Chapter 11
Discussion Questions
11-1.
Why do we use the overall cost of capital for investment decisions even when only one source of capital will be used (e.g.,debt)?
Though an investment financed by low-cost debt might appear acceptable at first glance,the use of debt could increase the overall risk of the firm and eventually make all forms of financing more expensive,Each project must be measured against the overall cost of funds to the firm.
11-2.
How does the cost of a source of capital relate to the valuation concepts presented previously in Chapter 10?
The cost of a source of financing directly relates to the required rate of return for that means of financing,Of course,the required rate of return is used to establish valuation.
11-3.
In computing the cost of capital,do we use the historical costs of existing debt and equity or the current costs as determined in the market? Why?
In computing the cost of capital,we use the current costs for the various sources of financing rather than the historical costs,We must consider what these funds will cost us to finance projects in the future rather than their past costs.
11-4.
Why is the cost of debt less than the cost of preferred stock if both securities are priced to yield 10 percent in the market?
Even though debt and preferred stock may be both priced to yield 10 percent in the market,the cost of debt is less because the interest on debt is a tax-deductible expense,A 10 percent market rate of interest on debt will only cost a firm in a 35 percent tax bracket an aftertax rate of 6.5 percent,The answer is the yield multiplied by the difference of (one minus the tax rate).
11-5.
What are the two sources of equity (ownership) capital for the firm?
The two sources of equity capital are retained earnings and new common stock.
11-6.
Explain why retained earnings have an opportunity cost associated?
Retained earnings belong to the existing common stockholders,If the funds are paid out instead of reinvested,the stockholders could earn a return on them,Thus,we say retaining funds for reinvestment carries an opportunity cost.
11-7.
Why is the cost of retained earnings the equivalent of the firm's own required rate of return on common stock (Ke)?
Because stockholders can earn a return at least equal to their present investment,For this reason,the firm's rate of return (Ke) serves as a means of approximating the opportunities for alternate investments.
11-8.
Why is the cost of issuing new common stock (Kn) higher than the cost of retained earnings (Ke)?
In issuing new common stock,we must earn a slightly higher return than the normal cost of common equity in order to cover the distribution costs of the new security,In the case of the Baker Corporation,the cost of new common stock was six percent higher.
11-9.
How are the weights determined to arrive at the optimal weighted average cost of capital?
The weights are determined by examining different capital structures and using that mix which gives the minimum cost of capital,We must solve a multidimensional problem to determine the proper weights.
11-10.
Explain the traditional,U-shaped approach to the cost of capital.
The logic of the U-shaped approach to cost of capital can be explained through Figure 11-1,It is assumed that as we initially increase the debt-to-equity mix the cost of capital will go down,After we reach an optimum point,the increase use of debt will increase the overall cost of financing to the firm,Thus we say the weighted average cost of capital curve is U-shaped.
11-11.
It has often been said that if the company can't earn a rate of return greater than the cost of capital it should not make investments,Explain.
If the firm cannot earn the overall cost of financing on a given project,the investment will have a negative impact on the firm's operations and will lower the overall wealth of the shareholders.
Clearly,it is undesirable to invest in a project yielding 8 percent if the financing cost is 10 percent.
11-12.
What effect would inflation have on a company's cost of capital? (Hint,Think about how inflation influences interest rates,stock prices,corporate profits,and growth.)
Inflation can only have a negative impact on a firm's cost of capital-forcing it to go up,This is true because inflation tends to increase interest rates and lower stock prices,thus raising the cost of debt and equity directly and the cost of preferred stock indirectly.
11-13.
What is the concept of marginal cost of capital?
The marginal cost of capital is the cost of incremental funds,After a firm reaches a given level of financing,capital costs will go up because the firm must tap more expensive sources,For example,new common stock may be needed to replace retained earnings as a source of equity capital.
Appendix A
Discussion Questions
11A-1.
How does the capital asset pricing model help explain changing costs of capital?
The capital asset pricing model explains the relationship between risk and return,and the price adjustment of capital assets to changes in risk and return,As investors react to their economic environment and their willingness to take risk,they change the prices of financial assets like common stock,bonds,and preferred stock,As the prices of these securities adjust to investors' required returns,the company's cost of capital is adjusted accordingly.
11A-2.
How does the SML react to changes in the rate of interest,changes in the rate of inflation,and changing investor expectations?
The SML,Security Market Line,reflects the risk-return tradeoffs of securities,As interest rates increase,the SML moves up parallel to the old SML,Now investors require a higher minimum return on risk free assets and an equally higher rate for all levels of risk,A change in the rate of inflation has a similar impact,The risk free rate goes up to provide the appropriate inflation premium and there is an upward shift in the SML.
In regard to changing investor expectations,as investors become more risk averse,the SML increases its slope,The more risk taken,the greater the return premium that is desired (see figure 11A-4).
Problems
11-1.
Rambo Exterminator Company bought a,Bug Eradicator” in April of 2004 that provided a return of 7 percent,It was financed by debt costing 6 percent,In August,Mr,Rambo came up with an,entire bug colony destroying” device that had a return of 12 percent,The Chief Financial Officer,Mr,Roach,told him it was impractical because it would require the issuance of common stock at a cost of 13.5 percent to finance the purchase,Is the company following a logical approach to using its cost of capital.
Solution:
Rambo Exterminator Company
No,each individual project should not be measured against the specific means of financing that project,but rather against the weighted average cost of financing all projects for the firm,This principle recognizes that the availability of one source of financing is dependent on other sources,Once a common overall cost is determined,the,colony destroying device” yielding 12 percent is much more likely to be accepted than the,bug eradicator” only yielding 7 percent.
11-2.
Sullivan Cement Company can issue debt yielding 13 percent,The company is paying a 36 percent rate,What is the aftertax cost of debt?
Solution:
Sullivan Cement Company
Kd = Yield (1 – T)
= 13% (1 –,36)
= 13% (.64)
= 8.32%
11-3.
Calculate the aftertax cost of debt under each of the following conditions.
Yield Corporate Tax Rate
a. 8.0% 18%
b. 12.0% 34%
c. 10.6% 15%
Solution:
Kd = Yield (1 – T)
Yield (1 – T) Yield (1 – T)
a. 8.0% (1 –,18) 6.56%
b. 12.0% (1 –,34) 7.92%
c. 10.6% (1 –,15) 9.01%
11-4.
The Millennium Charitable Foundation,which is tax-exempt,issued debt last year at 8 percent to help finance a new playground facility in Chicago,This year the cost of debt is 15 percent higher; that is,firms that paid 10 percent for debt last year would be paying 11.5 percent this year.
a. If the Millennium Charitable Foundation borrowed money this year,what would the aftertax cost of debt be,based on their cost last year and the 15 percent increase?
b. If the Foundation was found to be taxable by the IRS (at a rate of 35 percent) because it was involved in political activities,what would the aftertax cost of debt be?
Solution:
Millennium Charitable Foundation
a. Kd = Yield (1 – T)
Yield = 8% x 1.15 = 9.20%
Kd = 9.2% (1 – 0) = 9.2% (1) = 9.2%
b. Kd = 9.2% (1 – 35) = 9.2% (65) = 5.98%
11-5.
Waste Disposal Systems,Inc.,has an aftertax cost of debt of 6 percent,With a tax rate of 33 percent,what can you assume the yield on the debt is?
Solution:
Waste Disposal Systems,Inc.
9% is an acceptable answer.
11-6.
Addison Glass Company has a $1,000 par value bond outstanding with 25 years to maturity,The bond carries an annual interest payment of $88 and is currently selling for $925,Addison is in a 25 percent tax bracket,The firm wishes to know what the aftertax cost of a new bond issue is likely to be,The yield to maturity on the new issue will be the same as the yield to maturity on the old issue because the risk and maturity date will be similar.
a. Compute the approximate yield to maturity (Formula 11-1) on the old issue and use this as the yield for the new issue.
b. Make the appropriate tax adjustment to determine the aftertax cost of debt.
11-6,Continued
Solution:
Addison Glass Company
a.
b. Kd = Yield (1 – T)
= 9.53% (1 –,25)
= 9.53% (.75)
= 7.15%
11-7.
Hewlett Software Corporation has a $1,000 par value bond outstanding with 20 years to maturity,The bond carries an annual interest payment of $110 and is currently selling for $1,080 per bond,Hewlett is in a 35 percent tax bracket,The firm wishes to know what the aftertax cost of a new bond issue is likely to be,The yield to maturity on the new issue will be the same as the yield to maturity on the old issue because the risk and maturity date will be similar.
a. Compute the approximate yield to maturity (Formula 11-1) on the old issue and use this as the yield for the new issue.
b. Make the appropriate tax adjustment to determine the aftertax cost of debt.
Solution:
Hewlett Software Corporation
a.
11-7,Continued
b. Kd = Yield (1 – T)
= 10.11% (1 –,35)
= 10.11% (.65)
= 6.57%
11-8.
For Hewlett Software Corporation,described in problem 7,assume that the yield on the bonds goes up by 1 percentage point and that the tax rate is now 45 percent.
a. What is the new aftertax cost of debt?
b. Has the aftertax cost of debt gone up or down from problem 7? Explain why.
Solution:
Hewlett Software Corporation (Continued)
a. Kd = Yield (1 – T)
= 11.11% (1 –,45)
= 11.11% (.55)
= 6.11%
b. It has gone down,Although the before-tax yield is higher,the larger tax deduction (45 percent versus 35 percent) more than offsets the higher rate.
11-9.
Mead Corporation is planning to issue debt that will mature in the year 2025,In many respects the issue is similar to currently outstanding debt of the corporation,Using Table 11-2 in the chapter,
a. Identify the yield to maturity on similarly outstanding debt for the firm,in terms of maturity.
b. Assume that because the new debt will be issued at par,the required yield to maturity will be 0.15 percent higher than the value determined in part a,Add this factor to the answer in a,(New issues at par sometimes require a slightly higher yield than old issues that are trading below par,There is less leverage and fewer tax advantages.)
c. If the firm is in a 30 percent tax bracket,what is the aftertax cost of debt?
Solution:
Mead Corporation
a. 7.51%
b. 7.51% +,15% = 7.66%
c. Kd = Yield (1 – T)
= 7.66% (1 –,30)
= 7.66% (.70)
= 5.36%
11-10.
Burger Queen can sell preferred stock for $70 with an estimated flotation cost of $2.50,It is anticipated that the preferred stock will pay $6 per share in dividends.
a. Compute the cost of preferred stock for Burger Queen.
b. Do we need to make a tax adjustment for the issuing firm?
Solution:
Burger Queen
b. No tax adjustment is required,Preferred stock dividends are not a tax deductible expense for the issuing firm (the dividends,of course,are 70 percent tax exempt to a corporate recipient).
11-11.
Wallace Container Company issued $100 par value preferred stock 12 years ago,The stock provided a 9 percent yield at the time of issue,The preferred stock is now selling for $72,What is the current yield or cost of the preferred stock? (Disregard flotation costs.)
Solution:
Wallace Container Company
11-12.
The treasurer of Bio Science,Inc.,is asked to compute the cost of fixed income securities for her corporation,Even before making the calculations,she assumes the aftertax cost of debt is at least 2 percent less than that for preferred stock,Based on the following facts,is she correct?
Debt can be issued at a yield of 11 percent,and the corporate tax rate is 30 percent,Preferred stock will be priced at $50,and pay a dividend of $4.80,The floatation cost on the preferred stock is $2.10.
Solution:
Bio Science,Inc.
Aftertax cost of debt
Kd = Yield (1 – T)
= 11% (1 –,30) = 11% (.70) = 7.70%
Aftertax cost of preferred stock
Yes,the treasurer is correct,The difference is 2.32% (7.70% versus 10.02%).
11-13.
Murray Motor Company wants you to calculate its cost of common stock,During the next 12 months,the company expects to pay dividends (D1) of $2.50 per share,and the current price of its common stock is $50 per share,The expected growth rate is 8 percent.
a. Compute the cost of retained earnings (Ke),Use Formula 11-6.
b. If a $3 floatation cost is involved,compute the cost of new common stock (Kn),Use Formula 11-7.
Solution:
Murray Motor Co.
11-14.
Compute Ke and Kn under the following circumstances:
a. D1 = $4.20,P0 = $55,g = 5%,F = $3.80.
b. D1 = $0.40,P0 = $15,g = 8%,F = $1.
c. E1 (earnings at the end of period one) = $8,payout ratio equals 25 percent,P0 = $32,g = 5%,F = $2.
d. D0 (dividend at the beginning of the first period) = $3,growth rate for dividends and earnings (g) = 9%,P0 = $60,F = $3.50.
Solution:
11-14,Continued
11-14,Continued
11-15.
Business has been good for Keystone Control Systems,as indicated by the four-year growth in earnings per share,The earnings have grown from $1.00 to $1.63.
a. Use Appendix A at the back of the text to determine the compound annual rate of growth in earnings (n = 4).
b. Based on the growth rate determined in part a,project earnings for next year (E1),Round to two places to the right of the decimal point.
c. Assume the dividend payout ratio is 40 percent,Compute (D1),Round to two places to the right of the decimal point.
d. The current price of the stock is $50,Using the growth rate (g) from part a and (D1) from part c,compute Ke.
e. If the floatation cost is $3.75,compute the cost of new common stock (Kn).
11-15,Continued
Solution:
Keystone Control Systems
a.
b. E1 = Eo (1 + g)
= $1.63 (1.13)
= $1.84
c. D1 = E1 x 40%
= $1.84 x 40%
= $.74
d. Ke =
=
= 1.48% + 13%
= 14.48%
11-15,Continued
11-16.
Global Technology’s capital structure is as follows:
Debt 35%
Preferred stock 15
Common equity 50
The aftertax cost of debt is 6.5 percent; the cost of preferred stock is 10 percent; and the cost of common equity (in the form of retained earnings) is 13.5 percent.
Calculate Global Technology’s weighted average cost of capital in a manner similar to Table 11-1.
Solution:
Global Technology
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
Preferred stock (Kp)
Common equity (Ke)
(retained earnings)
Weighted average cost
of capital (Ka)
6.5%
10.0
13.5
35%
15
50
2.27%
1.50
6.75
10.52%
11-17.
As an alternative to the capital structure shown in problem 16 for Global Technology,an outside consultant has suggested the following modifications.
Debt 60%
Preferred stock 5
Common equity 35
Under this new,more debt-oriented arrangement,the aftertax cost of debt is 8.8 percent; the cost of preferred stock is 11 percent; and the cost of common equity (in the form of retained earnings) is 15.6 percent.
Recalculate Global’s weighted average cost of capital,Which plan is optimal in terms of minimizing the weighted average cost of capital?
Solution:
Global Technology (Continued)
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
Preferred stock (Kp)
Common equity (Ke)
(retained earnings)
Weighted average cost
of capital (Ka)
8.8%
11.0
15.6
60%
5
35
5.28%
0.55
5.46
11.29%
The plan presented in Problem 11-12 is the better alternative,Even though the second plan has more relatively cheap debt,the increased costs of all forms of financing more than offset this factor.
11-18.
Given the following information,calculate the weighted average cost of capital for Hamilton Corp,Line up the calculations in the order shown in Table 11-1.
Percent of capital structure:
Debt 30%
Preferred stock 15
Common equity 55
Additional information:
Bond coupon rate 13%
Bond yield to maturity 11%
Dividend,expected common $3.00
Dividend,preferred $10.00
Price,common $50.00
Price,preferred $98.00
Flotation cost,preferred $5.50
Growth rate 8%
Corporate tax rate 30%
Solution:
The Hamilton Corp.
Kd = Yield (1 – T)
= 11% (1 – 0.30)
= 11% (.70)
= 7.7%
The bond yield of 11% is used rather than the coupon rate of 13% because bonds are priced in the market according to competitive yields to maturity,The new bond would be sold to reflect yield to maturity.
11-18,Continued
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
Preferred stock (Kp)
Common equity (Ke)
(retained earnings)
Weighted average cost
of capital (Ka)
7.70%
10.81
14.00
30%
15
55
2.31%
1.62
7.70
11.63%
11-19.
Given the following information,calculate the weighted average cost of capital for Digital Processing,Inc,Line up the calculations in the order shown in Table 11-1.
Percent of capital structure:
Preferred stock 15%
Common equity 40%
Debt 45%
Additional information:
Corporate tax rate 34%
Dividend,preferred $8.50
Dividend,expected common $2.50
Price,preferred $105.00
Growth rate 7%
Bond yield 9.5%
Flotation cost,preferred $3.60
Price,common $75.00
Solution:
Digital Processing,Inc.
Kd = Yield (1 – T)
= 9.5% (1 –,34)
= 9.5% (.66)
= 6.27
Kp = Dp/(Pp – F)
= $8.50/($105 – 3.60) = $8.50/$101.40 = 8.38%
Ke = (D1/P0) + g
= ($2.50/$75) + 7% = 3.33% + 7% = 10.33%
11-19,Continued
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
Preferred stock (Kp)
Common equity (Ke)
(retained earnings)
Weighted average cost
of capital (Ka)
6.27%
8.38
10.33
45%
15
40
2.82%
1.26
4.13
8.21%
11-20.
Carr Auto Parts is trying to calculate its cost of capital for use in a capital budgeting decision,Mr,Horn,the vice president of finance,has given you the following information and has asked you to compute the weighted average cost of capital.
The company currently has outstanding a bond with a 12 percent coupon rate and a convertible bond with an 8.1 percent coupon rate,The firm has been informed by its investment banker,Axle,Wiell,and Axle,that bonds of equal risk and credit rating are now selling to yield 14 percent,The common stock has a price of $30 and an expected dividend (D1) of $1.30 per share,The firm's historical growth rate of earnings and dividends per share has been 15.5 percent,but security analysts on Wall Street expect this growth to slow to 12 percent in future,The preferred stock is selling at $60 per share and carries a dividend of $6.80 per share,The corporate tax rate is 30 percent,The flotation costs are 3 percent of the selling price for preferred stock,
The optimum capital structure for the firm seems to be 45 percent debt,5 percent preferred stock,and 55 percent common equity in the form of retained earnings.
Compute the cost of capital for the individual components in the capital structure,and then calculate the weighted average cost of capital (similar to Table 11-1).
11-20,Continued
Solution:
Carr Auto Parts
Kd = Yield (1 – T)
= 14% (1 –,30) = 9.80%
Kp = Dp/(Pp – F)
= $6.80/($60 – $1.80*) = $6.80/$58.20 = 11.68%
*3% x $60 = $1.80
Ke = (D1/Po) + g
= ($1.30/$30.00) + 12% = 4.33 + 12% = 16.33%
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
Preferred stock (Kp)
Common equity (Ke)
(retained earnings)
Weighted average cost
of capital (Ka)
9.80%
11.68
16.33
45%
5
55
4.41%
,58
8.98
13.97%
11-21.
First Tennessee Utility Company faces increasing needs for capital,Fortunately,it has an Aa2 credit rating,The corporate tax rate is 36 percent,First Tennessee’s treasurer is trying to determine the corporation's current weighted average cost of capital in order to assess the profitability of capital budgeting projects,Historically,the corporation's earning and dividends per share have increased at about 6 percent annual rate,
First Tennessee’s common stock is selling at $60 per share,and the company will pay a $4.80 per share dividend (D1),The company's $100 preferred stock has been yielding 9 percent in the current market,Flotation costs for the company have been estimated by its investment banker to be $1.50 for preferred stock,The company's optimum capital structure is 40 percent debt,10 percent preferred stock,and 50 percent common equity in the form of retained earnings,Refer to the table below on bond issues for comparative yields on bonds of equal risk to First Tennessee,Compute the answer to questions a,b,c,and d from the information given.
Data on Bond Issues
Issue
Moody's Rating
Price
Yield to Maturity
Utilities:
Balt,G&E 8?s 2010
Aa1
$ 975.25
8.60%
New York Tel,Co,7 1/2s 2009
Aa2
850.75
9.11
Miss,Pow,9.62s 2011
A1
960.50
9.67
Industrials:
IBM 9?s 2016
Aaa
$1,050.50
8.50
May Department St,7.95s 2010
Aa3
940.00
11.81
General Mills 9?s 2009
A2
1,030.75
9.05
Compute the answers to the following questions from the information given.
a. Cost of debt,Kd,(Use the above table—relate to the utility bond credit rating for yield).
b. Cost of preferred stock,Kp.
c. Cost of common equity in the form of retained earnings,Ke.
d. Weighted average cost of capital.
11-21,Continued
Solution:
First Tennessee Utility Company
The student must realize that the cost of debt is related to the cost of debt for other debt issues of the same risk class,Although,in actuality,the rate First Tennessee might pay will not be exactly equal to New York Telephone Company,it should be close enough to serve as an approximation,
a. Kd = Yield (1 – T)
= 9.11% (1 –,36) = 9.11% (.64) = 5.83%
b. Kp = Dp/(Pp – F)
= $9.00/($100 – $1.50) = $9.00/$98.50 = 9.14%
c. Ke = (D1/Po) + g
= ($4.80/$60.00) + 6% = 8% + 6% = 14.00%
d.
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
Preferred stock (Kp)
Common equity (Ke)
(retained earnings)
Weighted average cost
of capital (Ka)
5.83%
9.14
14.00
40%
10
50
2.33%
,91
7.00
10.24%
11-22.
Eaton International Corporation has the following capital structure:
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
Preferred stock (Kp)
Common equity (Ke)
(retained earnings)
Weighted average cost
of capital (Ka)
7.1%
8.6
14.1
25%
10
65
2.66%
,86
9.17
12.69%
a. If the firm has $19.5 million in retained earnings,at what size capital structure will the firm run out of retained earnings.
b. The 7.1 percent cost of debt referred to above applies only to the first $14 million of debt,After that the cost of debt will go up,At what size capital structure will there be a change in the cost of debt?
Solution:
Eaton International Corporation
11-23.
The Evans Corporation finds it is necessary to determine its marginal cost of capital,Evan's current capital structure calls for 45 percent debt,15 percent preferred stock,and 40 percent common equity,Initially,common equity will be in the form of retained earnings (Ke) and then new common stock (Kn),The costs of the various sources of financing are as follows,debt,6.2 percent; preferred stock,9.4 percent; retained earnings,12.0 percent; and new common stock,13.4 percent.
a. What is the initial weighted average cost of capital? (Include debt,preferred stock,and common equity in the form of retained earnings,Ke.)
b. If the firm has $20 million in retained earnings,at what size capital structure will the firm run out of retained earnings?
c. What will the marginal cost of capital be immediately after that point? (Equity will remain at 40 percent of the capital structure,but will all be in the form of new common stock,Kn.)
d. The 6.2 percent cost of debt referred to above applies only to the first $36 million of debt,After that the cost of debt will be 7.8 percent,At what size capital structure will there be a change in the cost of debt?
e. What will the marginal cost of capital be immediately after that point? (Consider the facts in both parts c and d.)
Solution:
The Evans Corporation
a.
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
Preferred stock (Kp)
Common equity (Ke)
(retained earnings)
Weighted average cost
of capital (Ka)
6.2%
9.4
12.0
45%
15
40
2.79%
1.41
4.80
9.00%
11-23,Continued
c.
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
Preferred stock (Kp)
New common stock
(Kn)
Marginal cost of capital
(Kmc)
6.2%
9.4
13.4
45%
15
40
2.79%
1.41
5.36
9.56%
e.
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
Preferred stock (Kp)
New common stock
(Kn)
Marginal cost of capital
(Kmc)
7.8%
9.4
13.4
45%
15
40
3.51%
1.41
5.36
10.28%
11-24.
The McGee Corporation finds it is necessary to determine its marginal cost of capital,McGee's current capital structure calls for 40 percent debt,5 percent preferred stock,and 55 percent common equity,Initially,common equity will be in the form of retained earnings (Ke) and then new common stock (Kn),The costs of the various sources of financing are as follows,debt,7.4 percent; preferred stock,10.0 percent; retained earnings,13.0 percent; and new common stock,14.4 percent.
a. What is the initial weighted average cost of capital? (Include debt,preferred stock,and common equity in the form of retained earnings,Ke.)
b. If the firm has $27.5 million in retained earnings,at what size capital structure will the firm run out of retained earnings?
c. What will the marginal cost of capital be immediately after that point? (Equity will remain at 55 percent of the capital structure,but will all be in the form of new common stock,Kn.)
d. The 7.4 percent cost of debt referred to above applies only to the first $32 million of debt,After that the cost of debt will be 8.6 percent,At what size capital structure will there be a change in the cost of debt?
e. What will the marginal cost of capital be immediately after that point? (Consider the facts in both parts c and d.)
Solution:
The McGee Corporation
a.
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
Preferred stock (Kp)
Common equity (Ke)
(retained earnings)
Weighted average cost
of capital (Ka)
7.40%
10.00
13.00
40%
5
55
2.96%
,50
7.15
10.61%
11-24,Continued
c.
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
Preferred stock (Kp)
New common stock
(Kn)
Marginal cost of capital
(Kmc)
7.40%
10.00
14.40
40%
5
55
2.96%
,50
7.92
11.38%
e.
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
Preferred stock (Kp)
New common stock
(Kn)
Marginal cost of capital
(Kmc)
8.60%
10.00
14.40
40%
5
55
3.44%
,50
7.92
11.86%
Comprehensive Problems
CP 11-1.
Medical Research Corporation is expanding its research and production capacity to introduce a new line of products,Current plans call for the expenditure of $100 million on four projects of equal size ($25 million each),but different returns,Project A is in blood clotting proteins and has an expected return of 18 percent,Project B relates to a hepatitis vaccine and carries a potential return of 14 percent,Project C,dealing with a cardiovascular compound,is expected to earn 11.8 percent,and Project D,an investment in orthopedic implants,is expected to show a 10.9 percent return.
The firm has $15 million in retained earnings,After capital structure with $15 million in retained earnings is reached (in which retained earnings represent 60 percent of the financing),all additional equity financing must come in the form of new common stock.
Common stock is selling for $25 per share and underwriting costs are estimated at $3 if new shares are issued,Dividends for the next year will be $.90 per share (D1),and earnings and dividends have grown consistently at 11 percent per year.
The yield on comparative bonds has been hovering at 11 percent,The investment banker feels that the first $20 million of bonds could be sold to yield 11 percent while additional debt might require a 2 percent premium and be sold to yield 13 percent,The corporate tax rate is 30 percent,Debt represents 40 percent of the capital structure.
a. Based on the two sources of financing,what is the initial weighted average cost of capital? (Use Kd and Ke.)
b. At what size capital structure will the firm run out of retained earnings?
c. What will the marginal cost of capital be immediately after that point?
d. At what size capital structure will there be a change in the cost of debt?
e. What will the marginal cost of capital be immediately after that point?
f. Based on the information about potential returns on investments in the first paragraph and information on marginal cost of capital (in parts a,c,and e),how large a capital investment budget should the firm use?
g. Graph the answer determined in part f.
CP 11-1,Continued
Solution:
Marginal Cost of
Capital and Investment Returns
Medical Research Corporation
a. Kd = Yield (1 – T)
= 11% (1 –,30) = 11% (.70) = 7.70%
Ke = (D1/Po) + g
= ($.90/$25.00) + 11.0% = 3.6% + 11.0% = 14.60%
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
Common equity (Ke)
(retained earnings)
Weighted average cost
of capital (Ka)
7.70%
14.60
40%
60
3.08%
8.76
11.84%
c. First compute Kn
Kn = (D1/(Po – F)) + g
= ($.90/($25 – $3)) + 11%
= ($.90/$22) + 11% = 4.09% + 11% = 15.09%
CP 11-1,Continued
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
New common stock
(Kn)
Marginal cost of capital
(Kmc)
7.70%
15.09
40%
60
3.08%
9.05
12.13%
e. First compute the new value for Kd
Kd = Yield (1 – T)
= 13% (1 –,30) = 13% (.70) = 9.10%
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
New common stock
(Kn)
Marginal cost of capital
(Kmc)
9.10%
15.09
40%
60
3.64%
9.05
12.69%
CP 11-1,Continued
f. The answer is $50 million.
Return on Investment
Marginal Cost of Capital
1st $25 million
18.0%
>
11.84%
$25 million - $50 million
14.0%
>
12.13%
$50 million - $75 million
11.8%
<
12.69%
$75 million - $100 million 10.9%
<
12.69%
g. Top bar represents return on investment
Dotted line represents marginal cost of capital (Kmc)
Invest up to $50 million
Percent (return)
18%
14%
12.69%
Kmc
12.13%
11.8%
11.84%
10.9%
0 25 50 75 100
Amount of Capital ($ millions)
CP 11-2.
Masco Oil and Gas Company is a very large company with common stock listed on the New York Stock Exchange and bonds traded over the counter,As of the current balance sheet,it has three bond issues outstanding:
Expiration
$150 million of 10% series 2015
$50 million of 7% series 2009
$75 million of 5% series 2006
The vice president of finance is planning to sell $75 million of bonds next year to replace the debt due to expire in 2006,Present market yields on similar Baa-rated bonds are 12.1 percent,Masco also has $90 million of 7.5 percent noncallable preferred stock outstanding,and it has no intentions of selling any preferred stock at any time in the future,The preferred stock is currently priced at $80 per share,and its dividend per share is $7.80.
The company has had very volatile earnings,but its dividends per share have had a very stable growth rate of 8 percent and this will continue,The expected dividend (D1) is $1.90 per share,and the common stock is selling for $40 per share,The company's investment banker has quoted the following flotation costs to Masco,$2.50 per share for preferred stock and $2.20 per share for common stock.
On the advice of its investment banker,Masco has kept its debt at 50 percent of assets and its equity at 50 percent,Masco sees no need to sell either common or preferred stock in the foreseeable future as it has generated enough internal funds for its investment needs when these funds are combined with debt financing,Masco’s corporate tax rate is 40 percent.
Compute the cost of capital for the following:
a. Bond (debt) (Kd).
b. Preferred stock (Kp).
c. Common equity in the form of retained earnings (Ke).
d. New common stock (Kn)
e. Weighted average cost of capital.
CP 11-2,Continued
Solution:
Cost of Capital with
Changing Financial Needs
Masco Oil and Gas Company
a. The before tax cost of debt will be equal to the market rate of 12.1%,The student must realize that the historical cost of the three bonds does not influence the cost of debt.
Kd = Yield (1 – T)
= 12.1% (1 –,4) = 12.1% (.6) = 7.26%
b. The fact that the preferred stock carries a coupon rate of 7.5% does not influence Kp,which is dependent upon current prices and the dividend.
Kp = (Dp)/(Pp – F)
= ($7.80)/($80 – $2.50) = ($7.80)/($77.50) = 10.06%
c. Ke = (D1/Po) + g
= ($1.90/$40.00) + 8.0% = 4.75% + 8.0% = 12.75%
d. Kn = (D1/Po – F)) + g
= ($1.90/($40 – $2.20)) + 8%
= ($1.90/$37.80) + 8% = 5.03% + 8% = 13.03%
CP 11-2,Continued
e. Only those sources of capital that are expected to be used as long-run optimum components of the capital structure should be included in the weighted average cost of capital,The firm states that all their funds can be supplied by retained earnings (50%),therefore,we do not need to include new common stock or preferred stock in our calculation of the weighted cost of capital.
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
Common equity (Ke)
(retained earnings)
Weighted average cost
of capital (Ka)
7.26%
12.75
50%
50
3.63%
6.37
10.00%
Appendix
11A-1.
Assume that Rf = 5 percent and Km = 10.5 percent,Compute Kj for the following betas,using Formula 11A-2.
a. 0.6
b. 1.3
c. 1.9
Solution:
a. Kj = Rf + β (Km – Rf)
= 5% +,6 (10.5% – 5%)
= 5% +,6 (5.5%)
= 5% + 3.3%
= 8.3%
b. Kj = 5% + 1.3 (10.5% – 5%)
= 5% + 1.3 (5.5%)
= 5% + 7.15%
= 12.15%
c. Kj = 5% + 1.9 (10.5% – 5%)
= 5% + 1.9 (5.5%)
= 5% + 10.45%
= 15.45%
11A-2.
In the preceding problem,assume an increase in interest rates changes Rf to 6.0 percent,and the market risk premium (Km – Rf) changes to 7.0 percent,Compute Kj for the three betas of 0.6,1.3,and 1.9.
Solution:
a. Kj = 6% +,6 (7%)
= 6% + 4.2%
= 10.2%
b. Kj = 6% + 1.3 (7%)
= 6% + 9.1%
= 15.1%
c. Kj = 6% + 1.9 (7%)
= 6% + 13.3%
= 19.3%
Discussion Questions
11-1.
Why do we use the overall cost of capital for investment decisions even when only one source of capital will be used (e.g.,debt)?
Though an investment financed by low-cost debt might appear acceptable at first glance,the use of debt could increase the overall risk of the firm and eventually make all forms of financing more expensive,Each project must be measured against the overall cost of funds to the firm.
11-2.
How does the cost of a source of capital relate to the valuation concepts presented previously in Chapter 10?
The cost of a source of financing directly relates to the required rate of return for that means of financing,Of course,the required rate of return is used to establish valuation.
11-3.
In computing the cost of capital,do we use the historical costs of existing debt and equity or the current costs as determined in the market? Why?
In computing the cost of capital,we use the current costs for the various sources of financing rather than the historical costs,We must consider what these funds will cost us to finance projects in the future rather than their past costs.
11-4.
Why is the cost of debt less than the cost of preferred stock if both securities are priced to yield 10 percent in the market?
Even though debt and preferred stock may be both priced to yield 10 percent in the market,the cost of debt is less because the interest on debt is a tax-deductible expense,A 10 percent market rate of interest on debt will only cost a firm in a 35 percent tax bracket an aftertax rate of 6.5 percent,The answer is the yield multiplied by the difference of (one minus the tax rate).
11-5.
What are the two sources of equity (ownership) capital for the firm?
The two sources of equity capital are retained earnings and new common stock.
11-6.
Explain why retained earnings have an opportunity cost associated?
Retained earnings belong to the existing common stockholders,If the funds are paid out instead of reinvested,the stockholders could earn a return on them,Thus,we say retaining funds for reinvestment carries an opportunity cost.
11-7.
Why is the cost of retained earnings the equivalent of the firm's own required rate of return on common stock (Ke)?
Because stockholders can earn a return at least equal to their present investment,For this reason,the firm's rate of return (Ke) serves as a means of approximating the opportunities for alternate investments.
11-8.
Why is the cost of issuing new common stock (Kn) higher than the cost of retained earnings (Ke)?
In issuing new common stock,we must earn a slightly higher return than the normal cost of common equity in order to cover the distribution costs of the new security,In the case of the Baker Corporation,the cost of new common stock was six percent higher.
11-9.
How are the weights determined to arrive at the optimal weighted average cost of capital?
The weights are determined by examining different capital structures and using that mix which gives the minimum cost of capital,We must solve a multidimensional problem to determine the proper weights.
11-10.
Explain the traditional,U-shaped approach to the cost of capital.
The logic of the U-shaped approach to cost of capital can be explained through Figure 11-1,It is assumed that as we initially increase the debt-to-equity mix the cost of capital will go down,After we reach an optimum point,the increase use of debt will increase the overall cost of financing to the firm,Thus we say the weighted average cost of capital curve is U-shaped.
11-11.
It has often been said that if the company can't earn a rate of return greater than the cost of capital it should not make investments,Explain.
If the firm cannot earn the overall cost of financing on a given project,the investment will have a negative impact on the firm's operations and will lower the overall wealth of the shareholders.
Clearly,it is undesirable to invest in a project yielding 8 percent if the financing cost is 10 percent.
11-12.
What effect would inflation have on a company's cost of capital? (Hint,Think about how inflation influences interest rates,stock prices,corporate profits,and growth.)
Inflation can only have a negative impact on a firm's cost of capital-forcing it to go up,This is true because inflation tends to increase interest rates and lower stock prices,thus raising the cost of debt and equity directly and the cost of preferred stock indirectly.
11-13.
What is the concept of marginal cost of capital?
The marginal cost of capital is the cost of incremental funds,After a firm reaches a given level of financing,capital costs will go up because the firm must tap more expensive sources,For example,new common stock may be needed to replace retained earnings as a source of equity capital.
Appendix A
Discussion Questions
11A-1.
How does the capital asset pricing model help explain changing costs of capital?
The capital asset pricing model explains the relationship between risk and return,and the price adjustment of capital assets to changes in risk and return,As investors react to their economic environment and their willingness to take risk,they change the prices of financial assets like common stock,bonds,and preferred stock,As the prices of these securities adjust to investors' required returns,the company's cost of capital is adjusted accordingly.
11A-2.
How does the SML react to changes in the rate of interest,changes in the rate of inflation,and changing investor expectations?
The SML,Security Market Line,reflects the risk-return tradeoffs of securities,As interest rates increase,the SML moves up parallel to the old SML,Now investors require a higher minimum return on risk free assets and an equally higher rate for all levels of risk,A change in the rate of inflation has a similar impact,The risk free rate goes up to provide the appropriate inflation premium and there is an upward shift in the SML.
In regard to changing investor expectations,as investors become more risk averse,the SML increases its slope,The more risk taken,the greater the return premium that is desired (see figure 11A-4).
Problems
11-1.
Rambo Exterminator Company bought a,Bug Eradicator” in April of 2004 that provided a return of 7 percent,It was financed by debt costing 6 percent,In August,Mr,Rambo came up with an,entire bug colony destroying” device that had a return of 12 percent,The Chief Financial Officer,Mr,Roach,told him it was impractical because it would require the issuance of common stock at a cost of 13.5 percent to finance the purchase,Is the company following a logical approach to using its cost of capital.
Solution:
Rambo Exterminator Company
No,each individual project should not be measured against the specific means of financing that project,but rather against the weighted average cost of financing all projects for the firm,This principle recognizes that the availability of one source of financing is dependent on other sources,Once a common overall cost is determined,the,colony destroying device” yielding 12 percent is much more likely to be accepted than the,bug eradicator” only yielding 7 percent.
11-2.
Sullivan Cement Company can issue debt yielding 13 percent,The company is paying a 36 percent rate,What is the aftertax cost of debt?
Solution:
Sullivan Cement Company
Kd = Yield (1 – T)
= 13% (1 –,36)
= 13% (.64)
= 8.32%
11-3.
Calculate the aftertax cost of debt under each of the following conditions.
Yield Corporate Tax Rate
a. 8.0% 18%
b. 12.0% 34%
c. 10.6% 15%
Solution:
Kd = Yield (1 – T)
Yield (1 – T) Yield (1 – T)
a. 8.0% (1 –,18) 6.56%
b. 12.0% (1 –,34) 7.92%
c. 10.6% (1 –,15) 9.01%
11-4.
The Millennium Charitable Foundation,which is tax-exempt,issued debt last year at 8 percent to help finance a new playground facility in Chicago,This year the cost of debt is 15 percent higher; that is,firms that paid 10 percent for debt last year would be paying 11.5 percent this year.
a. If the Millennium Charitable Foundation borrowed money this year,what would the aftertax cost of debt be,based on their cost last year and the 15 percent increase?
b. If the Foundation was found to be taxable by the IRS (at a rate of 35 percent) because it was involved in political activities,what would the aftertax cost of debt be?
Solution:
Millennium Charitable Foundation
a. Kd = Yield (1 – T)
Yield = 8% x 1.15 = 9.20%
Kd = 9.2% (1 – 0) = 9.2% (1) = 9.2%
b. Kd = 9.2% (1 – 35) = 9.2% (65) = 5.98%
11-5.
Waste Disposal Systems,Inc.,has an aftertax cost of debt of 6 percent,With a tax rate of 33 percent,what can you assume the yield on the debt is?
Solution:
Waste Disposal Systems,Inc.
9% is an acceptable answer.
11-6.
Addison Glass Company has a $1,000 par value bond outstanding with 25 years to maturity,The bond carries an annual interest payment of $88 and is currently selling for $925,Addison is in a 25 percent tax bracket,The firm wishes to know what the aftertax cost of a new bond issue is likely to be,The yield to maturity on the new issue will be the same as the yield to maturity on the old issue because the risk and maturity date will be similar.
a. Compute the approximate yield to maturity (Formula 11-1) on the old issue and use this as the yield for the new issue.
b. Make the appropriate tax adjustment to determine the aftertax cost of debt.
11-6,Continued
Solution:
Addison Glass Company
a.
b. Kd = Yield (1 – T)
= 9.53% (1 –,25)
= 9.53% (.75)
= 7.15%
11-7.
Hewlett Software Corporation has a $1,000 par value bond outstanding with 20 years to maturity,The bond carries an annual interest payment of $110 and is currently selling for $1,080 per bond,Hewlett is in a 35 percent tax bracket,The firm wishes to know what the aftertax cost of a new bond issue is likely to be,The yield to maturity on the new issue will be the same as the yield to maturity on the old issue because the risk and maturity date will be similar.
a. Compute the approximate yield to maturity (Formula 11-1) on the old issue and use this as the yield for the new issue.
b. Make the appropriate tax adjustment to determine the aftertax cost of debt.
Solution:
Hewlett Software Corporation
a.
11-7,Continued
b. Kd = Yield (1 – T)
= 10.11% (1 –,35)
= 10.11% (.65)
= 6.57%
11-8.
For Hewlett Software Corporation,described in problem 7,assume that the yield on the bonds goes up by 1 percentage point and that the tax rate is now 45 percent.
a. What is the new aftertax cost of debt?
b. Has the aftertax cost of debt gone up or down from problem 7? Explain why.
Solution:
Hewlett Software Corporation (Continued)
a. Kd = Yield (1 – T)
= 11.11% (1 –,45)
= 11.11% (.55)
= 6.11%
b. It has gone down,Although the before-tax yield is higher,the larger tax deduction (45 percent versus 35 percent) more than offsets the higher rate.
11-9.
Mead Corporation is planning to issue debt that will mature in the year 2025,In many respects the issue is similar to currently outstanding debt of the corporation,Using Table 11-2 in the chapter,
a. Identify the yield to maturity on similarly outstanding debt for the firm,in terms of maturity.
b. Assume that because the new debt will be issued at par,the required yield to maturity will be 0.15 percent higher than the value determined in part a,Add this factor to the answer in a,(New issues at par sometimes require a slightly higher yield than old issues that are trading below par,There is less leverage and fewer tax advantages.)
c. If the firm is in a 30 percent tax bracket,what is the aftertax cost of debt?
Solution:
Mead Corporation
a. 7.51%
b. 7.51% +,15% = 7.66%
c. Kd = Yield (1 – T)
= 7.66% (1 –,30)
= 7.66% (.70)
= 5.36%
11-10.
Burger Queen can sell preferred stock for $70 with an estimated flotation cost of $2.50,It is anticipated that the preferred stock will pay $6 per share in dividends.
a. Compute the cost of preferred stock for Burger Queen.
b. Do we need to make a tax adjustment for the issuing firm?
Solution:
Burger Queen
b. No tax adjustment is required,Preferred stock dividends are not a tax deductible expense for the issuing firm (the dividends,of course,are 70 percent tax exempt to a corporate recipient).
11-11.
Wallace Container Company issued $100 par value preferred stock 12 years ago,The stock provided a 9 percent yield at the time of issue,The preferred stock is now selling for $72,What is the current yield or cost of the preferred stock? (Disregard flotation costs.)
Solution:
Wallace Container Company
11-12.
The treasurer of Bio Science,Inc.,is asked to compute the cost of fixed income securities for her corporation,Even before making the calculations,she assumes the aftertax cost of debt is at least 2 percent less than that for preferred stock,Based on the following facts,is she correct?
Debt can be issued at a yield of 11 percent,and the corporate tax rate is 30 percent,Preferred stock will be priced at $50,and pay a dividend of $4.80,The floatation cost on the preferred stock is $2.10.
Solution:
Bio Science,Inc.
Aftertax cost of debt
Kd = Yield (1 – T)
= 11% (1 –,30) = 11% (.70) = 7.70%
Aftertax cost of preferred stock
Yes,the treasurer is correct,The difference is 2.32% (7.70% versus 10.02%).
11-13.
Murray Motor Company wants you to calculate its cost of common stock,During the next 12 months,the company expects to pay dividends (D1) of $2.50 per share,and the current price of its common stock is $50 per share,The expected growth rate is 8 percent.
a. Compute the cost of retained earnings (Ke),Use Formula 11-6.
b. If a $3 floatation cost is involved,compute the cost of new common stock (Kn),Use Formula 11-7.
Solution:
Murray Motor Co.
11-14.
Compute Ke and Kn under the following circumstances:
a. D1 = $4.20,P0 = $55,g = 5%,F = $3.80.
b. D1 = $0.40,P0 = $15,g = 8%,F = $1.
c. E1 (earnings at the end of period one) = $8,payout ratio equals 25 percent,P0 = $32,g = 5%,F = $2.
d. D0 (dividend at the beginning of the first period) = $3,growth rate for dividends and earnings (g) = 9%,P0 = $60,F = $3.50.
Solution:
11-14,Continued
11-14,Continued
11-15.
Business has been good for Keystone Control Systems,as indicated by the four-year growth in earnings per share,The earnings have grown from $1.00 to $1.63.
a. Use Appendix A at the back of the text to determine the compound annual rate of growth in earnings (n = 4).
b. Based on the growth rate determined in part a,project earnings for next year (E1),Round to two places to the right of the decimal point.
c. Assume the dividend payout ratio is 40 percent,Compute (D1),Round to two places to the right of the decimal point.
d. The current price of the stock is $50,Using the growth rate (g) from part a and (D1) from part c,compute Ke.
e. If the floatation cost is $3.75,compute the cost of new common stock (Kn).
11-15,Continued
Solution:
Keystone Control Systems
a.
b. E1 = Eo (1 + g)
= $1.63 (1.13)
= $1.84
c. D1 = E1 x 40%
= $1.84 x 40%
= $.74
d. Ke =
=
= 1.48% + 13%
= 14.48%
11-15,Continued
11-16.
Global Technology’s capital structure is as follows:
Debt 35%
Preferred stock 15
Common equity 50
The aftertax cost of debt is 6.5 percent; the cost of preferred stock is 10 percent; and the cost of common equity (in the form of retained earnings) is 13.5 percent.
Calculate Global Technology’s weighted average cost of capital in a manner similar to Table 11-1.
Solution:
Global Technology
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
Preferred stock (Kp)
Common equity (Ke)
(retained earnings)
Weighted average cost
of capital (Ka)
6.5%
10.0
13.5
35%
15
50
2.27%
1.50
6.75
10.52%
11-17.
As an alternative to the capital structure shown in problem 16 for Global Technology,an outside consultant has suggested the following modifications.
Debt 60%
Preferred stock 5
Common equity 35
Under this new,more debt-oriented arrangement,the aftertax cost of debt is 8.8 percent; the cost of preferred stock is 11 percent; and the cost of common equity (in the form of retained earnings) is 15.6 percent.
Recalculate Global’s weighted average cost of capital,Which plan is optimal in terms of minimizing the weighted average cost of capital?
Solution:
Global Technology (Continued)
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
Preferred stock (Kp)
Common equity (Ke)
(retained earnings)
Weighted average cost
of capital (Ka)
8.8%
11.0
15.6
60%
5
35
5.28%
0.55
5.46
11.29%
The plan presented in Problem 11-12 is the better alternative,Even though the second plan has more relatively cheap debt,the increased costs of all forms of financing more than offset this factor.
11-18.
Given the following information,calculate the weighted average cost of capital for Hamilton Corp,Line up the calculations in the order shown in Table 11-1.
Percent of capital structure:
Debt 30%
Preferred stock 15
Common equity 55
Additional information:
Bond coupon rate 13%
Bond yield to maturity 11%
Dividend,expected common $3.00
Dividend,preferred $10.00
Price,common $50.00
Price,preferred $98.00
Flotation cost,preferred $5.50
Growth rate 8%
Corporate tax rate 30%
Solution:
The Hamilton Corp.
Kd = Yield (1 – T)
= 11% (1 – 0.30)
= 11% (.70)
= 7.7%
The bond yield of 11% is used rather than the coupon rate of 13% because bonds are priced in the market according to competitive yields to maturity,The new bond would be sold to reflect yield to maturity.
11-18,Continued
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
Preferred stock (Kp)
Common equity (Ke)
(retained earnings)
Weighted average cost
of capital (Ka)
7.70%
10.81
14.00
30%
15
55
2.31%
1.62
7.70
11.63%
11-19.
Given the following information,calculate the weighted average cost of capital for Digital Processing,Inc,Line up the calculations in the order shown in Table 11-1.
Percent of capital structure:
Preferred stock 15%
Common equity 40%
Debt 45%
Additional information:
Corporate tax rate 34%
Dividend,preferred $8.50
Dividend,expected common $2.50
Price,preferred $105.00
Growth rate 7%
Bond yield 9.5%
Flotation cost,preferred $3.60
Price,common $75.00
Solution:
Digital Processing,Inc.
Kd = Yield (1 – T)
= 9.5% (1 –,34)
= 9.5% (.66)
= 6.27
Kp = Dp/(Pp – F)
= $8.50/($105 – 3.60) = $8.50/$101.40 = 8.38%
Ke = (D1/P0) + g
= ($2.50/$75) + 7% = 3.33% + 7% = 10.33%
11-19,Continued
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
Preferred stock (Kp)
Common equity (Ke)
(retained earnings)
Weighted average cost
of capital (Ka)
6.27%
8.38
10.33
45%
15
40
2.82%
1.26
4.13
8.21%
11-20.
Carr Auto Parts is trying to calculate its cost of capital for use in a capital budgeting decision,Mr,Horn,the vice president of finance,has given you the following information and has asked you to compute the weighted average cost of capital.
The company currently has outstanding a bond with a 12 percent coupon rate and a convertible bond with an 8.1 percent coupon rate,The firm has been informed by its investment banker,Axle,Wiell,and Axle,that bonds of equal risk and credit rating are now selling to yield 14 percent,The common stock has a price of $30 and an expected dividend (D1) of $1.30 per share,The firm's historical growth rate of earnings and dividends per share has been 15.5 percent,but security analysts on Wall Street expect this growth to slow to 12 percent in future,The preferred stock is selling at $60 per share and carries a dividend of $6.80 per share,The corporate tax rate is 30 percent,The flotation costs are 3 percent of the selling price for preferred stock,
The optimum capital structure for the firm seems to be 45 percent debt,5 percent preferred stock,and 55 percent common equity in the form of retained earnings.
Compute the cost of capital for the individual components in the capital structure,and then calculate the weighted average cost of capital (similar to Table 11-1).
11-20,Continued
Solution:
Carr Auto Parts
Kd = Yield (1 – T)
= 14% (1 –,30) = 9.80%
Kp = Dp/(Pp – F)
= $6.80/($60 – $1.80*) = $6.80/$58.20 = 11.68%
*3% x $60 = $1.80
Ke = (D1/Po) + g
= ($1.30/$30.00) + 12% = 4.33 + 12% = 16.33%
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
Preferred stock (Kp)
Common equity (Ke)
(retained earnings)
Weighted average cost
of capital (Ka)
9.80%
11.68
16.33
45%
5
55
4.41%
,58
8.98
13.97%
11-21.
First Tennessee Utility Company faces increasing needs for capital,Fortunately,it has an Aa2 credit rating,The corporate tax rate is 36 percent,First Tennessee’s treasurer is trying to determine the corporation's current weighted average cost of capital in order to assess the profitability of capital budgeting projects,Historically,the corporation's earning and dividends per share have increased at about 6 percent annual rate,
First Tennessee’s common stock is selling at $60 per share,and the company will pay a $4.80 per share dividend (D1),The company's $100 preferred stock has been yielding 9 percent in the current market,Flotation costs for the company have been estimated by its investment banker to be $1.50 for preferred stock,The company's optimum capital structure is 40 percent debt,10 percent preferred stock,and 50 percent common equity in the form of retained earnings,Refer to the table below on bond issues for comparative yields on bonds of equal risk to First Tennessee,Compute the answer to questions a,b,c,and d from the information given.
Data on Bond Issues
Issue
Moody's Rating
Price
Yield to Maturity
Utilities:
Balt,G&E 8?s 2010
Aa1
$ 975.25
8.60%
New York Tel,Co,7 1/2s 2009
Aa2
850.75
9.11
Miss,Pow,9.62s 2011
A1
960.50
9.67
Industrials:
IBM 9?s 2016
Aaa
$1,050.50
8.50
May Department St,7.95s 2010
Aa3
940.00
11.81
General Mills 9?s 2009
A2
1,030.75
9.05
Compute the answers to the following questions from the information given.
a. Cost of debt,Kd,(Use the above table—relate to the utility bond credit rating for yield).
b. Cost of preferred stock,Kp.
c. Cost of common equity in the form of retained earnings,Ke.
d. Weighted average cost of capital.
11-21,Continued
Solution:
First Tennessee Utility Company
The student must realize that the cost of debt is related to the cost of debt for other debt issues of the same risk class,Although,in actuality,the rate First Tennessee might pay will not be exactly equal to New York Telephone Company,it should be close enough to serve as an approximation,
a. Kd = Yield (1 – T)
= 9.11% (1 –,36) = 9.11% (.64) = 5.83%
b. Kp = Dp/(Pp – F)
= $9.00/($100 – $1.50) = $9.00/$98.50 = 9.14%
c. Ke = (D1/Po) + g
= ($4.80/$60.00) + 6% = 8% + 6% = 14.00%
d.
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
Preferred stock (Kp)
Common equity (Ke)
(retained earnings)
Weighted average cost
of capital (Ka)
5.83%
9.14
14.00
40%
10
50
2.33%
,91
7.00
10.24%
11-22.
Eaton International Corporation has the following capital structure:
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
Preferred stock (Kp)
Common equity (Ke)
(retained earnings)
Weighted average cost
of capital (Ka)
7.1%
8.6
14.1
25%
10
65
2.66%
,86
9.17
12.69%
a. If the firm has $19.5 million in retained earnings,at what size capital structure will the firm run out of retained earnings.
b. The 7.1 percent cost of debt referred to above applies only to the first $14 million of debt,After that the cost of debt will go up,At what size capital structure will there be a change in the cost of debt?
Solution:
Eaton International Corporation
11-23.
The Evans Corporation finds it is necessary to determine its marginal cost of capital,Evan's current capital structure calls for 45 percent debt,15 percent preferred stock,and 40 percent common equity,Initially,common equity will be in the form of retained earnings (Ke) and then new common stock (Kn),The costs of the various sources of financing are as follows,debt,6.2 percent; preferred stock,9.4 percent; retained earnings,12.0 percent; and new common stock,13.4 percent.
a. What is the initial weighted average cost of capital? (Include debt,preferred stock,and common equity in the form of retained earnings,Ke.)
b. If the firm has $20 million in retained earnings,at what size capital structure will the firm run out of retained earnings?
c. What will the marginal cost of capital be immediately after that point? (Equity will remain at 40 percent of the capital structure,but will all be in the form of new common stock,Kn.)
d. The 6.2 percent cost of debt referred to above applies only to the first $36 million of debt,After that the cost of debt will be 7.8 percent,At what size capital structure will there be a change in the cost of debt?
e. What will the marginal cost of capital be immediately after that point? (Consider the facts in both parts c and d.)
Solution:
The Evans Corporation
a.
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
Preferred stock (Kp)
Common equity (Ke)
(retained earnings)
Weighted average cost
of capital (Ka)
6.2%
9.4
12.0
45%
15
40
2.79%
1.41
4.80
9.00%
11-23,Continued
c.
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
Preferred stock (Kp)
New common stock
(Kn)
Marginal cost of capital
(Kmc)
6.2%
9.4
13.4
45%
15
40
2.79%
1.41
5.36
9.56%
e.
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
Preferred stock (Kp)
New common stock
(Kn)
Marginal cost of capital
(Kmc)
7.8%
9.4
13.4
45%
15
40
3.51%
1.41
5.36
10.28%
11-24.
The McGee Corporation finds it is necessary to determine its marginal cost of capital,McGee's current capital structure calls for 40 percent debt,5 percent preferred stock,and 55 percent common equity,Initially,common equity will be in the form of retained earnings (Ke) and then new common stock (Kn),The costs of the various sources of financing are as follows,debt,7.4 percent; preferred stock,10.0 percent; retained earnings,13.0 percent; and new common stock,14.4 percent.
a. What is the initial weighted average cost of capital? (Include debt,preferred stock,and common equity in the form of retained earnings,Ke.)
b. If the firm has $27.5 million in retained earnings,at what size capital structure will the firm run out of retained earnings?
c. What will the marginal cost of capital be immediately after that point? (Equity will remain at 55 percent of the capital structure,but will all be in the form of new common stock,Kn.)
d. The 7.4 percent cost of debt referred to above applies only to the first $32 million of debt,After that the cost of debt will be 8.6 percent,At what size capital structure will there be a change in the cost of debt?
e. What will the marginal cost of capital be immediately after that point? (Consider the facts in both parts c and d.)
Solution:
The McGee Corporation
a.
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
Preferred stock (Kp)
Common equity (Ke)
(retained earnings)
Weighted average cost
of capital (Ka)
7.40%
10.00
13.00
40%
5
55
2.96%
,50
7.15
10.61%
11-24,Continued
c.
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
Preferred stock (Kp)
New common stock
(Kn)
Marginal cost of capital
(Kmc)
7.40%
10.00
14.40
40%
5
55
2.96%
,50
7.92
11.38%
e.
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
Preferred stock (Kp)
New common stock
(Kn)
Marginal cost of capital
(Kmc)
8.60%
10.00
14.40
40%
5
55
3.44%
,50
7.92
11.86%
Comprehensive Problems
CP 11-1.
Medical Research Corporation is expanding its research and production capacity to introduce a new line of products,Current plans call for the expenditure of $100 million on four projects of equal size ($25 million each),but different returns,Project A is in blood clotting proteins and has an expected return of 18 percent,Project B relates to a hepatitis vaccine and carries a potential return of 14 percent,Project C,dealing with a cardiovascular compound,is expected to earn 11.8 percent,and Project D,an investment in orthopedic implants,is expected to show a 10.9 percent return.
The firm has $15 million in retained earnings,After capital structure with $15 million in retained earnings is reached (in which retained earnings represent 60 percent of the financing),all additional equity financing must come in the form of new common stock.
Common stock is selling for $25 per share and underwriting costs are estimated at $3 if new shares are issued,Dividends for the next year will be $.90 per share (D1),and earnings and dividends have grown consistently at 11 percent per year.
The yield on comparative bonds has been hovering at 11 percent,The investment banker feels that the first $20 million of bonds could be sold to yield 11 percent while additional debt might require a 2 percent premium and be sold to yield 13 percent,The corporate tax rate is 30 percent,Debt represents 40 percent of the capital structure.
a. Based on the two sources of financing,what is the initial weighted average cost of capital? (Use Kd and Ke.)
b. At what size capital structure will the firm run out of retained earnings?
c. What will the marginal cost of capital be immediately after that point?
d. At what size capital structure will there be a change in the cost of debt?
e. What will the marginal cost of capital be immediately after that point?
f. Based on the information about potential returns on investments in the first paragraph and information on marginal cost of capital (in parts a,c,and e),how large a capital investment budget should the firm use?
g. Graph the answer determined in part f.
CP 11-1,Continued
Solution:
Marginal Cost of
Capital and Investment Returns
Medical Research Corporation
a. Kd = Yield (1 – T)
= 11% (1 –,30) = 11% (.70) = 7.70%
Ke = (D1/Po) + g
= ($.90/$25.00) + 11.0% = 3.6% + 11.0% = 14.60%
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
Common equity (Ke)
(retained earnings)
Weighted average cost
of capital (Ka)
7.70%
14.60
40%
60
3.08%
8.76
11.84%
c. First compute Kn
Kn = (D1/(Po – F)) + g
= ($.90/($25 – $3)) + 11%
= ($.90/$22) + 11% = 4.09% + 11% = 15.09%
CP 11-1,Continued
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
New common stock
(Kn)
Marginal cost of capital
(Kmc)
7.70%
15.09
40%
60
3.08%
9.05
12.13%
e. First compute the new value for Kd
Kd = Yield (1 – T)
= 13% (1 –,30) = 13% (.70) = 9.10%
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
New common stock
(Kn)
Marginal cost of capital
(Kmc)
9.10%
15.09
40%
60
3.64%
9.05
12.69%
CP 11-1,Continued
f. The answer is $50 million.
Return on Investment
Marginal Cost of Capital
1st $25 million
18.0%
>
11.84%
$25 million - $50 million
14.0%
>
12.13%
$50 million - $75 million
11.8%
<
12.69%
$75 million - $100 million 10.9%
<
12.69%
g. Top bar represents return on investment
Dotted line represents marginal cost of capital (Kmc)
Invest up to $50 million
Percent (return)
18%
14%
12.69%
Kmc
12.13%
11.8%
11.84%
10.9%
0 25 50 75 100
Amount of Capital ($ millions)
CP 11-2.
Masco Oil and Gas Company is a very large company with common stock listed on the New York Stock Exchange and bonds traded over the counter,As of the current balance sheet,it has three bond issues outstanding:
Expiration
$150 million of 10% series 2015
$50 million of 7% series 2009
$75 million of 5% series 2006
The vice president of finance is planning to sell $75 million of bonds next year to replace the debt due to expire in 2006,Present market yields on similar Baa-rated bonds are 12.1 percent,Masco also has $90 million of 7.5 percent noncallable preferred stock outstanding,and it has no intentions of selling any preferred stock at any time in the future,The preferred stock is currently priced at $80 per share,and its dividend per share is $7.80.
The company has had very volatile earnings,but its dividends per share have had a very stable growth rate of 8 percent and this will continue,The expected dividend (D1) is $1.90 per share,and the common stock is selling for $40 per share,The company's investment banker has quoted the following flotation costs to Masco,$2.50 per share for preferred stock and $2.20 per share for common stock.
On the advice of its investment banker,Masco has kept its debt at 50 percent of assets and its equity at 50 percent,Masco sees no need to sell either common or preferred stock in the foreseeable future as it has generated enough internal funds for its investment needs when these funds are combined with debt financing,Masco’s corporate tax rate is 40 percent.
Compute the cost of capital for the following:
a. Bond (debt) (Kd).
b. Preferred stock (Kp).
c. Common equity in the form of retained earnings (Ke).
d. New common stock (Kn)
e. Weighted average cost of capital.
CP 11-2,Continued
Solution:
Cost of Capital with
Changing Financial Needs
Masco Oil and Gas Company
a. The before tax cost of debt will be equal to the market rate of 12.1%,The student must realize that the historical cost of the three bonds does not influence the cost of debt.
Kd = Yield (1 – T)
= 12.1% (1 –,4) = 12.1% (.6) = 7.26%
b. The fact that the preferred stock carries a coupon rate of 7.5% does not influence Kp,which is dependent upon current prices and the dividend.
Kp = (Dp)/(Pp – F)
= ($7.80)/($80 – $2.50) = ($7.80)/($77.50) = 10.06%
c. Ke = (D1/Po) + g
= ($1.90/$40.00) + 8.0% = 4.75% + 8.0% = 12.75%
d. Kn = (D1/Po – F)) + g
= ($1.90/($40 – $2.20)) + 8%
= ($1.90/$37.80) + 8% = 5.03% + 8% = 13.03%
CP 11-2,Continued
e. Only those sources of capital that are expected to be used as long-run optimum components of the capital structure should be included in the weighted average cost of capital,The firm states that all their funds can be supplied by retained earnings (50%),therefore,we do not need to include new common stock or preferred stock in our calculation of the weighted cost of capital.
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd)
Common equity (Ke)
(retained earnings)
Weighted average cost
of capital (Ka)
7.26%
12.75
50%
50
3.63%
6.37
10.00%
Appendix
11A-1.
Assume that Rf = 5 percent and Km = 10.5 percent,Compute Kj for the following betas,using Formula 11A-2.
a. 0.6
b. 1.3
c. 1.9
Solution:
a. Kj = Rf + β (Km – Rf)
= 5% +,6 (10.5% – 5%)
= 5% +,6 (5.5%)
= 5% + 3.3%
= 8.3%
b. Kj = 5% + 1.3 (10.5% – 5%)
= 5% + 1.3 (5.5%)
= 5% + 7.15%
= 12.15%
c. Kj = 5% + 1.9 (10.5% – 5%)
= 5% + 1.9 (5.5%)
= 5% + 10.45%
= 15.45%
11A-2.
In the preceding problem,assume an increase in interest rates changes Rf to 6.0 percent,and the market risk premium (Km – Rf) changes to 7.0 percent,Compute Kj for the three betas of 0.6,1.3,and 1.9.
Solution:
a. Kj = 6% +,6 (7%)
= 6% + 4.2%
= 10.2%
b. Kj = 6% + 1.3 (7%)
= 6% + 9.1%
= 15.1%
c. Kj = 6% + 1.9 (7%)
= 6% + 13.3%
= 19.3%
