CHAPTER 18: CAPITAL BUDGETING WITH LEVERAGE
Topics
• 18.1 – 18.6
• 18.7
Valuation
Beta and Leverage
Core Question: How to determine the NPV of a project if it is
financed with debt?
1
Background
• In chapter 8, there was a four step procedure for evaluating corporate investment
decisions:
– Forecast cash flows
– assess project risk
– estimate opportunity cost of capital
– compute NPV
• This procedure treats each project like an independent firm that is all-equity
financed
• If financing decisions did not matter, this is all that is required. But if they do
matter, there are three basic approaches
– Adjusted present value (APV)
– Flow to equity (FTE)
– Weighted average cost of capital (WACC)
2
18.1 APV Approach
APV = NPVU + NPVF
• NPVU (NPV of unlevered firm)
– project value under all-equity financing
– PV of unlevered cash flows (UCF)
– discount rate: r0
• NPVF (net present value of financing side effects)
•
•
•
•
PV of tax shields to debt
costs of issuing new securities
costs of financial distress
subsidies to debt financing
3
APV Example
• A project costs $60,000 and generates expected pre-tax operating
cash flows of $10,000 per year in perpetuity. The corporate tax
rate is 40% and the cost of capital under all-equity financing is
12%. Should the firm make this investment under all-equity
financing? What is there is debt, and the debt-value ratio is 0.06?
4
18.2 FTE Approach
1. Estimate levered cash flows = cash flow to equityholders of
levered firm (LCF)
2. Calculate discount rate rS
3. Compute PV of LCF---Use 1 & 2
4. PV of the project: PV of LCF subtract equity contribution
(equity contribution = initial investment - amount borrowed)
–
–
it is possible for the equity contribution to be negative—this
means that the amount borrowed exceeds the initial cost of
the investment
in such cases, the excess can be thought of as a dividend paid
out to equity holders
5
FTE Example
• Consider the same example as for APV above, assuming that
the rate of interest on debt is rB = 6%
6
18.3 WACC
• Discount unlevered cash flows (UCF) at rWACC where
 S 
 B 
rWACC  
rS  
( 1  TC )rB
SB
SB
• Compute PV of UCF, subtract initial investment
– The unlevered cash flows (UCF) are the same as used in the
APV approach for calculating the present value of future cash
flows under all-equity financing
– This method was discussed previously in Chapter 13
7
WACC Example
• Continue with the same example from APV and FTE.
8
Comparison of Approaches
• In the simple example above in a perpetual no-growth
setting, all three approaches (APV, FTE, WACC) gave the
same answer
• In theory, this should always be the case, but in practice it is
usually far simpler to use one method than either of the
others
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WACC
• Consider the following example. A project costs $80,000
today and generates expected pre-tax operating cash flows of
$50,000 per year for four years. The corporate tax rate is
40%, the (levered) cost of equity (rS ) is 20%, the cost of
debt is 8%, and the equity-value ratio is 60%
• WACC approach:
rWACC = .60(.20) + .40(.08)(1 − .4) = .1392
NPV = −$80,000 + $50,000(1 − .4) × A.13924
= $7,554.92
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What about APV
• Since the debt-value ratio is 40% and the PV of the future
cash flows is $87,554.92, the amount to be borrowed is
.4($87,554.92) = $35,021.97
• The discount rate under all-equity financing can be
calculated as follows. Since the effects of debt are to be
incorporated later, use the weighted average cost of capital
but assume that there are no corporate taxes, i.e.
• the value of the project under all-equity financing would be
NPVU = −$80,000 + $50,000(1 − .4) × A.15204 = $5,304.00
• If the debt of $35,021.97 is assumed to be perpetual, then
NPVF = .4($35,021.97) = $14,008.79
APV = $5,304.00 + $14,008.79 = $19,312.79
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What about APV cont’d
• What if the debt is assumed to be repaid at the end of the
project (i.e. after four years)?
• The amount of interest paid per year is
.08($35,021.97) = $2,801.76
• then
NPVF = $2,801.76(.4) × A.084 = $3,711.91
APV = $5,304.00 + $3,711.91 = $9,015.91
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What About APV? (Cont’d)
• The basic problem here is that the assumptions underlying
WACC and APV (so far) are inconsistent
• In particular, WACC assumes that the debt-value ratio is
constant over time, whereas (so far) in APV the assumption
has been that debt is constant over time
– This was consistent in the perpetual case since value is
constant over time in that context
• In general, in order to maintain a constant debt-value ratio,
the amount of debt must change throughout the project life
– Define a project’s debt capacity d as the amount of debt
needed to maintain the firm’s target debt-value ratio over the
life of the project (note that d varies over time)
– Then calculate NPVF assuming that the firm borrows an
amount that is equal to its debt capacity d
13
What About FTE?
• We need to calculate levered cash flows, assuming the same
borrowing pattern as for APV, and then discount at rS = 20%:
• This gives
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Comparison
Initial Investment
Cash flows
Discount rates
PV of financing side effects
APV
FTE
WACC
All
Equity portion
All
UCF
LCF
UCF
r0
rs
rwacc
Yes
No
No
• General rule:
– Use APV when debt level is constant
– Use WACC and FTE when firm’s debt ratio is constant
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More on APV and Discount rate
• Note that the discount rate of r0 specified for APV above
applies to the unlevered cash flows, not the debt tax shield
• The appropriate discount rate for the debt tax shield under
APV depends on the debt policy of the firm:
– if debt level is constant (e.g. as in perpetuity case), use rB
– if debt level varies with project value (e.g. non-perpetual
case), use r0
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18.6 More APV examples: Issuing Costs
An investment project costs $3 million and generates pretax
operating cash flows of $825,000 per year for 10 years. The
corporate tax rate is 40% and r0 is 10%.
(1) What is the all-equity NPV? ($41,561)
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Example cont’d
Financing alternative #1: the firm has no cash and will
finance the project with $3 million of new equity, issue costs
are 7% of the gross proceeds and are tax deductible. What
is APV
Answer: ($-93,923)
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Example cont’d
Financing alternative #2: the firm has $1.5 million in cash on
hand and can borrow the remaining $1.5 million for 6 years
at 8% interest (annual coupon payment). The bond will be
issued at par. (Assume no issuing costs of debt.) (Answer:
263,460)
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Example cont’d (A more complicated version of last slide)
Financing alternative #2: the firm has $1.5 million in cash on hand
and can obtain the remaining $1.5 million through a 6 years, 8%
coupon (annual coupon payment) bond issued at par. The issuing
costs for the bond is 1% of the amount raised. (Assume that
issuing costs for debt are tax-deductible but amortized over the
life of the bond.)
APV = NPV + NPV(Floatation costs) + NPV(Loan)
Amount raised:
Discount rate:
1. NPV(Floatation costs)
floatation costs =
Amortized over 6 years, annual tax deduction is
Annual tax shield =
NPV(Floatation costs) or Net floatation costs
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Cont’d
2. NPV (Loan) = Amount borrowed – PV (after-tax interest
payments) – PV (principal repayment)
= PV(interest tax shield)
or PV(interest tax shields)
3. APV = 41,561 -10,482 + 224,141 =255,220
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Example cont’d
Financing alternative #3: Subsidized financing
The firm has $1.5 million in cash on hand and can borrow the
remaining $1.5 million for 6 years from the government at a
special interest rate of 5% with no floatation costs (gov’t
takes care of it.) Note that if the firm does not use gov’t loan,
it has to borrow from the open market at 8%.
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18.7 Beta and Leverage
• To use APV, you have to know r0, the cost of unlevered equity.
• If the firm already has debt, you cannot simply use historical stock
return data to compute beta, even if the project’s risk is identical to that
of the existing firm. The following formula can be derived:
• Risky Corporate Debt:


 S  1 
( 1  TC )B 
B


(
1

T
)
B
C
 U
S
S

where  S is the beta computed using historical returns and U is the
corresponding beta for an identical (but unlevered) firm
• Risk-free Corporate Debt:
Usually assume  B  0   S  1  (1  TC ) B  U



S

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Example
• A firm has a debt-equity ratio of 0.5. Based on historical
stock return data, the firm’s equity is 1.25. The firm faces a
corporate tax rate of 40%. The risk free rate of interest is 5%
and the expected market risk premium is 6%. Determine r0
assuming the the firm’s debt has (i) zero systematic risk, and
(ii) βB of 0.10.
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• Assigned Problems: # 18.1, 4, 7, 8, 9(change the company
name to NEC), 12, 14, 16, 17
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