Assignment4 Solution - Assignment 4 Solutions Problem 1(a...

Assignment 4 Solutions.
Problem 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(CCA Tax Shield)
Let P equal the purchase price of the fleet.
NPV = -P + (1-0.40)($300,000)A
5
0.10
+ PVCCATS
10 . 5 0 ( )
[] [ ]
1
0.40 0.25 1 0.50(0.10)
[ ][ ] 0.2727
0.25 0.10 1 0.10
InvestmentxTaxRatexCCA DiscountRate
PVCCATS
CCA DiscountRate DiscountRate
Px x
P
+
=
++
+
==
Set the NPV equal to zero.
0 = -P + (1-0.40)($300,000)A
5
0.10
+ 0.2727P
0.7273P= $682,341.62
P= $938,184.55
Therefore, the most that Hertz should be willing to pay for
the fleet of cars with all-equity funding is $938,184.55.
(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(CCATS)
Hertz paid $975,000 for the fleet of cars.
10 . 5 0 ( )
[] [ ]
1
975,000 0.40 0.25 1 0.50(0.10)
[ ][ ] $265,909.09
0.25 0.10 1 0.10
InvestmentxTaxRatexCCA DiscountRate
PVCCATS
CCA DiscountRate DiscountRate
xx
+
=
++
+
==
NPV = -$975,000 + (1- 0.4)($300,000)A
5
0.10
+ 265,909.09
= -975,000 + 682,341.62+265,909.09
= -$26,749.29
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) = $600,000 – (1 –
0.40)(0.08)($600,000)A
5
0.08
– [$600,000/(1.08)
5
]
= $600,000 – 114,990.05 – 408,349.92
= 76,660.03
A P V
APV = NPV(All-Equity) + NPV(Financing Side Effects)
= -$26,749.29+ $76,660.03
= $ 49,910.74

Therefore, if Hertz uses $600,000 of five-year, 8% debt to
fund the $975,000 purchase, the Adjusted Present Value
(APV) of the project is $ 49,910.74.
(c ). To determine the maximum price, set the
APV=0 = NPV (All equity) + NPV(Loan)
0 = -P + (1-0.40)($300,000)A
5
0.10
+ 0.2727P + $600,000 –
(1 – 0.40)(0.05)($600,000)A
5
0.08
– [$600,000/(1.08)
5
]
0 = -0.7273P +682,341.62 + 600,000 – 71,868.78 – 408,350
0.7273P = 802,122.84
P = 1,102,877.55
Problem 2:
The adjusted present value of a project equals the net present value
of the project under all-equity financing plus the net present value of
any financing side effects. In the joint venture’s case, the NPV of
financing side effects equals the after-tax present value of cash
flows resulting from the firms’ debt.
APV = NPV(All-Equity) + NPV(Financing Side Effects)
NPV(All-Equity)
NPV = -Initial Investment + PV[(1 – T
C
)(Earnings Before
Interest, Taxes, and Depreciation )] + PV(CCA Tax Shield)
Assuming that the company has other assets in the class,
1 0.50( )
[] [ ]
1
20,000,000 0.25 0.30 1 0.50(0.12)
[ ][ ] $3,380,102
0.30 0.12 1 0.12
InvestmentxTaxRatexCCA DiscountRate
PVCCATS
CCA DiscountRate DiscountRate
xx
+
=
++
+
==
NPV = -$20,000,000 + [(1-0.25)($3,000,000)A
20
0.12
] + 3,380,102
= -$20,000,000 + $16,806,248 + 3,380,102

= $186,350
NPV(Financing Side Effects)
The NPV of financing side effects equals the after-tax present
value of cash flows resulting from the firms’ debt.