Chapter 17: Valuation and Capital Budgeting for the Levered Firm
17.1
a.
The maximum price that Hertz should be willing to pay for the fleet of cars with all-equity funding
is the price that makes the NPV of the transaction equal to zero.
NPV = -Purchase Price + PV[(1- T
C
)(Earnings Before Taxes and Depreciation)] +
PV(Depreciation Tax Shield)
Let P equal the purchase price of the fleet.
NPV =
-P + (1-0.34)($100,000)A
5
0.10
+ (0.34)(P/5)A
5
0.10
Set the NPV equal to zero.
0 =
-P + (1-0.34)($100,000)A
5
0.10
+ (0.34)(P/5)A
5
0.10
P = $250,191.93 + (P)(0.34/5)A
5
0.10
P = $250,191.93 + 0.2578P
0.7422P = $250,191.93
P = $337,095
Therefore, the most that Hertz should be willing to pay for the fleet of cars with all-equity
funding is $337,095.
b.
The adjusted present value (APV) of a project equals the net present value of the project if it were
funded completely by equity plus the net present value of any financing side effects.
In Hertz’s
case, the NPV of financing side effects equals the after-tax present value of the cash flows
resulting from the firm’s debt.
APV = NPV(All-Equity) + NPV(Financing Side Effects)
NPV(All-Equity)
NPV =
-Purchase Price + PV[(1- T
C
)(Earnings Before Taxes and Depreciation)] +
PV(Depreciation Tax Shield)
Hertz paid $325,000 for the fleet of cars.
Because this fleet will be fully depreciated over five
years using the straight-line method, annual depreciation expense equals $65,000 (= $325,000/5).
NPV
=
-$325,000 + (1-0.34)($100,000)A
5
0.10
+ (0.34)($65,000)A
5
0.10
=
$8,968
NPV(Financing Side Effects)
The net present value of financing side effects equals the after-tax present value of cash flows
resulting from the firm’s debt.
NPV(Financing Side Effects)
= Proceeds – After-Tax PV(Interest Payments) – PV(Principal
Payments)
Given a known level of debt, debt cash flows should be discounted at the pre-tax cost of debt (r
B
),
8%.
NPV(Financing Side Effects)
= $200,000 – (1 – 0.34)(0.08)($200,000)A
5
0.08
– [$200,000/(1.08)
5
]
= $21,720
B-60