Quantitative questions
Chapter 2, question 13:
If a firm with a $5 billion fund charges a 2 percent management fee for eight years,
and 20 percent carried interest on all profits, and earns a 3 return on its
investments, what is the true multiple of investment and IRR for the LP?
Firm invests $5 billion and sells for $15 billion (3 times return on its investment)
Management fee expense=2%*$5 billion=$0.1 billion
Carried interest expense=20%*$10 billion=$2 billion
Investment multiple=(final cost of investment-expenses)/initial investment=($15 billion-$0.1 billion-$2
billion)/$5 billion=$12.9/$5=2.58
At the same time, Investment multiple=(1+IRR)^8
IRR=12.58%
Chapter 4, question 6:
Calculate the WACC using the following assumptions:
D
= $200 million
rd = 4%
rf
= 3%
E
= $400 million
τ
= 30%
β = 1.9
(rm -
rf ) = 7.5%
Cost of equity=rf+ β(rm-rf)=3%+1.9*7.5%=17.25%
WACC=(D/D+E)*rd*(1- τ )+(E/D+E)*re=0.33*4%*0.7+0.67*17.25%=12.43%
Chapter 4, question 7:
Recalculate the NPV of Hi-Tech using the data in Table 4.6; but assume that the company is currently not
at its target capital structure, which is 30 percent debt and 70 percent equity. Also assume the firm’s cost
of debt is 8 percent.

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Step 1: Value Cash Flows
Year
0
1
2
3
4
5
6
7
8
9
Revenues
100
140
210
250
290
380
500
650
900
Less: Costs
230
240
260
275
290
310
350
400
470
EBIT
-130
-100
-50
-25
0
70
150
250
430
Less: Tax
0
0
0
0
0
0
0
26
172
EBIAT
-130
-100
-50
-25
0
70
150
224
258
Less: Ch. NWC
10
4
7
4
4
9
12
15
25
Net Cash Flow
-140
-104
-57
-29
-4
61
138
209
233
Discount Factor
0.87
2
0.76
1
0.66
4
0.57
9
0.50
5
0.44
1
0.38
4
0.33
5
0.29
2
Present Value (Cash Flow)
-122
-79
-38
-17
-2
27
53
70
68
Present Value (Cash Flows)
-40
Terminal Value
2,06
2
Present Value (Terminal Value)
602
Present Value (Cash Flows)
-40
Present Value (Terminal Value)
602
Net Present Value
$562
β
u
= β
t
× (E/V) = β
t
× [E/(E + D)]
β
u
= 1.2
β
t
= β
u
× (V/E)
β
t
= 1.2 (100/70) = 1.714
r
e
=
r
f
+ β
t
(r
m
− r
f
)
r
e
=
18.86% = 6% + 1.714 (7.5%)
WACC =D/V.r
d
(1−
τ) + E/V.r
e
14.64 = 30/100 × 8% × (1 − 40%) + 70/100 × 18.86%
Chapter 4, question 10:
Calculate the APV for Hi-Tech using the assumptions in Table 4.6 and assuming the firm takes on $100
million debt at the time of the sale. At the end of each subsequent year to the sale, $25 million of this
debt is retired.

Step 1: Value Cash Flows
Year
0
1
2
3
4
5
6
7
8
9
Revenues
100
140
210
250
290
380
500
650
900
Less: Costs
230
240
260
275
290
310
350
400
470
EBIT
-130
-100
-50
-25
0
70
150
250
430
Less: Tax
0
0
0
0
0
28
60
100
172
EBIAT
-130
-100
-50
-25
0
42
90
150
258
Less: Ch. NWC
10
4
7
4
4
9
12
15
25
Net Cash Flow
-140
-104
-57
-29
-4
33
78
135
233
Discount Factor
0.870
0.756
0.658
0.572
0.497
0.432
0.376
0.327
0.28
4
Present Value (Cash
Flow)
-122
-79
-38
-17
-2
14
29
44
66
Present Value (Cash
Flows)
-105
Terminal Value
2,000
Present Value (Terminal

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- Fall '13
- YEST