FIN2101
Business Finance II
Module 9
Investment and
Financing Decisions
Student Activities
Reading
Study Book,Module 9
Selected Reading 9.1
Tutorial Activities
Tutorial Workbook,Self Assessment
Activity 9.1
Introduction
The cost of capital is used to discount after-
tax cash flows expected from a firm’s
investment decision,This,in turn,
determines whether the investment should be
accepted or rejected according to the value it
is expected to create.
Cost of capital is thought of as the rate of
return required by the market suppliers of
capital in order to attract their funds to the
firm.
Introduction
Does the financing mix affect the firm’s
overall cost of funds,either favourably or
unfavourably?
MM say NO - financing decisions are
irrelevant.
Firms should therefore concentrate on the
investment decisions.
Introduction
In reality,the cost of capital may decrease
with financial leverage,resulting in some
negative NPV projects becoming
acceptable (positive NPV).
This factor therefore needs to be
incorporated into our investment decision
analysis!
Introduction
Under MM assumptions,investment
decisions can be separated from the
financing decisions.
In reality,these decisions can’t be
separated!
The effects of financing decisions must be
included in the analysis.
Valuation Methods
WACC method – adjusts the discount rate.
Adjusted present value (APV) method –
adjusts the NPV for the impact of the
financing decision.
Flow-to-equity (FTE) method –
combination of the other 2 methods.
WACC
V
D
T - 1k
V
S
k k dsa
WACC
Reflects,on average,the firm’s cost of long-term
financing.
Recognises the mix of different financing
sources that fund the firm’s long-term assets.
Is the average of the rates of return that
providers of capital require,with each source’s
contribution being weighted according to the
proportion of capital it provided.
Is found by weighting the cost of each specific
type of capital by its proportion in the firm’s
capital structure.
WACC Assumptions
The risk of the project is identical to the
risk of the firm’s existing assets.
The project will be financed in the same
way (same D:E) as the firm as a whole.
WACC Method
The after-tax WACC will be less than the
firm’s opportunity cost of capital because
of the tax advantages of debt financing.
Discount the unlevered cash flows (UCFs)
at the after-tax WACC to get the NPV.
Example
Cash inflows = $1 200 000
Costs = 77.5% of sales
Initial cost = $960 000
Tax rate = 30%
Opportunity cost of capital = 21%
Cost of debt = 12%
Cost of equity = 23.7%
Debt-to-value ratio = 0.30
WACC Solution
Step 1 – Calculate unlevered cash flow (UCF)
Cash inflows $1 200 000
Cash costs (77.5%) 930 000
Operating income 270 000
Tax (30%) 81 000
UCF $ 189 000
WACC Solution
Step 2 – Calculate after-tax WACC
1 9,1 1 %o r 0,1 9 1 1
0,0 2 5 2 0,1 6 5 9
0,3 0 - 1 0,1 2
100
30
0,2 3 7
100
70
k
a
WACC Solution
0 1 1 $ 2 9
0 0 0 $ 9 6 0 -
0,1 9 1 1
0 0 0 $ 1 8 9
N PV
Step 3 – Calculate NPV
Accept – positive NPV
Cost of Equity
23,7%or 0,237
0,09 0,30 0,21
0,12 - 0,21 0,30 - 1
7
3
0,21
k - k T - 1
E
D
k k
doos
Adjusted Present Value (APV)
A firm should only undertake investments
that create value and thereby increase the
owners’ wealth.
This therefore requires that for any
investment proposal to be acceptable,the
NPV of the combined investment and
financing decisions must be positive.
APV Method
For any new investment whose risk is in
the same risk class as the firm’s average,
the firm’s after-tax overall cost of capital
(WACC) can be used to discount the
investment’s cash flows and determine its
acceptability.
Any new investment should also use the
same proportions of debt and equity as the
firm’s overall capital structure.
APV Method
It is implicit that whenever the WACC is used
to evaluate a project,the financing decision
side-effects are included and their risk is
assumed to replicate that of the firm as a
whole.
This means that the firm’s WACC is suitable
for evaluating the,average” project and that
WACC is an adjusted cost of capital which
captures the project’s financing side-effects.
APV Method
To evaluate projects that fall outside the
“average” risk class for a firm,the adjusted
present value (APV) approach should be
used so as to evaluate the effects of the
investment and financing decisions.
Appendix 9.1 provides a good overview of
the APV method.
APV Method
Initially calculate the base-case NPV
assuming the project will be all-equity
financed.
Then consider the side effects of
financing:
– tax subsidy on debt;
– cost of issuing new securities.
APV Method
e f f e c t s s i de f i n a n c i n g
of l u epr e s e n t v an e t t h e N P V F w h e r e
N P V F N P V A P V
APV Solution
Step 1 – Calculate base-case NPV assuming all-
equity financed
0 0 0 $ 6 0 -
0 0 0 $ 9 6 0 -
0,2 1
0 0 0 $ 1 8 9
N PV
APV Solution
Step 2 – Calculate PV of tax shield
400 $86
000 $960 0,3 0 0,3 0
T D
k
T D k
s h i e l dt a x PV
d
d
APV Solution
400 $26
400 $86 000 $60 - A PV
Accept – positive APV
PV of Tax Shield
The previous example assumed perpetual debt,
but this is obviously not always the case.
Many loans are for a fixed term.
Assume that as part of its funding arrangements
for a project,a company takes out a $500 000
loan over 4 years.
Assume 10% p.a,interest,a cost of capital of
12%,and a tax rate of 30%.
Must prepare a loan amortisation schedule to
identify the annual interest expense.
PV of Tax Shield
7 28,7 1 $ 15 7
3,1 7 0
0 00 $ 50 0
PM T
PV I FA PM T 0 00 $ 50 0
PV I FA PM T PV A
0,1 0,4
nk,
First,calculate the annual repayments
PV of Tax Shield
Yr Opening
Principal
Repayment Interest
Component
Principal
Component
Ending
Principal
1 500 000 157 729 50 000 107 729 392 271
2 392 271 157 729 39 227 118 502 273 769
3 273 769 157 729 27 377 130 352 143 417
4 143 417 157 729 14 342 143 387 30
PV of Tax Shield
354 $31
734 $2 846 $5 381 $9 393 $13
1.1 2
0.3 0 342 $14
1.1 2
0.3 0 377 $27
1.1 2
0.3 0 227 $39
1.1 2
0.3 0 000 $50
s h i e l dt a x PV
43
2
APV Method
The previous approach assumed that debt
was a fixed proportion of the initial
investment.
However,in reality,debt should be
expressed as a proportion of the present
value of the project.
APV Solution
011 $ 9 8 9 V
000 $ 9 0 0 0,9 1 V
0,0 9 V 000 $ 9 0 0 V
V 0,3 00,3 0
0,2 1
000 $ 1 8 9
V
D T p r o j e c t u n l e v e r e d of PV p r o j e c t l e v e r e d of PV
d e b tw i t h
d e b tw i t h
d e b tw i t h d e b tw i t h
d e b tw i t h d e b tw i t h
7 0 3 $ 2 9 6
0 1 1 $ 9 8 9 0,3 0 D e b t
APV Solution
011 $29
011 $ 9 8 9 0,3 0 0,3 0 000 $60 - A PV
Accept – positive APV
Another APV Example
Assume that the project is to be financed
by issuing shares.
Issue costs will be 4% of the gross
proceeds of the issue.
What is the project’s APV?
APV Solution
Calculate amount to be raised from the issue to
generate $960 000 required for the project.
0 0 0 0 0 0 $1
0,0 4 - 1
0 0 0 $ 9 6 0
p r o c e e d s G r o s s
The firm must raise $1 000 000 to have $960 000 to fund
the project,The remaining $40 000 represents issue
costs.
APV Solution
000 $100 -
000 $40 - 000 $60 -
N PV F N PV A PV
Reject – negative APV
Flow-to-Equity (FTE) Approach
Discounts the levered cash flows (LCFs)
at the cost of equity to give the PV of the
levered cash flows.
NPV is the difference between the PV of
the project’s levered cash flows and that
part of the investment financed out of
equity.
FTE Solution
Step 1 – Determine levered cash flow (LCF)
Cash inflows $1 200 000
Cash costs (77.5%) 930 000
Interest (12% × $296 703) 35 604
Income after interest 234 396
Tax (@ 30%) 70 319
Levered cash flow (LCF) $ 164 077
Level of Debt
Note that to calculate interest expense you
must know the level of debt.
In the APV approach we calculated debt to
be $296 703.
If the level of debt hasn’t been calculated,
we must do so.
Calculate UCF,Vwith debt and then the
amount of debt.
Levered Cash Flow (LCF)
077 $164
923 $24 - 000 $189
703 $296 0.1 2 0.3 0 - 1 - 000 $189
D k T - 1 - U C F L C F
d
FTE Solution
Step 2 – Calculate PV of LCF
30 8 $6 92
0,23 7
07 7 $1 64
k
L C F
PV
s
FTE Solution
Step 3 – Determine amount funded from equity
Initial investment $960 000
Less Amount borrowed 296 703
Funded from equity $663 297
FTE Solution
Step 4 – Calculate NPV
011 $29
297 $663 - 308 $692
f u n d i n gE q u i t y - L C F of PV N PV
Accept – positive NPV
Summary
WACC discounts UCFs at WACC,which
lowers the opportunity cost of capital.
APV discounts UCFs at opportunity cost of
capital and then adjusts for the side effects
of funding.
FTE uses LCFs (UCFs less interest
payments),The initial investment is the
firm’s contribution to the initial cost.
Which Method?
Use WACC or FTE if the project’s risk
(and therefore opportunity cost of capital)
and the debt-to-value ratio remain
constant.
Use APV when the project’s debt level is
known over the life of the project.
In practice,WACC is the most widely used
method.
Business Finance II
Module 9
Investment and
Financing Decisions
Student Activities
Reading
Study Book,Module 9
Selected Reading 9.1
Tutorial Activities
Tutorial Workbook,Self Assessment
Activity 9.1
Introduction
The cost of capital is used to discount after-
tax cash flows expected from a firm’s
investment decision,This,in turn,
determines whether the investment should be
accepted or rejected according to the value it
is expected to create.
Cost of capital is thought of as the rate of
return required by the market suppliers of
capital in order to attract their funds to the
firm.
Introduction
Does the financing mix affect the firm’s
overall cost of funds,either favourably or
unfavourably?
MM say NO - financing decisions are
irrelevant.
Firms should therefore concentrate on the
investment decisions.
Introduction
In reality,the cost of capital may decrease
with financial leverage,resulting in some
negative NPV projects becoming
acceptable (positive NPV).
This factor therefore needs to be
incorporated into our investment decision
analysis!
Introduction
Under MM assumptions,investment
decisions can be separated from the
financing decisions.
In reality,these decisions can’t be
separated!
The effects of financing decisions must be
included in the analysis.
Valuation Methods
WACC method – adjusts the discount rate.
Adjusted present value (APV) method –
adjusts the NPV for the impact of the
financing decision.
Flow-to-equity (FTE) method –
combination of the other 2 methods.
WACC
V
D
T - 1k
V
S
k k dsa
WACC
Reflects,on average,the firm’s cost of long-term
financing.
Recognises the mix of different financing
sources that fund the firm’s long-term assets.
Is the average of the rates of return that
providers of capital require,with each source’s
contribution being weighted according to the
proportion of capital it provided.
Is found by weighting the cost of each specific
type of capital by its proportion in the firm’s
capital structure.
WACC Assumptions
The risk of the project is identical to the
risk of the firm’s existing assets.
The project will be financed in the same
way (same D:E) as the firm as a whole.
WACC Method
The after-tax WACC will be less than the
firm’s opportunity cost of capital because
of the tax advantages of debt financing.
Discount the unlevered cash flows (UCFs)
at the after-tax WACC to get the NPV.
Example
Cash inflows = $1 200 000
Costs = 77.5% of sales
Initial cost = $960 000
Tax rate = 30%
Opportunity cost of capital = 21%
Cost of debt = 12%
Cost of equity = 23.7%
Debt-to-value ratio = 0.30
WACC Solution
Step 1 – Calculate unlevered cash flow (UCF)
Cash inflows $1 200 000
Cash costs (77.5%) 930 000
Operating income 270 000
Tax (30%) 81 000
UCF $ 189 000
WACC Solution
Step 2 – Calculate after-tax WACC
1 9,1 1 %o r 0,1 9 1 1
0,0 2 5 2 0,1 6 5 9
0,3 0 - 1 0,1 2
100
30
0,2 3 7
100
70
k
a
WACC Solution
0 1 1 $ 2 9
0 0 0 $ 9 6 0 -
0,1 9 1 1
0 0 0 $ 1 8 9
N PV
Step 3 – Calculate NPV
Accept – positive NPV
Cost of Equity
23,7%or 0,237
0,09 0,30 0,21
0,12 - 0,21 0,30 - 1
7
3
0,21
k - k T - 1
E
D
k k
doos
Adjusted Present Value (APV)
A firm should only undertake investments
that create value and thereby increase the
owners’ wealth.
This therefore requires that for any
investment proposal to be acceptable,the
NPV of the combined investment and
financing decisions must be positive.
APV Method
For any new investment whose risk is in
the same risk class as the firm’s average,
the firm’s after-tax overall cost of capital
(WACC) can be used to discount the
investment’s cash flows and determine its
acceptability.
Any new investment should also use the
same proportions of debt and equity as the
firm’s overall capital structure.
APV Method
It is implicit that whenever the WACC is used
to evaluate a project,the financing decision
side-effects are included and their risk is
assumed to replicate that of the firm as a
whole.
This means that the firm’s WACC is suitable
for evaluating the,average” project and that
WACC is an adjusted cost of capital which
captures the project’s financing side-effects.
APV Method
To evaluate projects that fall outside the
“average” risk class for a firm,the adjusted
present value (APV) approach should be
used so as to evaluate the effects of the
investment and financing decisions.
Appendix 9.1 provides a good overview of
the APV method.
APV Method
Initially calculate the base-case NPV
assuming the project will be all-equity
financed.
Then consider the side effects of
financing:
– tax subsidy on debt;
– cost of issuing new securities.
APV Method
e f f e c t s s i de f i n a n c i n g
of l u epr e s e n t v an e t t h e N P V F w h e r e
N P V F N P V A P V
APV Solution
Step 1 – Calculate base-case NPV assuming all-
equity financed
0 0 0 $ 6 0 -
0 0 0 $ 9 6 0 -
0,2 1
0 0 0 $ 1 8 9
N PV
APV Solution
Step 2 – Calculate PV of tax shield
400 $86
000 $960 0,3 0 0,3 0
T D
k
T D k
s h i e l dt a x PV
d
d
APV Solution
400 $26
400 $86 000 $60 - A PV
Accept – positive APV
PV of Tax Shield
The previous example assumed perpetual debt,
but this is obviously not always the case.
Many loans are for a fixed term.
Assume that as part of its funding arrangements
for a project,a company takes out a $500 000
loan over 4 years.
Assume 10% p.a,interest,a cost of capital of
12%,and a tax rate of 30%.
Must prepare a loan amortisation schedule to
identify the annual interest expense.
PV of Tax Shield
7 28,7 1 $ 15 7
3,1 7 0
0 00 $ 50 0
PM T
PV I FA PM T 0 00 $ 50 0
PV I FA PM T PV A
0,1 0,4
nk,
First,calculate the annual repayments
PV of Tax Shield
Yr Opening
Principal
Repayment Interest
Component
Principal
Component
Ending
Principal
1 500 000 157 729 50 000 107 729 392 271
2 392 271 157 729 39 227 118 502 273 769
3 273 769 157 729 27 377 130 352 143 417
4 143 417 157 729 14 342 143 387 30
PV of Tax Shield
354 $31
734 $2 846 $5 381 $9 393 $13
1.1 2
0.3 0 342 $14
1.1 2
0.3 0 377 $27
1.1 2
0.3 0 227 $39
1.1 2
0.3 0 000 $50
s h i e l dt a x PV
43
2
APV Method
The previous approach assumed that debt
was a fixed proportion of the initial
investment.
However,in reality,debt should be
expressed as a proportion of the present
value of the project.
APV Solution
011 $ 9 8 9 V
000 $ 9 0 0 0,9 1 V
0,0 9 V 000 $ 9 0 0 V
V 0,3 00,3 0
0,2 1
000 $ 1 8 9
V
D T p r o j e c t u n l e v e r e d of PV p r o j e c t l e v e r e d of PV
d e b tw i t h
d e b tw i t h
d e b tw i t h d e b tw i t h
d e b tw i t h d e b tw i t h
7 0 3 $ 2 9 6
0 1 1 $ 9 8 9 0,3 0 D e b t
APV Solution
011 $29
011 $ 9 8 9 0,3 0 0,3 0 000 $60 - A PV
Accept – positive APV
Another APV Example
Assume that the project is to be financed
by issuing shares.
Issue costs will be 4% of the gross
proceeds of the issue.
What is the project’s APV?
APV Solution
Calculate amount to be raised from the issue to
generate $960 000 required for the project.
0 0 0 0 0 0 $1
0,0 4 - 1
0 0 0 $ 9 6 0
p r o c e e d s G r o s s
The firm must raise $1 000 000 to have $960 000 to fund
the project,The remaining $40 000 represents issue
costs.
APV Solution
000 $100 -
000 $40 - 000 $60 -
N PV F N PV A PV
Reject – negative APV
Flow-to-Equity (FTE) Approach
Discounts the levered cash flows (LCFs)
at the cost of equity to give the PV of the
levered cash flows.
NPV is the difference between the PV of
the project’s levered cash flows and that
part of the investment financed out of
equity.
FTE Solution
Step 1 – Determine levered cash flow (LCF)
Cash inflows $1 200 000
Cash costs (77.5%) 930 000
Interest (12% × $296 703) 35 604
Income after interest 234 396
Tax (@ 30%) 70 319
Levered cash flow (LCF) $ 164 077
Level of Debt
Note that to calculate interest expense you
must know the level of debt.
In the APV approach we calculated debt to
be $296 703.
If the level of debt hasn’t been calculated,
we must do so.
Calculate UCF,Vwith debt and then the
amount of debt.
Levered Cash Flow (LCF)
077 $164
923 $24 - 000 $189
703 $296 0.1 2 0.3 0 - 1 - 000 $189
D k T - 1 - U C F L C F
d
FTE Solution
Step 2 – Calculate PV of LCF
30 8 $6 92
0,23 7
07 7 $1 64
k
L C F
PV
s
FTE Solution
Step 3 – Determine amount funded from equity
Initial investment $960 000
Less Amount borrowed 296 703
Funded from equity $663 297
FTE Solution
Step 4 – Calculate NPV
011 $29
297 $663 - 308 $692
f u n d i n gE q u i t y - L C F of PV N PV
Accept – positive NPV
Summary
WACC discounts UCFs at WACC,which
lowers the opportunity cost of capital.
APV discounts UCFs at opportunity cost of
capital and then adjusts for the side effects
of funding.
FTE uses LCFs (UCFs less interest
payments),The initial investment is the
firm’s contribution to the initial cost.
Which Method?
Use WACC or FTE if the project’s risk
(and therefore opportunity cost of capital)
and the debt-to-value ratio remain
constant.
Use APV when the project’s debt level is
known over the life of the project.
In practice,WACC is the most widely used
method.
