510
Present Value of inflows
$64,325
Present Value of outflows
67,510
Net present value
($ 3,185)
The net present value is negative and the project should not be undertaken.
Note,the $10,000 outflow could have been subtracted out of the $40,000 inflow in the third year and the same answer would result.
12-13.
Skyline Corp,will invest $130,000 in a project that will not begin to produce returns until after the 3rd year,From the end of the 3rd year until the end of the 12th year (10 periods),the annual cash flow will be $34,000,If the cost of capital is 12 percent,should this project be undertaken?
Solution:
Skyline Corporation
Present Value of Inflows
Find the Present Value of a Deferred Annuity
A = $34,000,n = 10,i = 12%
PVA = A x PVIFA (Appendix D)
PVA = $34,000 x 5.650 = $192,100
Discount from Beginning of the third period (end of second period to present):
FV = $192,100,n = 2,i = 12%
PV = FV x PVIF (Appendix B)
PV = $192,100 x,797 = $153,104
Present value of inflows $153,104
Present value of outflows 130,000
Net present value $ 23,104
The net present value is positive and the project should be undertaken.
12-14.
The Ogden Corporation makes an investment of $25,000,which yields the following cash flows:
Year Cash Flow
1 $ 5,000
2 5,000
3 8,000
4 9,000
5 10,000
a. What is the present value with a 9 percent discount rate (cost of capital)?
b. What is the internal rate of return? Use the interpolation procedure shown in this chapter.
c. In this problem would you make the same decision under both parts a and b?
Solution:
Ogden Corporation
a.
Year
Cash Flow
x PVIF @ 9% =
Present Value
1
$ 5,000
.917
$ 4,585
2
5,000
.842
4,210
3
8,000
.772
6,176
4
9,000
.708
6,372
5
10,000
.650
6,500
Present value of inflows
$27,843
Present value of outflows
–25,000
Net present value
$ 2,843
b. Since we have a positive net present value,the internal rate of return must be larger than 9%,Because of uneven cash flows,we need to use trial and error,Counting the net present value calculation as the first trial,we now try 11% for our second trial.
12-14,Continued
Year
Cash Flow
x PVIF @ 11% =
Present Value
1
$ 5,000
.901
$ 4,505
2
5,000
.812
4,060
3
8,000
.731
5,848
4
9,000
.659
5,931
5
10,000
.593
5,930
Present value of inflows
$26,274
A two percent increase in the discount rate has eliminated over one-half of the net present value so another two percent should be close to the answer.
Year
Cash Flow
x PVIF @ 13% =
Present Value
1
$ 5,000
.885
$ 4,425
2
5,000
.783
3,915
3
8,000
.693
5,544
4
9,000
.613
5,517
5
10,000
.543
5,430
Present value of inflows
$24,831
$26,274 PV @ 11%
24,831 PV @ 13%
$ 1,443
$26,274 PV @ 11%
25,000 Cost
$ 1,274
11% + (2%) = 11% +,883 (2%) = 11% + 1.77% = 12.77%
Approximately the same answer can be derived by interpolating between 12% and 13% instead of 11% and 13%.
c. Yes,both the NPV is greater than 0 and the IRR is greater than the cost of capital.
12-15.
The Danforth Tire Company is considering the purchase of a new machine that would increase the speed of manufacturing and save money,The net cost of this machine is $66,000,The annual cash flows have the following projections.
Year Cash Flow
1 $21,000
2 29,000
3 36,000
4 16,000
5 8,000
a. If the cost of capital is 10 percent,what is the net present value?
b. What is the internal rate of return?
c. Should the project be accepted? Why?
Solution:
The Danforth Tire Company
a. Net Present Value
Year
Cash Flow
x 10% PVIF
Present Value
1
$21,000
.909
$19,089
2
29,000
.826
23,954
3
36,000
.751
27,036
4
16,000
.683
10,928
5
8,000
.621
4,968
Present value of inflows
$85,975
Present value of outflows
–66,000
Net present value
$19,975
12-15,Continued
b. Internal Rate of Return
We will average the inflows to arrive at an assumed annuity.
$ 21,000
29,000
36,000
16,000
8,000
$110,000/5 = $22,000
We divide the investment by the assumed annuity value.
Using Appendix D for n = 5,20% appears to be a reasonable first approximation (2.991),We try 20%.
Year
Cash Flow
x 20% PVIF =
Present Value
1
$21,000
.833
$17,493
2
29,000
.694
20,126
3
36,000
.579
20,844
4
16,000
.482
7,712
5
8,000
.402
3,216
Present value of inflows
$69,391
Since 20% is not high enough,we try the next highest rate at 25%.
12-15,Continued
Year
Cash Flow
x 25% PVIF =
Present Value
1
$21,000
.800
$16,800
2
29,000
.640
18,560
3
36,000
.512
18,432
4
16,000
.410
6,560
5
8,000
.328
2,624
Present value of inflows
$62,976
The correct answer must fall between 20% and 25%,We interpolate.
$69,391 PV @ 20%
62,976 PV @ 25%
$ 6,415
$69,391 PV @ 20%
66,000 (Cost)
$ 3,391
20% + (5%) = 20% +,529 (5%) = 20% + 2.657% = 22.65%
c. The project should be accepted because the net present value is positive and the IRR exceeds the cost of capital.
12-16.
You are asked to evaluate two projects for Adventures Club,Inc,Using the net present value method combined with the profitability index approach described in footnote 2 of this chapter,which project would you select? Use a discount rate of 12 percent.
Project X (trips to Disneyland)
($10,000 investment)
Project Y (international film festivals);
($22,000 investment)
Year Cash Flow
1 $4,000
2 5,000
3 4,200
4 3,600
Year Cash Flow
1 $10,800
2 9,600
3 6,000
4 7,000
12-16,Continued
Solution:
Adventures Club,Inc.
NPV for Project X
Year
Cash Flow
PVIF at 12%
Present Value
1
$4,000
.893
$ 3,572
2
5,000
.797
3,985
3
4,200
.712
2,990
4
3,600
.636
2,290
Present value of inflows
$12,837
Present value of outflows (Cost) –10,000
Net present value
$ 2,837
NPV for Project Y
Year
Cash Flow
x PVIF at 12% =
Present Value
1
$10,800
.893
$ 9,644
2
9,600
.797
7,651
3
6,000
.712
4,272
4
7,000
.636
4,452
Present value of inflows
$26,019
Present value of outflows –22,000
Net present value
$ 4,019
12-16,Continued
You should select Project X because it has the higher profitability index,This is true in spite of the fact that it has a lower net present value,The profitability index may be appropriate when you have different size investments,It tells you that for every dollar of outflows,the present value of the inflows is worth x dollars,For project x we get 1.2837 vs 1.1827 for project y,Project x has the higher internal rate of return but project y will add more value to the firm.
12-17.
Cablevision,Inc,will invest $48,000 in a project,The firm's discount rate (cost of capital) is 9 percent,The investment will provide the following inflows.
Year Inflow
1 $10,000
2 10,000
3 16,000
4 19,000
5 20,000
The internal rate of return is 15 percent.
a. If the reinvestment assumption of the net present value method is used,what will be the total value of the inflows after five years? (Assume the inflows come at the end of each year.)
b. If the reinvestment assumption of the internal rate of return method is used,what will be the total value of the inflows after five years?
c. Generally,is one investment assumption likely to be better than another?
12-17,Continued
Solution:
Cablevision,Inc.
a. Reinvestment assumption of NPV
Year
Inflows
Rate
No,of
Periods
Future
Value Factor
Value
1
$10,000
9%
4
1.412
$14,120
2
10,000
9%
3
1.295
12,950
3
16,000
9%
2
1.188
19,008
4
19,000
9%
1
1.090
20,710
5
20,000
--
0
1.000
20,000
$86,788
b. Reinvestment assumption of IRR
Year
Inflows
Rate
No,of
Periods
Future
Value Factor
Value
1
$10,000
15%
4
1.749
$17,490
2
10,000
15%
3
1.521
15,210
3
16,000
15%
2
1.323
21,168
4
19,000
15%
1
1.150
21,850
5
20,000
–
0
1.000
20,000
$95,718
c. Not necessarily,However,for investments with a very high IRR,it may be unrealistic to assume that reinvestment can take place at an equally high rate,The net present value method makes the more conservative assumption of reinvestment at the cost of capital.
12-18.
The 21st Century Corporation uses the modified internal rate of return,The firm has a cost of capital of 8 percent,The project being analyzed is as follows ($20,000 investment):
Year Cash Flow
1 $10,000
2 9,000
3 6,800
a. What is the modified internal rate of return? An approximation from Appendix B is adequate,(You do not need to interpolate.)
b. Assume the traditional internal rate of return on the investment is 14.9 percent,Explain why your answer is part a would be lower.
Solution:
21st Century Corporation
Terminal Value (end of year 3)
a.
Period of Growth FV factor (8%) Future Value
Year 1 $10,000 2 1.166 $11,660
Year 2 9,000 1 1.080 9,720
Year 3 6,800 0 1.000 6,800
Terminal Value $28,180
To determine the modified internal rate of return,calculate the yield on the investment.
Use Appendix B for 3 periods,the answer is approximately 12 percent (.712).
12-18,Continued
b. The modified internal rate of return (MIRR) is lower than the traditional internal rate of return because with the MIRR you are assuming inflows are being reinvested at the cost of capital (8%) whereas with the traditional internal rate of return,you are assuming inflows are being reinvested at the IRR (14.9 percent).
12-19.
Oliver Stone and Rock Company uses a process of capital rationing in its decision making,The firm's cost of capital is 12 percent,It will only invest $80,000 this year,It has determined the internal rate of return for each of the following projects.
Project
Project Size
Percent of
Internal Rate
of Return
A
$15,000
14%
B
25,000
19
C
30,000
10
D
25,000
16.5
E
20,000
21
F
15,000
11
G
25,000
18
H
10,000
17.5
a. Pick out the projects that the firm should accept.
b. If Projects B and G are mutually exclusive,how would that affect your overall answer? That is,which projects would you accept in spending the $80,000?
12-19,Continued
Solution:
Oliver Stone and Rock Company
You should rank the investments in terms of IRR.
Project
IRR
Project Size
Total Budget
E
21%
$20,000
$ 20,000
B
19
25,000
45,000
G
18
25,000
70,000
H
17.5
10,000
80,000
D
16.5
25,000
105,000
A
14
15,000
120,000
F
11
15,000
135,000
C
10
30,000
165,000
a. Because of capital rationing,only $80,000 worth of projects can be accepted,The four projects to accept are E,B,G and H,Projects D and A provide positive benefits also,but cannot be undertaken under capital rationing.
b. If Projects B and G are mutually exclusive,you would select Project B in preference to G,In summary,you would accept E,B,H and D,Project D would replace G and is of the same $25,000 magnitude.
12-20.
Miller Electronics is considering two new investments,Project C calls for the purchase of a coolant recovery system,Project H represents an investment in a heat recovery system,The firm wishes to use a net present value profile in comparing the projects,The investment and cash flow patterns are as follows:
Project C
($25,000 investment)
Project H
($25,000 investment)
Year Cash Flow
1 $ 6,000
2 7,000
3 9,000
4 13,000
Year Cash Flow
1 $20,000
2 6,000
3 5,000
a. Determine the net present value of the projects based on a zero discount rate.
b. Determine the net present value of the projects based on a 9 percent discount rate.
c. The internal rate of return on Project C is 13.01 percent,and the internal rate of return on Project H is 15.68 percent,Graph a net present value profile for the two investments similar to Figure 12-3,(Use a scale up to $10,000 on the vertical axis,with $2,000 increments,Use a scale up to 20 percent on the horizontal axis,with 5 percent increments.)
d. If the two projects are not mutually exclusive,what would your acceptance or rejection decision be if the cost of capital (discount rate) is 8 percent? (Use the net present value profile for your decision; no actual numbers are necessary.)
e. If the two projects are mutually exclusive (the selection of one precludes the selection of the other),what would be your decision if the cost of capital is (1) 5 percent,(2) 13 percent,(3) 19 percent? Use the net present value profile for your answer.
12-20,Continued
Solution:
Miller Electronics
a. Zero discount rate
Project c
Inflows Outflow
$10,000 = ($6,000 + $7,000 + $9,000 + $13,000) – $25,000
Project H
Inflows Outflow
$ 6,000 = ($20,000 + $6,000 + $5,000) – $25,000
b. 9% discount rate
Project C
Year
Cash Flow
PVIF at 9%
Present Value
1
$ 6,000
.917
$ 5,502
2
7,000
.842
5,894
3
9,000
.772
6,948
4
13,000
.708
9,204
Present value of inflows
$27,548
Present value of outflows
25,000
Net present value
$ 2,548
12-20,Continued
Project H
Year
Cash Flow
PVIF at 9%
Present Value
1
$20,000
.917
$18,340
2
6,000
.842
5,052
3
5,000
.772
3,860
Present value of inflows
$27,252
Present value of outflows
25,000
Net present value
$ 2,252
c. Net Present Value Profile
12-20,Continued
d. Since the projects are not mutually exclusive,they both can be selected if they have a positive net present value,At an 8% rate,they should both be accepted,As a side note,we can see Project C is superior to Project H.
e. With mutually exclusive projects,only one can be accepted,Of course,that project must still have a positive net present value,Based on the visual evidence,we see:
(i) 5% cost of capital—select Project C
(ii) 13% cost of capital—select Project H
(iii) 19% cost of capital—do not select either project
12-21.
Software Systems is considering an investment of $20,000,which produces the following inflows.
Year Cash Flow
1 $11,000
2 9,000
3 5,800
You are going to use the net present value profile to approximate the value for the internal rate of return,Please follow these steps.
a. Determine the net present value project based on a zero discount rate.
b. Determine the net present value of the project based on a 10 percent discount rate.
c. Determine the net present value of the project based on a 20 percent discount rate (it will be negative).
d. Draw a net present value profile for the investment,(Use a scale up to $6,000 on the vertical axis,with $2,000 increments,Use a scale up to 20 percent on the horizontal axis,with 5 percent increments.) Observe the discount rate at which the net present value is zero,This is an approximation of the internal rate of return on the project.
e. Actually compute the internal rate of return based on the interpolation procedure presented in this chapter,Compare your answers in parts d and e.
12-21,Continued
Solution:
Software Systems
a. NPV @ 0% discount rate
Inflows Outflow
$5,800 = ($11,000 + $9,000 + $5,800) – $20,000
b. 10% Discount Rate
Year
Cash Flow
PVIF @ 10%
Present Value
1
$11,000
.909
$ 9,999
2
9,000
.826
7,434
3
5,800
.751
4,356
Present value of inflows
$21,789
Present value of outflows
20,000
Net present value
$ 1,789
c. 20% Discount Rate
Year
Cash Flow
PVIF @ 20%
Present Value
1
$11,000
.833
$ 9,163
2
9,000
.694
6,246
3
5,800
.579
3,358
Present value of inflows
$18,767
Present value of outflows
20,000
Net present value
($ 1,233)
12-21,Continued
d. Net Present Value Profile
e. The answer appears to be slightly above 15%,We will use 15% as the first approximation.
Year
Cash Flow
PVIF @ 15%
Present Value
1
$11,000
.870
$ 9,570
2
9,000
.756
6,804
3
5,800
.658
3,816
Present value of inflows
$20,190
The second approximation is at 16%.
Year
Cash Flow
PVIF @ 16%
Present Value
1
$11,000
.862
$ 9,482
2
9,000
.743
6,687
3
5,800
.641
3,718
Present value of inflows
$19,887
12-21,Continued
We interpolate between 15% and 16%.
$20,190 PV @ 15%
19,887 PV @ 16%
$ 303
$20,190 PV @ 15%
20,000 Cost
$ 190
15% + ($190/$303) (1%) = 15% +,63 = 15.63%
The interpolation value of 15.63% appears to be very close to the graphically determined value in part d.
12-22.
Howell Magnetics Corporation is going to purchase an asset for $400,000 that will produce $180,000 per year for the next four years in earnings before depreciation and taxes,The asset will be depreciated using the three-year MACRS depreciation schedule in Table 12-9,(This represents four years of depreciation based on the half-year convention.) The firm is in a 34 percent tax bracket,Fill in the schedule below for the next four years,(You need to first determine annual depreciation.)
Earnings before depreciation and taxes
Depreciation
Earnings before taxes
Taxes
Earnings after taxes
+ Depreciation
Cash flow
12-22,Continued
Solution:
Howell Magnetics Corporation
First determine annual depreciation.
Year
Depreciation Base
Percentage Depreciation (Table 12-9)
Annual Depreciation
1
$400,000
.333
$133,200
2
400,000
.445
178,000
3
400,000
.148
59,200
4
400,000
.074
29,600
$400,000
Then determine the annual cash flow,Earnings before depreciation and taxes (EBDT) will be the same for each year,but depreciation and cash flow will differ.
1
2
3
4
EBDT
$180,000
$180,000
$180,000
$180,000
– D
133,200
178,000
59,200
29,600
EBT
46,800
2,000
120,800
150,400
T (34%)
15,912
680
41,072
51,136
EAT
30,888
1,320
79,728
99,264
+ D
133,200
178,000
59,200
29,600
Cash Flow
$164,088
$179,320
$138,928
$128,864
12-23.
Assume $80,000 is going to be invested in each of the following assets,Using Tables 12-8 and 12-9,indicate the dollar amount of the first year's depreciation.
a. Computers
b. Petroleum refining product
c. Office furniture
d. Pipeline distribution
Solution:
a. Computers – Based on Table 12-8,this falls under 5-year ACRS depreciation,Then examining Table 12-9,the first year depreciation rate is,200,Thus:
$80,000 x,200 = $16,000
b. Petroleum refining product – This falls under 10-year ACRS depreciation,This first year depreciation rate is,100.
$80,000 x,100 = $8,000
c. Office furniture – This falls under 7-year ACRS depreciation,The first year depreciation rate is,143.
$80,000 x,143 = $11,440
d. Pipeline distribution – This falls under 15-year ACRS depreciation,This first year depreciation rate is,050.
$80,000 x,050 = $4,000
12-24.
The Keystone Corporation will purchase an asset that qualifies for three-year MACRS depreciation,The cost is $60,000 and the asset will provide the following stream of earnings before depreciation and taxes for the next four years:
Year 1 $27,000
Year 2 30,000
Year 3 23,000
Year 4 15,000
The firm is in a 36 percent tax bracket and has an 11 percent cost of capital,Should it purchase the asset?
Solution:
The Keystone Corporation
Year
Depreciation Base
Percentage Depreciation (Table 12-9)
Annual Depreciation
1
$60,000
.333
$19,980
2
60,000
.445
26,700
3
60,000
.148
8,880
4
60,000
.074
4,440
$60,000
Then determine the annual cash flow.
1
2
3
4
EBDT
$27,000
$30,000
$23,000
$15,000
– D
19,980
26,700
8,880
4,440
EBT
7,020
3,300
14,120
10,560
T (36%)
2,527
1,188
5,083
3,802
EAT
4,493
2,112
9,037
6,758
+ D
19,980
26,700
8,880
4,440
Cash Flow
$24,473
$28,812
$17,917
$11,198
12-24,Continued
Then determine the net present value.
Year
Cash Flow
(inflows)
PVIF @ 11%
Present Value
1
$24,473
.901
$22,050
2
28,812
.812
23,395
3
17,917
.731
13,097
4
11,198
.659
7,379
Present value of inflows
$65,921
Present value of outflows
60,000
Net present value
$ 5,921
The asset should be purchased based on the net present value.
12-25.
Oregon Forest Products will acquire new equipment that falls under the five-year MACRS category,The cost is $300,000,If the equipment is purchased,the following earnings before depreciation and taxes will be generated for the next six years.
Year 1 $112,000
Year 2 105,000
Year 3 82,000
Year 4 53,000
Year 5 37,000
Year 6 32,000
The firm is in a 30 percent tax bracket and has a 14 percent cost of capital,Should Oregon Forest Products purchase the equipment? Use the net present value method.
12-25,Continued
Solution:
Oregon Forest Products
First determine annual depreciation.
Year
Depreciation Base
Percentage Depreciation (Table 12-9)
Annual Depreciation
1
$300,000
.200
$ 60,000
2
300,000
.320
96,000
3
300,000
.192
57,600
4
300,000
.115
34,500
5
300,000
.115
34,500
6
300,000
.058
17,400
$300,000
Then determine the annual cash flow.
Annual Cash Flow
1
2
3
4
5
6
EBDT
$112,000
$105,000
$82,000
$53,000
$37,000
$32,000
– D
60,000
96,000
57,600
34,500
34,500
17,400
EBT
52,000
9,000
24,400
18,500
2,500
14,600
T (30%)
15,600
2,700
7,320
5,550
750
4,380
EAT
36,400
6,300
17,080
12,950
1,750
10,220
+ D
60,000
96,000
57,600
34,500
34,500
17,400
Cash Flow
$ 96,400
$102,300
$74,680
$47,450
$36,250
$27,620
Then determine the net present value.
12-25,Continued
Year
Cash Flow
(inflows)
PVIF @ 14%
Present Value
1
$ 96,400
.877
$ 84,543
2
102,300
.769
78,669
3
74,680
.675
50,409
4
47,450
.592
28,090
5
36,250
.519
18,814
6
27,620
.456
12,595
Present value of inflows
$273,120
Present value of outflows
300,000
Net present value
($ 26,880)
The equipment should not be purchased.
12-26.
The Thorpe Corporation is considering the purchase of manufacturing equipment with a 10-year midpoint in its asset depreciation range (ADR),Carefully refer to Table 12-8 to determine in what depreciation category the asset falls,(Hint,It is not 10 years.) The asset will cost $80,000,and it will produce earnings before depreciation and taxes of $28,000 per year for three years,and then $12,000 a year for seven more years,The firm has a tax rate of 34 percent,With a cost of capital of 12 percent,should it purchase the asset? Use the net present value method,In doing your analysis,if you have years in which there is no depreciation,merely enter a zero for depreciation.
Solution:
The Thorpe Corporation
Because the manufacturing equipment has a 10-year midpoint of its asset depreciation range (ADR),it falls into the seven-year MACRS category as indicated in Table 12-8,Furthermore,we see that most types of manufacturing equipment fall into the seven-year MACRS category.
12-26,Continued
With seven-year MACRS depreciation,the asset will be depreciated over eight years (based on the half-year convention),Also,we observe that the equipment will produce earnings for 10 years,so in the last two years there will be no depreciation write-off.
We first determine the annual depreciation.
Year
Depreciation Base
Percentage Depreciation (Table 12-9)
Annual Depreciation
1
$80,000
.143
$11,440
2
80,000
.245
19,600
3
80,000
.175
14,000
4
80,000
.125
10,000
5
80,000
.089
7,120
6
80,000
.089
7,120
7
80,000
.089
7,120
8
80,000
.045
3,600
$80,000
12-26,Continued
Then determine the annual cash flow:
Annual Cash Flow
1
2
3
4
5
6
7
8
9
10
EBDT
$28,000
$28,000
$28,000
$12,000
$12,000
$12,000
$12,000
$12,000
$12,000
$12,000
– D
11,440
19,600
14,000
10,000
7,120
7,120
7,120
3,600
0
0
EBT
$16,560
$ 8,400
$14,000
$ 2,000
$ 4,880
$ 4,880
$ 4,880
$ 8,400
$12,000
$12,000
T (34%)
5,630
2,856
4,760
680
1,659
1,659
1,659
2,856
4,080
4,080
EAT
$10,930
$ 5,544
$ 9,240
$ 1,320
$ 3,221
$ 3,221
$ 3,221
$ 5,544
$ 7,920
$ 7,920
+ D
11,440
19,600
14,000
10,000
7,120
7,120
7,120
3,600
0
0
Cash Flow
$22,370
$25,144
$23,240
$11,320
$10,341
$10,341
$10,341
$ 9,144
$ 7,920
$ 7,920
12-26,Continued
Next determine the net present value.
Year
Cash Flow
(inflows)
PVIF @ 12%
Present Value
1
$22,370
.893
$19,976
2
25,144
.797
20,040
3
23,240
.712
16,547
4
11,320
.636
7,200
5
10,341
.567
5,863
6
10,341
.507
5,243
7
10,341
.452
4,674
8
9,144
.404
3,694
9
7,920
.361
2,859
10
7,920
.322
2,550
Present value of inflows
$88,646
Present value of outflows
80,000
Net present value
$ 8,646
The asset should be purchased.
12-27.
The Spartan Technology Company has a proposed contract with the Digital Systems Company of Michigan,The initial investment in land and equipment will be $120,000,Of this amount,$70,000 is subject to five-year MACRS depreciation,The balance is in nondepreciable property,The contract covers six years; at the end of six years the nondepreciable assets will be sold for $50,000,The depreciated assets will have zero resale value.
The contract will require an additional investment of $55,000 in working capital at the beginning of the first year and,of this amount,$25,000 will be returned to the Spartan Technology Company after six years.
The investment will produce $50,000 in income before depreciation and taxes for each of the six years,The corporation is in a 40 percent tax bracket and has a 10 percent cost of capital.
Should the investment be undertaken? Use the net present value method.
12-27,Continued
Solution:
Spartan Technology Company
Although there are some complicating features in the problem,we are still comparing the present value of cash flows to the total initial investment.
The initial investment is:
Land and equipment $120,000
Working capital 55,000
Initial investment $175,000
In computed the present value of the cash flows,we first determine annual depreciation based on a $70,000 depreciation base.
Year
Depreciation Base
Percentage Depreciation (Table 12-9)
Annual Depreciation
1
$70,000
.200
$14,000
2
70,000
.320
22,400
3
70,000
.192
13,440
4
70,000
.115
8,050
5
70,000
.115
8,050
6
70,000
.058
4,060
$70,000
We then determine the annual cash flow,In addition to normal cash flow from operations; we also consider the funds generated in the sixth year from the sale of the nondepreciable property (land) and from the recovery of working capital.
12-27,Continued
Then determine the annual cash flow.
Annual Cash Flow
1
2
3
4
5
6
EBDT
$50,000
$50,000
$50,000
$50,000
$50,000
$50,000
– D
14,000
22,400
13,440
8,050
8,050
4,060
EBT
36,000
27,600
36,560
41,950
41,950
45,940
T (40%)
14,400
11,040
14,624
16,780
16,780
18,376
EAT
21,600
16,560
21,936
25,170
25,170
27,564
+ D
14,000
22,400
13,440
8,050
8,050
4,060
+ Sale of non-depreciable assets
50,000
+ Recovery
of working
capital ______
______
______
______
______
25,000
Cash Flow
$35,600
$38,960
$35,376
$33,220
$33,220
$106,624
We then determine the net present value.
Year
Cash Flow
(inflows)
PVIF @ 10%
Present Value
1
$ 35,600
.909
$ 32,360
2
38,960
.826
32,181
3
35,376
.751
26,567
4
33,220
.683
22,689
5
33,220
.621
20,630
6
106,624
.564
60,136
Present value of inflows
$194,563
Present value of outflows
175,000
Net present value
$ 19,563
The investment should be undertaken.
12-28.
An asset was purchased three years ago for $140,000,It falls into the five-year category for MACRS depreciation,The firm is in a 35 percent tax bracket,Compute the:
a. Tax loss on the sale and the related tax benefit if the asset is sold now for $15,320.
b. Gain and related tax on the sale if the asset is sold now for $58,820,(Refer to footnote 3.)
Solution:
First determine the book value of the asset.
Year
Depreciation Base
Percentage Depreciation (Table 12-9)
Annual Depreciation
1
$140,000
.200
$28,000
2
140,000
.320
44,800
3
140,000
.192
26,880
Total depreciation to date
$99,680
Purchase price $140,000
– Total depreciation to date 99,680
Book value $ 40,320
a. $15,320 sales price
Book value $40,320
Sales price 15,320
Tax loss on the sale $25,000
Tax loss on the sale $25,000
Tax rate 35%
Tax benefit $ 8,750
12-28,Continued
b. $58,820 sales price
Sales price $58,820
Book value 40,320
Taxable gain 18,500
Tax rate 35%
Tax obligation $ 6,475
12-29.
Graphic Systems purchased a computerized measuring device two years ago for $80,000,It falls into the five-year category for MACRS depreciation,The equipment can currently be sold for $28,400.
A new piece of equipment will cost $210,000,It also falls into the five-year category for MACRS depreciation.
Assume the new equipment would provide the following stream of added cost savings for the next six years.
Year Cost Savings
1 $76,000
2 66,000
3 62,000
4 60,000
5 56,000
6 42,000
The tax rate is 34 percent and the cost of capital is 12 percent.
a. What is the book value of the old equipment?
b. What is the tax loss on the sale of the old equipment?
c. What is the tax benefit from the sale?
d. What is the cash inflow from the sale of the old equipment?
e. What is the net cost of the new equipment? (Include the inflow from the sale of the old equipment.)
f. Determine the depreciation schedule for the new equipment.
g. Determine the depreciation schedule for the remaining years of the old equipment.
h. Determine the incremental depreciation between the old and new equipment and the related tax shield benefits.
12-29,Continued
i. Compute the aftertax benefits of the cost savings.
j. Add the depreciation tax shield benefits and the aftertax cost savings,and determine the present value,(See Table 12-17 on page ___ as an example.)
k. Compare the present value of the incremental benefits (j) to the net cost of the new equipment (e),Should the replacement be undertaken?
Solution:
Replacement Decision Analysis
Graphic Systems
a.
Year
Depreciation Base
Percentage Depreciation (Table 12-9)
Annual Depreciation
1
$80,000
.200
$16,000
2
80,000
.320
25,600
Total depreciation to date
$41,600
Purchase price $80,000
– Total depreciation to date 41,600
Book value $38,400
b. Book value $38,400
Sales price 28,400
Tax loss on the sale $10,000
c. Tax loss on the sale $10,000
Tax rate 34%
Tax benefit $ 3,400
d. Sales price of the old equipment $28,400
Tax benefit from the sale 3,400
Cash inflow from the sale of the old equipment $31,800
12-29,Continued
e. Price of the new equipment $210,000
– Cash inflow from the sale of the old equipment 31,800
Net cost of the new equipment $178,200
f. Depreciation schedule on the new equipment.
Year
Depreciation Base
Percentage Depreciation (Table 12-9)
Annual Depreciation
1
$210,000
.200
$ 42,000
2
210,000
.320
67,200
3
210,000
.192
40,320
4
210,000
.115
24,150
5
210,000
.115
24,150
6
210,000
.058
12,180
$210,000
g. Depreciation schedule for the remaining years of the old equipment.
Year*
Depreciation Base
Percentage Depreciation (Table 12-9)
Annual Depreciation
1
$80,000
.192
$15,360
2
80,000
.115
9,200
3
80,000
.115
9,200
4
80,000
.058
4,640
* The next four years represent the last four years on the old equipment.
12-29,Continued
h. Incremental depreciation and tax shield benefits.
(1)
Year
(2)
Depreciation on new Equipment
(3)
Depreciation on old Equipment
(4)
Incremental
Depreciation
(5)
Tax Rate
(6)
Tax
Shield
Benefits
1
$42,000
$15,360
$26,640
.34
$ 9,058
2
67,200
9,200
58,000
.34
19,720
3
40,320
9,200
31,120
.34
10,581
4
24,150
4,640
19,510
.34
6,633
5
24,150
24,150
.34
8,211
6
12,180
12,180
.34
4,141
i. Aftertax cost savings
Year
Savings
(1-Tax Rate)
After tax Savings
1
$76,000
.66
$50,160
2
66,000
.66
43,560
3
62,000
.66
40,920
4
60,000
.66
39,600
5
56,000
.66
36,960
6
42,000
.66
27,720
12-29,Continued
j. Present value of the total incremental benefits.
(1)
Year
(2)
Tax Shield Benefits from
Depreciation
(3)
After Tax
Cost
Savings
(4)
Total
Annuity
Benefits
(5)
Present
Value
Factor 12%
(6)
Present
Value
1
$ 9,058
$50,160
$59,218
.893
$ 52,882
2
19,720
43,560
63,280
.797
50,434
3
10,581
40,920
51,501
.712
36,669
4
6,633
39,600
46,233
.636
29,404
5
8,211
36,960
45,171
.567
25,612
6
4,141
27,720
31,861
.507
16,154
Present value of incremental benefits
$211,155
k. Present value of incremental benefits $211,155
Net cost of new equipment 178,200
Net present value $ 32,955
Based on the present value analysis,the equipment should be replaced.
Comprehensive Problem
CP 12-1.
The Woodruff Corporation purchased a piece of equipment three years ago for $230,000,It has an asset depreciation range (ADR) midpoint of eight years,The old equipment can be sold for $90,000.
A new piece of equipment can be purchased for $320,000,It also has an ADR of eight years.
Assume the old and new equipment would provide the following operating gains (or losses) over the next six years.
Year
New Equipment
Old Equipment
1
$80,000
$25,000
2
76,000
16,000
3
70,000
9,000
4
60,000
8,000
5
50,000
6,000
6
45,000
(7,000)
The firm has a 36 percent tax rate and a 9 percent cost of capital,Should the new equipment be purchased to replace the old equipment?
Solution:
Replacement Decision Analysis
Woodruff Corporation
Book Value of Old Equipment
(ADR of 8 years indicates the use of the 5-year MACRS schedule)
Year
Depreciation Base
Percentage Depreciation (Table 12-9)
Annual Depreciation
1
$230,000
.200
$ 46,000
2
230,000
.320
73,600
3
230,000
.192
44,160
Total depreciation to date
$163,760
CP 12-1,Continued
Purchase price $230,000
– Total depreciation to date 163,760
Book value $ 66,240
Tax Obligation on the Sale
Sales price $90,000
Book value 66,240
Taxable gain 23,760
Tax rate 36%
Taxes $ 8,554
Cash Inflow From the Sale of the Old Equipment
Sales price $90,000
Taxes 8,554
$81,446
Net Cost of the New Equipment
Purchase price $320,000
– Cash inflow from the sale of the old equipment 81,446
Net cost $238,554
Depreciation Schedule of the New Equipment.
(ADR of 8 years indicates the use of 5-year MACRS Schedule)
CP 12-1,Continued
Year
Depreciation Base
Percentage Depreciation (Table 12-9)
Annual Depreciation
1
$320,000
.200
$ 64,000
2
320,000
.320
102,400
3
320,000
.192
61,440
4
320,000
.115
36,800
5
320,000
.115
36,800
6
320,000
.058
18,560
$320,000
Depreciation Schedule for the Remaining Years of the Old Equipment.
Year*
Depreciation Base
Percentage Depreciation (Table 12-9)
Annual Depreciation
1
$230,000
.115
$26,450
2
230,000
.115
26,450
3
230,000
.058
13,340
* The next three years represent the last three years of the old equipment.
CP 12-1,Continued
Incremental Depreciation and Tax Shield Benefits.
(1)
Year
(2)
Depreciation on New Equipment
(3)
Depreciation on Old Equipment
(4)
Incremental
Depreciation
(5)
Tax Rate
(6)
Tax
Shield
Benefits
1
$ 64,000
$26,450
$37,550
.36
$13,518
2
102,400
26,450
75,950
.36
27,342
3
61,440
13,340
48,100
.36
17,316
4
36,800
36,800
.36
13,248
5
36,800
36,800
.36
13,248
6
18,560
18,560
.36
6,682
Aftertax cost savings
New Equipment
Old Equipment
Cost Savings
(1 – Tax
Rate)
Aftertax
Savings
$80,000
$25,000
$55,000
.64
$35,200
76,000
16,000
60,000
.64
38,400
70,000
9,000
61,000
.64
39,040
60,000
8,000
52,000
.64
33,280
50,000
6,000
44,000
.64
28,160
45,000
(7,000)
52,000
.64
33,280
CP 12-1,Continued
Present value of the total incremental benefits.
(1)
Year
(2)
Tax Shield Benefits from
Depreciation
(3)
After Tax
Cost
Savings
(4)
Total
Annuity
Benefits
(5)
Present
Value
Factor 9%
(6)
Present
Value
1
$13,518
$35,200
$48,718
.917
$ 44,674
2
27,342
38,400
65,742
.842
55,355
3
17,316
39,040
56,356
.772
43,507
4
13,248
33,280
46,528
.708
32,942
5
13,248
28,160
41,408
.650
26,915
6
6,682
33,280
39,962
.596
23,817
Present value of incremental Benefits
$227,210
Net Present Value
Present value of incremental benefits $227,210
Net cost of new equipment 238,554
Net present value ($ 11,344)
Based on the net present value analysis,the equipment should not be replaced.
Discussion Questions
12-1.
What are the important administrative considerations in the capital budgeting process?
Important administrative considerations relate to,the search for and discovery of investment opportunities,the collection of data,the evaluation of projects,and the reevaluation of prior decisions.
12-2.
Why does capital budgeting rely on analysis of cash flows rather than on net income?
Cash flow rather than net income is used in capital budgeting analysis because the primary concern is with the amount of actual dollars generated,For example,depreciation is subtracted out in arriving at net income,but this noncash deduction should be added back in to determine cash flow or actual dollars generated.
12-3.
What are the weaknesses of the payback method?
The weaknesses of the payback method are:
There is no consideration of inflows after the cutoff period.
The concept fails to consider the time value of money.
12-4.
What is normally used as the discount rate in the net present value method?
The cost of capital as determined in Chapter 11.
12-5.
What does the term mutually exclusive investments mean?
The selection of one investment precludes the selection of other alternative investments.
12-6.
How does the modified internal rate of return include concepts from both the traditional internal rate and the net present value methods?
The modified internal ratio of return calls for the determination of the interest rate that equates future inflows to the investment as does the traditional internal rate or return,However,it incorporates the reinvestment rate assumption of the net present value method,That is that inflows are reinvested at the cost of capital.
12-7.
If a corporation has projects that will earn more than the cost of capital,should it ration capital?
From a purely economic viewpoint,a firm should not ration capital,The firm should be able to find additional funds and increases its overall profitability and wealth through accepting investments to the point where marginal return equals marginal cost.
12-8.
What is the net present value profile? What three points should be determined to graph the profile?
The net present value profile allows for the graphic portrayal of the net present value of a project at different discount rates,Net present values are shown along the vertical axis and discount rates are shown along the horizontal axis.
The points that must be determined to graph the profile are:
The net present value at zero discount rate.
The net present value as determined by a normal discount rate.
The internal rate of return for the investment.
12-9.
How does an asset's ADR (asset depreciation range) relate to its MACRS category?
The ADR represents the asset depreciation range or the expected physical life of the asset,Generally,the midpoint of the range or life is utilized,The longer the ADR midpoint,the longer the MACRS category in which the asset is placed,However,most assets can still be written off more rapidly than the midpoint of the ADR,For example,assets with ADR midpoints of 10 years to 15 years can be placed in the 7-year MACRS category for depreciation purposes.
Problems
12-1.
Assume a corporation has earnings before depreciation and taxes of $90,000,and depreciation of $40,000,and that it has a 30 percent tax bracket,Compute its cash flow using the format below.
Earnings before depreciation and taxes
Depreciation
Earnings before taxes
Taxes @ 30%
Earnings after taxes
Depreciation
Cash flow
Solution:
Earnings before depreciation and taxes $90,000
Depreciation –40,000
Earnings before taxes 50,000
Taxes @ 30% –15,000
Earnings after taxes $35,000
Depreciation +40,000
Cash flow $75,000
12-2.
a. In problem 1,how much would cash flow be if there were only $10,000 in depreciation? All other factors are the same.
b. How much cash flow is lost due to the reduced depreciation between problems 1 and 2a?
Solution:
a. Earnings before depreciation and taxes $90,000
Depreciation –10,000
Earnings before taxes $80,000
Taxes @ 30% –24,000
Earnings after taxes $56,000
Depreciation +10,000
Cash flow $66,000
b. Cash flow (problem 1) $75,000
Cash flow (problem 2) 66,000
Difference in cash flow $ 9,000
12-3.
Assume a firm has earnings before depreciation and taxes of $200,000 and no depreciation,It is in a 40 percent tax bracket.
a. Compute its cash flow.
b. Assume it has $200,000 in depreciation,Recompute its cash flow.
c. How large a cash flow benefit did the depreciation provide?
d. Would the president of a firm on the New York Stock Exchange likely be satisfied with the earnings after taxes results in part c?
Solution:
a. Earnings before depreciation and taxes $200,000
Depreciation – 0
Earnings before taxes 200,000
Taxes @ 40% – 80,000
Earnings after taxes 120,000
Depreciation – 0
Cash flow $120,000
b. Earnings before depreciation and taxes $200,000
Depreciation –200,000
Earnings before taxes 0
Taxes @ 40% 0
Earnings after taxes 0
Depreciation 200,000
Cash flow $200,000
12-3,Continued
c. The $200,000 in depreciation provided a cash flow benefit of $80,000.
Cash flow (b) $200,000
Cash flow (a) 120,000
Cash flow benefit $ 80,000
d. The president of a New York Stock Exchange firm might not be satisfied by the results provided by depreciation,Although depreciation increased cash flow by $80,000,it decreased earnings after taxes by $120,000 down to zero,CEOs tend to be very sensitive to earnings performance,Although this is not necessarily rational,it is likely to be true.
12-4.
Assume a $40,000 investment and the following cash flows for two alternatives.
Year
Investment X
Investment Y
1
$ 6,000
$15,000
2
8,000
20,000
3
9,000
10,000
4
17,000
5
20,000
Which of the alternatives would you select under the payback method?
Solution:
Payback for Investment X
Payback for Investment Y
$40,000 – $ 6,000 1 year
$40,000 – $15,000 1 year
34,000 – 8,000 2 years
25,000 – 20,000 2 years
26,000 – 9,000 3 years
5,000/10,000 ,5 years
17,000 – 17,000 4 years
Payback Investment X = 4.00 years
Payback Investment Y = 2.50 years
Investment Y would be selected because of the faster payback.
12-5.
Referring back to problem 4,if the inflow in the fifth year for investment X were $20,000,000 instead of $20,000,would your answer change under the payback method?
Solution,
The $20,000,000 inflow would still leave the payback period for Investment X at 4 years,It would remain inferior to Investment Y under the payback method.
12-6.
The Short-Line Railroad is considering a $100,000 investment in either of two companies,The cash flows are as follows:
Year
Electric Co.
Water Works
1
$70,000
$15,000
2
15,000
15,000
3
15,000
70,000
4-10
10,000
10,000
a. Using the payback method,what will the decision be?
b. Explain why the answer in part a can be misleading.
Solution:
Short-Line Railroad
a.
Payback for Electric Co.
Payback for Water Works
$100,000 – $70,000 1 year
$100,000 – $15,000 1 year
30,000 – 15,000 2 years
85,000 – 15,000 2 years
15,000 – 15,000 3 years
70,000 – 70,000 3 years
Payback (Electric Co.) = 3 years
Payback (Water Works) = 3 years
12-6,Continued
b. The answer in part a is misleading because the two investments seem to be equal with the same payback period of three year,Nevertheless,the Electric Co,is a superior investment because it recovers large cash flows in the first year,while the large recovery for Water Works is not until the third year,The problem is that the payback method does not consider the time value of money.
12-7.
X-treme Vitamin Company is considering two investments,both of which cost $10,000,The cash flows are as follows:
Year
Project A
Project B
1
$12,000
$10,000
2
8,000
6,000
3
6,000
16,000
a. Which of the two projects should be chosen based on the payback method?
b. Which of the two projects should be chosen based on the net present value method? Assume a cost of capital of 10 percent.
c. Should a firm normally have more confidence in answer a or answer b?
Solution:
X-treme Vitamin Company
a. Payback Method
Payback for Project A
Payback for Project B
Under the Payback Method,you should select Project A because of the shorter payback period.
12-7,Continued
b. Net Present Value Method
Project A
Year
Cash Flow
PVIF at 10%
Present Value
1
$12,000
.909
$10,908
2
$ 8,000
.826
$ 6,608
3
$ 6,000
.751
$ 4,506
Present Value of Inflows
$22,022
Present Value of Outflows
10,000
Net Present Value
$12,022
Project B
Year
Cash Flow
PVIF at 10%
Present Value
1
$10,000
.909
$ 9,090
2
$ 6,000
.826
$ 4,956
3
$16,000
.751
$12,016
Present Value of Inflows
$26,062
Present Value of Outflows
10,000
Net Present Value
$16,062
Under the net present value method,you should select Project B because of the higher net present value.
c. A company should normally have more confidence in answer b because the net present value considers all inflows as well as the time value of money,The heavy late inflow for Project B was partially ignored under the payback method.
12-8.
You buy a new piece of equipment for $16,980,and you receive a cash inflow of $3,000 per year for 12 years,What is the internal rate of return?
Solution:
Appendix D
PVIFA =
IRR = 14%
For n = 12,we find 5.660 under the 14% column.
12-9.
Warner Business Products is considering the purchase of a new machine at a cost of $11,070,The machine will provide $2,000 per year in cash flow for eight years,Warner’s cost of capital is 13 percent,Using the internal rate of return method,evaluate this project and indicate whether it should be undertaken.
Solution:
Warner Business Products
Appendix D
PVIFA = $11,070/$2,000 = 5.535
IRR = 9%
For n = 8,we find 5.353 under the 9% column.
The machine should not be purchased since its return is under 13 percent.
12-10.
Elgin Restaurant Supplies is analyzing the purchase of manufacturing equipment that will cost $20,000,The annual cash inflows for the next three years will be:
Year Cash Flow
1 $10,000
2 9,000
3 6,500
a. Determine the internal rate of return using interpolation.
b. With a cost of capital of 12 percent,should the machine be purchased?
Solution:
Elgin Restaurant Supplies
a. Step 1 Average the inflows.
$10,000
9,000
6,500
$25,500 ÷ 3 = $8,500
Step 2 Divide the inflows by the assumed annuity in Step 1.
Step 3 Go to Appendix D for the 1st approximation,The value in Step 2 (for n = 3) falls between 13% and 14%.
Step 4 Try a first approximation of discounting back the inflows,Because the inflows are biased toward the early years,we will use the higher rate of 14%.
12-10,Continued
Year
Cash Flow
PVIF at 14%
Present Value
1
$10,000
.877
$ 8,770
2
9,000
.769
6,921
3
6,500
.675
4,388
$20,079
Step 5 Since the NPV is slightly over $20,000,we need to try a higher rate,We will try 15%.
Year
Cash Flow
PVIF at 15%
Present Value
1
$10,000
.870
$ 8,700
2
9,000
.756
6,804
3
6,500
.658
4,277
$19,781
Because the NPV is now below $20,000,we know the IRR is between 14% and 15%,We will interpolate.
$20,079 PV @ 14%
–19,781 PV @ 15%
$ 298
$20,079 PV @ 14%
–20,000 Cost
$ 79
14% + ($79/$298) (1%) =,265
14% +,265 (1%) = 14.265% IRR
The IRR is 14.265%
12-10,Continued
If the student skipped from 14% to 16%,the calculations to find the IRR would be as follows:
Year
Cash Flow
PVIF at 16%
Present Value
1
$10,000
.862
$ 8,620
2
9,000
.743
6,687
3
6,500
.641
4,167
$19,474
$20,079 PV @ 14%
–19,474 PV @ 16%
$ 605
$20,079 PV @ 14%
–20,000 Cost
$ 79
14% + ($79/$605) (2%) =,131 (2%)
14% + (.131) (2%) = 14.262%
This answer is very close to the previous answer,the difference is due to rounding.
b. Since the IRR of 14.265% (or 14.262%) is greater than the cost of capital of 12%,the project should be accepted.
12-11.
Aerospace Dynamics will invest $110,000 in a project that will produce the following cash flows,The cost of capital is 11 percent,Should the project be undertaken? (Note that the fourth year's cash flow is negative.)
Year Cash Flow
1 $36,000
2 44,000
3 38,000
4 (44,000)
5 81,000
Solution:
Aerospace Dynamics
Year
Cash Flow
PVIF at 11%
Present Value
1
$36,000
.901
$ 32,436
2
44,000
.812
35,728
3
38,000
.731
27,778
4
(44,000)
.659
(28,996)
5
81,000
.593
48,033
Present value of inflows
$114,979
Present value of outflows
110,000
Net present value
$ 4,979
The net present value is positive and the project should be undertaken
12-12.
The Horizon Company will invest $60,000 in a temporary project that will generate the following cash inflows for the next three years.
Year Cash Flow
1 $15,000
2 25,000
3 40,000
The firm will be required to spend $10,000 to close down the project at the end of the three years,If the cost of capital is 10 percent,should the investment be undertaken?
Solution:
Horizon Company
Present Value of Inflows
Year
Cash Flow
x PVIF at 10%
Present Value
1
$15,000
.909
$13,635
2
25,000
.826
20,650
3
40,000
.751
30,040
$64,325
Present Value of Outflows
0
$60,000
1.000
$60,000
3
10,000
.751
7,510
$67,510
Present Value of inflows
$64,325
Present Value of outflows
67,510
Net present value
($ 3,185)
The net present value is negative and the project should not be undertaken.
Note,the $10,000 outflow could have been subtracted out of the $40,000 inflow in the third year and the same answer would result.
12-13.
Skyline Corp,will invest $130,000 in a project that will not begin to produce returns until after the 3rd year,From the end of the 3rd year until the end of the 12th year (10 periods),the annual cash flow will be $34,000,If the cost of capital is 12 percent,should this project be undertaken?
Solution:
Skyline Corporation
Present Value of Inflows
Find the Present Value of a Deferred Annuity
A = $34,000,n = 10,i = 12%
PVA = A x PVIFA (Appendix D)
PVA = $34,000 x 5.650 = $192,100
Discount from Beginning of the third period (end of second period to present):
FV = $192,100,n = 2,i = 12%
PV = FV x PVIF (Appendix B)
PV = $192,100 x,797 = $153,104
Present value of inflows $153,104
Present value of outflows 130,000
Net present value $ 23,104
The net present value is positive and the project should be undertaken.
12-14.
The Ogden Corporation makes an investment of $25,000,which yields the following cash flows:
Year Cash Flow
1 $ 5,000
2 5,000
3 8,000
4 9,000
5 10,000
a. What is the present value with a 9 percent discount rate (cost of capital)?
b. What is the internal rate of return? Use the interpolation procedure shown in this chapter.
c. In this problem would you make the same decision under both parts a and b?
Solution:
Ogden Corporation
a.
Year
Cash Flow
x PVIF @ 9% =
Present Value
1
$ 5,000
.917
$ 4,585
2
5,000
.842
4,210
3
8,000
.772
6,176
4
9,000
.708
6,372
5
10,000
.650
6,500
Present value of inflows
$27,843
Present value of outflows
–25,000
Net present value
$ 2,843
b. Since we have a positive net present value,the internal rate of return must be larger than 9%,Because of uneven cash flows,we need to use trial and error,Counting the net present value calculation as the first trial,we now try 11% for our second trial.
12-14,Continued
Year
Cash Flow
x PVIF @ 11% =
Present Value
1
$ 5,000
.901
$ 4,505
2
5,000
.812
4,060
3
8,000
.731
5,848
4
9,000
.659
5,931
5
10,000
.593
5,930
Present value of inflows
$26,274
A two percent increase in the discount rate has eliminated over one-half of the net present value so another two percent should be close to the answer.
Year
Cash Flow
x PVIF @ 13% =
Present Value
1
$ 5,000
.885
$ 4,425
2
5,000
.783
3,915
3
8,000
.693
5,544
4
9,000
.613
5,517
5
10,000
.543
5,430
Present value of inflows
$24,831
$26,274 PV @ 11%
24,831 PV @ 13%
$ 1,443
$26,274 PV @ 11%
25,000 Cost
$ 1,274
11% + (2%) = 11% +,883 (2%) = 11% + 1.77% = 12.77%
Approximately the same answer can be derived by interpolating between 12% and 13% instead of 11% and 13%.
c. Yes,both the NPV is greater than 0 and the IRR is greater than the cost of capital.
12-15.
The Danforth Tire Company is considering the purchase of a new machine that would increase the speed of manufacturing and save money,The net cost of this machine is $66,000,The annual cash flows have the following projections.
Year Cash Flow
1 $21,000
2 29,000
3 36,000
4 16,000
5 8,000
a. If the cost of capital is 10 percent,what is the net present value?
b. What is the internal rate of return?
c. Should the project be accepted? Why?
Solution:
The Danforth Tire Company
a. Net Present Value
Year
Cash Flow
x 10% PVIF
Present Value
1
$21,000
.909
$19,089
2
29,000
.826
23,954
3
36,000
.751
27,036
4
16,000
.683
10,928
5
8,000
.621
4,968
Present value of inflows
$85,975
Present value of outflows
–66,000
Net present value
$19,975
12-15,Continued
b. Internal Rate of Return
We will average the inflows to arrive at an assumed annuity.
$ 21,000
29,000
36,000
16,000
8,000
$110,000/5 = $22,000
We divide the investment by the assumed annuity value.
Using Appendix D for n = 5,20% appears to be a reasonable first approximation (2.991),We try 20%.
Year
Cash Flow
x 20% PVIF =
Present Value
1
$21,000
.833
$17,493
2
29,000
.694
20,126
3
36,000
.579
20,844
4
16,000
.482
7,712
5
8,000
.402
3,216
Present value of inflows
$69,391
Since 20% is not high enough,we try the next highest rate at 25%.
12-15,Continued
Year
Cash Flow
x 25% PVIF =
Present Value
1
$21,000
.800
$16,800
2
29,000
.640
18,560
3
36,000
.512
18,432
4
16,000
.410
6,560
5
8,000
.328
2,624
Present value of inflows
$62,976
The correct answer must fall between 20% and 25%,We interpolate.
$69,391 PV @ 20%
62,976 PV @ 25%
$ 6,415
$69,391 PV @ 20%
66,000 (Cost)
$ 3,391
20% + (5%) = 20% +,529 (5%) = 20% + 2.657% = 22.65%
c. The project should be accepted because the net present value is positive and the IRR exceeds the cost of capital.
12-16.
You are asked to evaluate two projects for Adventures Club,Inc,Using the net present value method combined with the profitability index approach described in footnote 2 of this chapter,which project would you select? Use a discount rate of 12 percent.
Project X (trips to Disneyland)
($10,000 investment)
Project Y (international film festivals);
($22,000 investment)
Year Cash Flow
1 $4,000
2 5,000
3 4,200
4 3,600
Year Cash Flow
1 $10,800
2 9,600
3 6,000
4 7,000
12-16,Continued
Solution:
Adventures Club,Inc.
NPV for Project X
Year
Cash Flow
PVIF at 12%
Present Value
1
$4,000
.893
$ 3,572
2
5,000
.797
3,985
3
4,200
.712
2,990
4
3,600
.636
2,290
Present value of inflows
$12,837
Present value of outflows (Cost) –10,000
Net present value
$ 2,837
NPV for Project Y
Year
Cash Flow
x PVIF at 12% =
Present Value
1
$10,800
.893
$ 9,644
2
9,600
.797
7,651
3
6,000
.712
4,272
4
7,000
.636
4,452
Present value of inflows
$26,019
Present value of outflows –22,000
Net present value
$ 4,019
12-16,Continued
You should select Project X because it has the higher profitability index,This is true in spite of the fact that it has a lower net present value,The profitability index may be appropriate when you have different size investments,It tells you that for every dollar of outflows,the present value of the inflows is worth x dollars,For project x we get 1.2837 vs 1.1827 for project y,Project x has the higher internal rate of return but project y will add more value to the firm.
12-17.
Cablevision,Inc,will invest $48,000 in a project,The firm's discount rate (cost of capital) is 9 percent,The investment will provide the following inflows.
Year Inflow
1 $10,000
2 10,000
3 16,000
4 19,000
5 20,000
The internal rate of return is 15 percent.
a. If the reinvestment assumption of the net present value method is used,what will be the total value of the inflows after five years? (Assume the inflows come at the end of each year.)
b. If the reinvestment assumption of the internal rate of return method is used,what will be the total value of the inflows after five years?
c. Generally,is one investment assumption likely to be better than another?
12-17,Continued
Solution:
Cablevision,Inc.
a. Reinvestment assumption of NPV
Year
Inflows
Rate
No,of
Periods
Future
Value Factor
Value
1
$10,000
9%
4
1.412
$14,120
2
10,000
9%
3
1.295
12,950
3
16,000
9%
2
1.188
19,008
4
19,000
9%
1
1.090
20,710
5
20,000
--
0
1.000
20,000
$86,788
b. Reinvestment assumption of IRR
Year
Inflows
Rate
No,of
Periods
Future
Value Factor
Value
1
$10,000
15%
4
1.749
$17,490
2
10,000
15%
3
1.521
15,210
3
16,000
15%
2
1.323
21,168
4
19,000
15%
1
1.150
21,850
5
20,000
–
0
1.000
20,000
$95,718
c. Not necessarily,However,for investments with a very high IRR,it may be unrealistic to assume that reinvestment can take place at an equally high rate,The net present value method makes the more conservative assumption of reinvestment at the cost of capital.
12-18.
The 21st Century Corporation uses the modified internal rate of return,The firm has a cost of capital of 8 percent,The project being analyzed is as follows ($20,000 investment):
Year Cash Flow
1 $10,000
2 9,000
3 6,800
a. What is the modified internal rate of return? An approximation from Appendix B is adequate,(You do not need to interpolate.)
b. Assume the traditional internal rate of return on the investment is 14.9 percent,Explain why your answer is part a would be lower.
Solution:
21st Century Corporation
Terminal Value (end of year 3)
a.
Period of Growth FV factor (8%) Future Value
Year 1 $10,000 2 1.166 $11,660
Year 2 9,000 1 1.080 9,720
Year 3 6,800 0 1.000 6,800
Terminal Value $28,180
To determine the modified internal rate of return,calculate the yield on the investment.
Use Appendix B for 3 periods,the answer is approximately 12 percent (.712).
12-18,Continued
b. The modified internal rate of return (MIRR) is lower than the traditional internal rate of return because with the MIRR you are assuming inflows are being reinvested at the cost of capital (8%) whereas with the traditional internal rate of return,you are assuming inflows are being reinvested at the IRR (14.9 percent).
12-19.
Oliver Stone and Rock Company uses a process of capital rationing in its decision making,The firm's cost of capital is 12 percent,It will only invest $80,000 this year,It has determined the internal rate of return for each of the following projects.
Project
Project Size
Percent of
Internal Rate
of Return
A
$15,000
14%
B
25,000
19
C
30,000
10
D
25,000
16.5
E
20,000
21
F
15,000
11
G
25,000
18
H
10,000
17.5
a. Pick out the projects that the firm should accept.
b. If Projects B and G are mutually exclusive,how would that affect your overall answer? That is,which projects would you accept in spending the $80,000?
12-19,Continued
Solution:
Oliver Stone and Rock Company
You should rank the investments in terms of IRR.
Project
IRR
Project Size
Total Budget
E
21%
$20,000
$ 20,000
B
19
25,000
45,000
G
18
25,000
70,000
H
17.5
10,000
80,000
D
16.5
25,000
105,000
A
14
15,000
120,000
F
11
15,000
135,000
C
10
30,000
165,000
a. Because of capital rationing,only $80,000 worth of projects can be accepted,The four projects to accept are E,B,G and H,Projects D and A provide positive benefits also,but cannot be undertaken under capital rationing.
b. If Projects B and G are mutually exclusive,you would select Project B in preference to G,In summary,you would accept E,B,H and D,Project D would replace G and is of the same $25,000 magnitude.
12-20.
Miller Electronics is considering two new investments,Project C calls for the purchase of a coolant recovery system,Project H represents an investment in a heat recovery system,The firm wishes to use a net present value profile in comparing the projects,The investment and cash flow patterns are as follows:
Project C
($25,000 investment)
Project H
($25,000 investment)
Year Cash Flow
1 $ 6,000
2 7,000
3 9,000
4 13,000
Year Cash Flow
1 $20,000
2 6,000
3 5,000
a. Determine the net present value of the projects based on a zero discount rate.
b. Determine the net present value of the projects based on a 9 percent discount rate.
c. The internal rate of return on Project C is 13.01 percent,and the internal rate of return on Project H is 15.68 percent,Graph a net present value profile for the two investments similar to Figure 12-3,(Use a scale up to $10,000 on the vertical axis,with $2,000 increments,Use a scale up to 20 percent on the horizontal axis,with 5 percent increments.)
d. If the two projects are not mutually exclusive,what would your acceptance or rejection decision be if the cost of capital (discount rate) is 8 percent? (Use the net present value profile for your decision; no actual numbers are necessary.)
e. If the two projects are mutually exclusive (the selection of one precludes the selection of the other),what would be your decision if the cost of capital is (1) 5 percent,(2) 13 percent,(3) 19 percent? Use the net present value profile for your answer.
12-20,Continued
Solution:
Miller Electronics
a. Zero discount rate
Project c
Inflows Outflow
$10,000 = ($6,000 + $7,000 + $9,000 + $13,000) – $25,000
Project H
Inflows Outflow
$ 6,000 = ($20,000 + $6,000 + $5,000) – $25,000
b. 9% discount rate
Project C
Year
Cash Flow
PVIF at 9%
Present Value
1
$ 6,000
.917
$ 5,502
2
7,000
.842
5,894
3
9,000
.772
6,948
4
13,000
.708
9,204
Present value of inflows
$27,548
Present value of outflows
25,000
Net present value
$ 2,548
12-20,Continued
Project H
Year
Cash Flow
PVIF at 9%
Present Value
1
$20,000
.917
$18,340
2
6,000
.842
5,052
3
5,000
.772
3,860
Present value of inflows
$27,252
Present value of outflows
25,000
Net present value
$ 2,252
c. Net Present Value Profile
12-20,Continued
d. Since the projects are not mutually exclusive,they both can be selected if they have a positive net present value,At an 8% rate,they should both be accepted,As a side note,we can see Project C is superior to Project H.
e. With mutually exclusive projects,only one can be accepted,Of course,that project must still have a positive net present value,Based on the visual evidence,we see:
(i) 5% cost of capital—select Project C
(ii) 13% cost of capital—select Project H
(iii) 19% cost of capital—do not select either project
12-21.
Software Systems is considering an investment of $20,000,which produces the following inflows.
Year Cash Flow
1 $11,000
2 9,000
3 5,800
You are going to use the net present value profile to approximate the value for the internal rate of return,Please follow these steps.
a. Determine the net present value project based on a zero discount rate.
b. Determine the net present value of the project based on a 10 percent discount rate.
c. Determine the net present value of the project based on a 20 percent discount rate (it will be negative).
d. Draw a net present value profile for the investment,(Use a scale up to $6,000 on the vertical axis,with $2,000 increments,Use a scale up to 20 percent on the horizontal axis,with 5 percent increments.) Observe the discount rate at which the net present value is zero,This is an approximation of the internal rate of return on the project.
e. Actually compute the internal rate of return based on the interpolation procedure presented in this chapter,Compare your answers in parts d and e.
12-21,Continued
Solution:
Software Systems
a. NPV @ 0% discount rate
Inflows Outflow
$5,800 = ($11,000 + $9,000 + $5,800) – $20,000
b. 10% Discount Rate
Year
Cash Flow
PVIF @ 10%
Present Value
1
$11,000
.909
$ 9,999
2
9,000
.826
7,434
3
5,800
.751
4,356
Present value of inflows
$21,789
Present value of outflows
20,000
Net present value
$ 1,789
c. 20% Discount Rate
Year
Cash Flow
PVIF @ 20%
Present Value
1
$11,000
.833
$ 9,163
2
9,000
.694
6,246
3
5,800
.579
3,358
Present value of inflows
$18,767
Present value of outflows
20,000
Net present value
($ 1,233)
12-21,Continued
d. Net Present Value Profile
e. The answer appears to be slightly above 15%,We will use 15% as the first approximation.
Year
Cash Flow
PVIF @ 15%
Present Value
1
$11,000
.870
$ 9,570
2
9,000
.756
6,804
3
5,800
.658
3,816
Present value of inflows
$20,190
The second approximation is at 16%.
Year
Cash Flow
PVIF @ 16%
Present Value
1
$11,000
.862
$ 9,482
2
9,000
.743
6,687
3
5,800
.641
3,718
Present value of inflows
$19,887
12-21,Continued
We interpolate between 15% and 16%.
$20,190 PV @ 15%
19,887 PV @ 16%
$ 303
$20,190 PV @ 15%
20,000 Cost
$ 190
15% + ($190/$303) (1%) = 15% +,63 = 15.63%
The interpolation value of 15.63% appears to be very close to the graphically determined value in part d.
12-22.
Howell Magnetics Corporation is going to purchase an asset for $400,000 that will produce $180,000 per year for the next four years in earnings before depreciation and taxes,The asset will be depreciated using the three-year MACRS depreciation schedule in Table 12-9,(This represents four years of depreciation based on the half-year convention.) The firm is in a 34 percent tax bracket,Fill in the schedule below for the next four years,(You need to first determine annual depreciation.)
Earnings before depreciation and taxes
Depreciation
Earnings before taxes
Taxes
Earnings after taxes
+ Depreciation
Cash flow
12-22,Continued
Solution:
Howell Magnetics Corporation
First determine annual depreciation.
Year
Depreciation Base
Percentage Depreciation (Table 12-9)
Annual Depreciation
1
$400,000
.333
$133,200
2
400,000
.445
178,000
3
400,000
.148
59,200
4
400,000
.074
29,600
$400,000
Then determine the annual cash flow,Earnings before depreciation and taxes (EBDT) will be the same for each year,but depreciation and cash flow will differ.
1
2
3
4
EBDT
$180,000
$180,000
$180,000
$180,000
– D
133,200
178,000
59,200
29,600
EBT
46,800
2,000
120,800
150,400
T (34%)
15,912
680
41,072
51,136
EAT
30,888
1,320
79,728
99,264
+ D
133,200
178,000
59,200
29,600
Cash Flow
$164,088
$179,320
$138,928
$128,864
12-23.
Assume $80,000 is going to be invested in each of the following assets,Using Tables 12-8 and 12-9,indicate the dollar amount of the first year's depreciation.
a. Computers
b. Petroleum refining product
c. Office furniture
d. Pipeline distribution
Solution:
a. Computers – Based on Table 12-8,this falls under 5-year ACRS depreciation,Then examining Table 12-9,the first year depreciation rate is,200,Thus:
$80,000 x,200 = $16,000
b. Petroleum refining product – This falls under 10-year ACRS depreciation,This first year depreciation rate is,100.
$80,000 x,100 = $8,000
c. Office furniture – This falls under 7-year ACRS depreciation,The first year depreciation rate is,143.
$80,000 x,143 = $11,440
d. Pipeline distribution – This falls under 15-year ACRS depreciation,This first year depreciation rate is,050.
$80,000 x,050 = $4,000
12-24.
The Keystone Corporation will purchase an asset that qualifies for three-year MACRS depreciation,The cost is $60,000 and the asset will provide the following stream of earnings before depreciation and taxes for the next four years:
Year 1 $27,000
Year 2 30,000
Year 3 23,000
Year 4 15,000
The firm is in a 36 percent tax bracket and has an 11 percent cost of capital,Should it purchase the asset?
Solution:
The Keystone Corporation
Year
Depreciation Base
Percentage Depreciation (Table 12-9)
Annual Depreciation
1
$60,000
.333
$19,980
2
60,000
.445
26,700
3
60,000
.148
8,880
4
60,000
.074
4,440
$60,000
Then determine the annual cash flow.
1
2
3
4
EBDT
$27,000
$30,000
$23,000
$15,000
– D
19,980
26,700
8,880
4,440
EBT
7,020
3,300
14,120
10,560
T (36%)
2,527
1,188
5,083
3,802
EAT
4,493
2,112
9,037
6,758
+ D
19,980
26,700
8,880
4,440
Cash Flow
$24,473
$28,812
$17,917
$11,198
12-24,Continued
Then determine the net present value.
Year
Cash Flow
(inflows)
PVIF @ 11%
Present Value
1
$24,473
.901
$22,050
2
28,812
.812
23,395
3
17,917
.731
13,097
4
11,198
.659
7,379
Present value of inflows
$65,921
Present value of outflows
60,000
Net present value
$ 5,921
The asset should be purchased based on the net present value.
12-25.
Oregon Forest Products will acquire new equipment that falls under the five-year MACRS category,The cost is $300,000,If the equipment is purchased,the following earnings before depreciation and taxes will be generated for the next six years.
Year 1 $112,000
Year 2 105,000
Year 3 82,000
Year 4 53,000
Year 5 37,000
Year 6 32,000
The firm is in a 30 percent tax bracket and has a 14 percent cost of capital,Should Oregon Forest Products purchase the equipment? Use the net present value method.
12-25,Continued
Solution:
Oregon Forest Products
First determine annual depreciation.
Year
Depreciation Base
Percentage Depreciation (Table 12-9)
Annual Depreciation
1
$300,000
.200
$ 60,000
2
300,000
.320
96,000
3
300,000
.192
57,600
4
300,000
.115
34,500
5
300,000
.115
34,500
6
300,000
.058
17,400
$300,000
Then determine the annual cash flow.
Annual Cash Flow
1
2
3
4
5
6
EBDT
$112,000
$105,000
$82,000
$53,000
$37,000
$32,000
– D
60,000
96,000
57,600
34,500
34,500
17,400
EBT
52,000
9,000
24,400
18,500
2,500
14,600
T (30%)
15,600
2,700
7,320
5,550
750
4,380
EAT
36,400
6,300
17,080
12,950
1,750
10,220
+ D
60,000
96,000
57,600
34,500
34,500
17,400
Cash Flow
$ 96,400
$102,300
$74,680
$47,450
$36,250
$27,620
Then determine the net present value.
12-25,Continued
Year
Cash Flow
(inflows)
PVIF @ 14%
Present Value
1
$ 96,400
.877
$ 84,543
2
102,300
.769
78,669
3
74,680
.675
50,409
4
47,450
.592
28,090
5
36,250
.519
18,814
6
27,620
.456
12,595
Present value of inflows
$273,120
Present value of outflows
300,000
Net present value
($ 26,880)
The equipment should not be purchased.
12-26.
The Thorpe Corporation is considering the purchase of manufacturing equipment with a 10-year midpoint in its asset depreciation range (ADR),Carefully refer to Table 12-8 to determine in what depreciation category the asset falls,(Hint,It is not 10 years.) The asset will cost $80,000,and it will produce earnings before depreciation and taxes of $28,000 per year for three years,and then $12,000 a year for seven more years,The firm has a tax rate of 34 percent,With a cost of capital of 12 percent,should it purchase the asset? Use the net present value method,In doing your analysis,if you have years in which there is no depreciation,merely enter a zero for depreciation.
Solution:
The Thorpe Corporation
Because the manufacturing equipment has a 10-year midpoint of its asset depreciation range (ADR),it falls into the seven-year MACRS category as indicated in Table 12-8,Furthermore,we see that most types of manufacturing equipment fall into the seven-year MACRS category.
12-26,Continued
With seven-year MACRS depreciation,the asset will be depreciated over eight years (based on the half-year convention),Also,we observe that the equipment will produce earnings for 10 years,so in the last two years there will be no depreciation write-off.
We first determine the annual depreciation.
Year
Depreciation Base
Percentage Depreciation (Table 12-9)
Annual Depreciation
1
$80,000
.143
$11,440
2
80,000
.245
19,600
3
80,000
.175
14,000
4
80,000
.125
10,000
5
80,000
.089
7,120
6
80,000
.089
7,120
7
80,000
.089
7,120
8
80,000
.045
3,600
$80,000
12-26,Continued
Then determine the annual cash flow:
Annual Cash Flow
1
2
3
4
5
6
7
8
9
10
EBDT
$28,000
$28,000
$28,000
$12,000
$12,000
$12,000
$12,000
$12,000
$12,000
$12,000
– D
11,440
19,600
14,000
10,000
7,120
7,120
7,120
3,600
0
0
EBT
$16,560
$ 8,400
$14,000
$ 2,000
$ 4,880
$ 4,880
$ 4,880
$ 8,400
$12,000
$12,000
T (34%)
5,630
2,856
4,760
680
1,659
1,659
1,659
2,856
4,080
4,080
EAT
$10,930
$ 5,544
$ 9,240
$ 1,320
$ 3,221
$ 3,221
$ 3,221
$ 5,544
$ 7,920
$ 7,920
+ D
11,440
19,600
14,000
10,000
7,120
7,120
7,120
3,600
0
0
Cash Flow
$22,370
$25,144
$23,240
$11,320
$10,341
$10,341
$10,341
$ 9,144
$ 7,920
$ 7,920
12-26,Continued
Next determine the net present value.
Year
Cash Flow
(inflows)
PVIF @ 12%
Present Value
1
$22,370
.893
$19,976
2
25,144
.797
20,040
3
23,240
.712
16,547
4
11,320
.636
7,200
5
10,341
.567
5,863
6
10,341
.507
5,243
7
10,341
.452
4,674
8
9,144
.404
3,694
9
7,920
.361
2,859
10
7,920
.322
2,550
Present value of inflows
$88,646
Present value of outflows
80,000
Net present value
$ 8,646
The asset should be purchased.
12-27.
The Spartan Technology Company has a proposed contract with the Digital Systems Company of Michigan,The initial investment in land and equipment will be $120,000,Of this amount,$70,000 is subject to five-year MACRS depreciation,The balance is in nondepreciable property,The contract covers six years; at the end of six years the nondepreciable assets will be sold for $50,000,The depreciated assets will have zero resale value.
The contract will require an additional investment of $55,000 in working capital at the beginning of the first year and,of this amount,$25,000 will be returned to the Spartan Technology Company after six years.
The investment will produce $50,000 in income before depreciation and taxes for each of the six years,The corporation is in a 40 percent tax bracket and has a 10 percent cost of capital.
Should the investment be undertaken? Use the net present value method.
12-27,Continued
Solution:
Spartan Technology Company
Although there are some complicating features in the problem,we are still comparing the present value of cash flows to the total initial investment.
The initial investment is:
Land and equipment $120,000
Working capital 55,000
Initial investment $175,000
In computed the present value of the cash flows,we first determine annual depreciation based on a $70,000 depreciation base.
Year
Depreciation Base
Percentage Depreciation (Table 12-9)
Annual Depreciation
1
$70,000
.200
$14,000
2
70,000
.320
22,400
3
70,000
.192
13,440
4
70,000
.115
8,050
5
70,000
.115
8,050
6
70,000
.058
4,060
$70,000
We then determine the annual cash flow,In addition to normal cash flow from operations; we also consider the funds generated in the sixth year from the sale of the nondepreciable property (land) and from the recovery of working capital.
12-27,Continued
Then determine the annual cash flow.
Annual Cash Flow
1
2
3
4
5
6
EBDT
$50,000
$50,000
$50,000
$50,000
$50,000
$50,000
– D
14,000
22,400
13,440
8,050
8,050
4,060
EBT
36,000
27,600
36,560
41,950
41,950
45,940
T (40%)
14,400
11,040
14,624
16,780
16,780
18,376
EAT
21,600
16,560
21,936
25,170
25,170
27,564
+ D
14,000
22,400
13,440
8,050
8,050
4,060
+ Sale of non-depreciable assets
50,000
+ Recovery
of working
capital ______
______
______
______
______
25,000
Cash Flow
$35,600
$38,960
$35,376
$33,220
$33,220
$106,624
We then determine the net present value.
Year
Cash Flow
(inflows)
PVIF @ 10%
Present Value
1
$ 35,600
.909
$ 32,360
2
38,960
.826
32,181
3
35,376
.751
26,567
4
33,220
.683
22,689
5
33,220
.621
20,630
6
106,624
.564
60,136
Present value of inflows
$194,563
Present value of outflows
175,000
Net present value
$ 19,563
The investment should be undertaken.
12-28.
An asset was purchased three years ago for $140,000,It falls into the five-year category for MACRS depreciation,The firm is in a 35 percent tax bracket,Compute the:
a. Tax loss on the sale and the related tax benefit if the asset is sold now for $15,320.
b. Gain and related tax on the sale if the asset is sold now for $58,820,(Refer to footnote 3.)
Solution:
First determine the book value of the asset.
Year
Depreciation Base
Percentage Depreciation (Table 12-9)
Annual Depreciation
1
$140,000
.200
$28,000
2
140,000
.320
44,800
3
140,000
.192
26,880
Total depreciation to date
$99,680
Purchase price $140,000
– Total depreciation to date 99,680
Book value $ 40,320
a. $15,320 sales price
Book value $40,320
Sales price 15,320
Tax loss on the sale $25,000
Tax loss on the sale $25,000
Tax rate 35%
Tax benefit $ 8,750
12-28,Continued
b. $58,820 sales price
Sales price $58,820
Book value 40,320
Taxable gain 18,500
Tax rate 35%
Tax obligation $ 6,475
12-29.
Graphic Systems purchased a computerized measuring device two years ago for $80,000,It falls into the five-year category for MACRS depreciation,The equipment can currently be sold for $28,400.
A new piece of equipment will cost $210,000,It also falls into the five-year category for MACRS depreciation.
Assume the new equipment would provide the following stream of added cost savings for the next six years.
Year Cost Savings
1 $76,000
2 66,000
3 62,000
4 60,000
5 56,000
6 42,000
The tax rate is 34 percent and the cost of capital is 12 percent.
a. What is the book value of the old equipment?
b. What is the tax loss on the sale of the old equipment?
c. What is the tax benefit from the sale?
d. What is the cash inflow from the sale of the old equipment?
e. What is the net cost of the new equipment? (Include the inflow from the sale of the old equipment.)
f. Determine the depreciation schedule for the new equipment.
g. Determine the depreciation schedule for the remaining years of the old equipment.
h. Determine the incremental depreciation between the old and new equipment and the related tax shield benefits.
12-29,Continued
i. Compute the aftertax benefits of the cost savings.
j. Add the depreciation tax shield benefits and the aftertax cost savings,and determine the present value,(See Table 12-17 on page ___ as an example.)
k. Compare the present value of the incremental benefits (j) to the net cost of the new equipment (e),Should the replacement be undertaken?
Solution:
Replacement Decision Analysis
Graphic Systems
a.
Year
Depreciation Base
Percentage Depreciation (Table 12-9)
Annual Depreciation
1
$80,000
.200
$16,000
2
80,000
.320
25,600
Total depreciation to date
$41,600
Purchase price $80,000
– Total depreciation to date 41,600
Book value $38,400
b. Book value $38,400
Sales price 28,400
Tax loss on the sale $10,000
c. Tax loss on the sale $10,000
Tax rate 34%
Tax benefit $ 3,400
d. Sales price of the old equipment $28,400
Tax benefit from the sale 3,400
Cash inflow from the sale of the old equipment $31,800
12-29,Continued
e. Price of the new equipment $210,000
– Cash inflow from the sale of the old equipment 31,800
Net cost of the new equipment $178,200
f. Depreciation schedule on the new equipment.
Year
Depreciation Base
Percentage Depreciation (Table 12-9)
Annual Depreciation
1
$210,000
.200
$ 42,000
2
210,000
.320
67,200
3
210,000
.192
40,320
4
210,000
.115
24,150
5
210,000
.115
24,150
6
210,000
.058
12,180
$210,000
g. Depreciation schedule for the remaining years of the old equipment.
Year*
Depreciation Base
Percentage Depreciation (Table 12-9)
Annual Depreciation
1
$80,000
.192
$15,360
2
80,000
.115
9,200
3
80,000
.115
9,200
4
80,000
.058
4,640
* The next four years represent the last four years on the old equipment.
12-29,Continued
h. Incremental depreciation and tax shield benefits.
(1)
Year
(2)
Depreciation on new Equipment
(3)
Depreciation on old Equipment
(4)
Incremental
Depreciation
(5)
Tax Rate
(6)
Tax
Shield
Benefits
1
$42,000
$15,360
$26,640
.34
$ 9,058
2
67,200
9,200
58,000
.34
19,720
3
40,320
9,200
31,120
.34
10,581
4
24,150
4,640
19,510
.34
6,633
5
24,150
24,150
.34
8,211
6
12,180
12,180
.34
4,141
i. Aftertax cost savings
Year
Savings
(1-Tax Rate)
After tax Savings
1
$76,000
.66
$50,160
2
66,000
.66
43,560
3
62,000
.66
40,920
4
60,000
.66
39,600
5
56,000
.66
36,960
6
42,000
.66
27,720
12-29,Continued
j. Present value of the total incremental benefits.
(1)
Year
(2)
Tax Shield Benefits from
Depreciation
(3)
After Tax
Cost
Savings
(4)
Total
Annuity
Benefits
(5)
Present
Value
Factor 12%
(6)
Present
Value
1
$ 9,058
$50,160
$59,218
.893
$ 52,882
2
19,720
43,560
63,280
.797
50,434
3
10,581
40,920
51,501
.712
36,669
4
6,633
39,600
46,233
.636
29,404
5
8,211
36,960
45,171
.567
25,612
6
4,141
27,720
31,861
.507
16,154
Present value of incremental benefits
$211,155
k. Present value of incremental benefits $211,155
Net cost of new equipment 178,200
Net present value $ 32,955
Based on the present value analysis,the equipment should be replaced.
Comprehensive Problem
CP 12-1.
The Woodruff Corporation purchased a piece of equipment three years ago for $230,000,It has an asset depreciation range (ADR) midpoint of eight years,The old equipment can be sold for $90,000.
A new piece of equipment can be purchased for $320,000,It also has an ADR of eight years.
Assume the old and new equipment would provide the following operating gains (or losses) over the next six years.
Year
New Equipment
Old Equipment
1
$80,000
$25,000
2
76,000
16,000
3
70,000
9,000
4
60,000
8,000
5
50,000
6,000
6
45,000
(7,000)
The firm has a 36 percent tax rate and a 9 percent cost of capital,Should the new equipment be purchased to replace the old equipment?
Solution:
Replacement Decision Analysis
Woodruff Corporation
Book Value of Old Equipment
(ADR of 8 years indicates the use of the 5-year MACRS schedule)
Year
Depreciation Base
Percentage Depreciation (Table 12-9)
Annual Depreciation
1
$230,000
.200
$ 46,000
2
230,000
.320
73,600
3
230,000
.192
44,160
Total depreciation to date
$163,760
CP 12-1,Continued
Purchase price $230,000
– Total depreciation to date 163,760
Book value $ 66,240
Tax Obligation on the Sale
Sales price $90,000
Book value 66,240
Taxable gain 23,760
Tax rate 36%
Taxes $ 8,554
Cash Inflow From the Sale of the Old Equipment
Sales price $90,000
Taxes 8,554
$81,446
Net Cost of the New Equipment
Purchase price $320,000
– Cash inflow from the sale of the old equipment 81,446
Net cost $238,554
Depreciation Schedule of the New Equipment.
(ADR of 8 years indicates the use of 5-year MACRS Schedule)
CP 12-1,Continued
Year
Depreciation Base
Percentage Depreciation (Table 12-9)
Annual Depreciation
1
$320,000
.200
$ 64,000
2
320,000
.320
102,400
3
320,000
.192
61,440
4
320,000
.115
36,800
5
320,000
.115
36,800
6
320,000
.058
18,560
$320,000
Depreciation Schedule for the Remaining Years of the Old Equipment.
Year*
Depreciation Base
Percentage Depreciation (Table 12-9)
Annual Depreciation
1
$230,000
.115
$26,450
2
230,000
.115
26,450
3
230,000
.058
13,340
* The next three years represent the last three years of the old equipment.
CP 12-1,Continued
Incremental Depreciation and Tax Shield Benefits.
(1)
Year
(2)
Depreciation on New Equipment
(3)
Depreciation on Old Equipment
(4)
Incremental
Depreciation
(5)
Tax Rate
(6)
Tax
Shield
Benefits
1
$ 64,000
$26,450
$37,550
.36
$13,518
2
102,400
26,450
75,950
.36
27,342
3
61,440
13,340
48,100
.36
17,316
4
36,800
36,800
.36
13,248
5
36,800
36,800
.36
13,248
6
18,560
18,560
.36
6,682
Aftertax cost savings
New Equipment
Old Equipment
Cost Savings
(1 – Tax
Rate)
Aftertax
Savings
$80,000
$25,000
$55,000
.64
$35,200
76,000
16,000
60,000
.64
38,400
70,000
9,000
61,000
.64
39,040
60,000
8,000
52,000
.64
33,280
50,000
6,000
44,000
.64
28,160
45,000
(7,000)
52,000
.64
33,280
CP 12-1,Continued
Present value of the total incremental benefits.
(1)
Year
(2)
Tax Shield Benefits from
Depreciation
(3)
After Tax
Cost
Savings
(4)
Total
Annuity
Benefits
(5)
Present
Value
Factor 9%
(6)
Present
Value
1
$13,518
$35,200
$48,718
.917
$ 44,674
2
27,342
38,400
65,742
.842
55,355
3
17,316
39,040
56,356
.772
43,507
4
13,248
33,280
46,528
.708
32,942
5
13,248
28,160
41,408
.650
26,915
6
6,682
33,280
39,962
.596
23,817
Present value of incremental Benefits
$227,210
Net Present Value
Present value of incremental benefits $227,210
Net cost of new equipment 238,554
Net present value ($ 11,344)
Based on the net present value analysis,the equipment should not be replaced.
