EBIT (1-t)
$30.00
$41.20
$53.05
$65.56
$67.53
+ Deprecn
$20.00
$20.00
$20.00
$20.00
- Cap Ex
$15.00
$15.00
$15.00
$15.00
$20.26
FCFF
$35.00
$46.20
$58.05
$70.56
$47.27
PV (@12%)
$41.25
$46.27
$50.23
b. Terminal value = 47.27/(.10-.03) =
$675.31
PV of terminal value =
$480.67
! Discount back at 12%
c. Value today =
$618.42
+ Cash
$25.00
- Debt =
$150.00
Value of equity =
$493.42
Value per share =
$49.34
Problem 2
After-tax operating margin for Springbok =
0.15
Expected EV/Sales = 0.25 + 0.10 (15) =
1.75
Value of Springbok =
175
b. Expected growth in revenues, since this is a firm value regression
c.
Value attached by the private equity investor to 33.33% equity =
40
Value attached to all of the equity =
120
Value attached to the firm =
150
d.
Value of the firm in the 3 years =
211.75
Value of the outstanding debt =
50
Value of equity =
161.75
Annual return = (182.925/120)^(1/3)-1 =
10.46%
Problem 3
Value of the firm today =
100
! Gave full credit even if you
Value of firm = 15*(1-.03/ROC)*1.03/(.09-.03)
! Computed return on capital
Solving for the ROC
Return on capital =
4.85%
b. Value of firm at optimal debt ratio with return on capital = cost of capital
Reinvestment rate =
0.375
! Interesting variations possib
Value of firm =
193.125
I did give full credit if you sub
- Debt =
25
The two inputs are incompat
Value of equity =
168.125
Value per share =
$11.21
c. Value per non-voting share =
$5.00
Value per voting share =
$8.73
! 5 + (168.125-75)/5…. I am
Problem 4
a. EV/BV ratio for Ludmilla = (.12-.04)/(.08-.04) =
2
Book value of Ludmilla =
500
PV of depreciation tax benefits on existing book value =
134.201628
New book value for Ludmilla =
1250

PV of depreciation tax benefits on new book value =
335.5040699
Value of synergy =
201.302442
b. If Lybov pays $1,250 million for Ludmilla, it has overpaid by about $49 million
Its value will decrease by $49 million
New value of Lybov =
1451.302442
! Add synergy and subtract premium
- Debt
250
! Subtract out debt
Value of equity =
$12.01
Problem 5
a. PV of cashflows over next 20 years =
926.8677818
NPV of project =
-273.132218
b.
S =
926.8677818
K =
1200
t =
10
r =
4%
Std devn =
31.43%
Cost of delay
0.043156101
! The loss of exclusivity seems to cost $40 million in after-tax cashflows
Value of the rights to this project =
$177 million

! Common errors
1. The margin changes each year, not the operating income (-0.5 to -1)
2. The net cap ex is a cash inflow, not an outflow (-0.5 to -1)
1. Used year 3 cashflow instead of computing new reinvestment rate (-1)
2. Used wrong cost of capital (12% instead of 10%) (-1)
! Discount terminal value back at 12%, not 10% (-0.5 to -1)
2. Add back cash, not subtract (-0.5)
3. Subtract out debt (-0.5)
! Mechanical errors (-0.5)
! -1 for any other answer
! 1. Added debt to 1/3 value (-0.5)
2. Mechanical errors (-0.5)
! Year 1 is 100 million… I did give full credit if you pushed it out and extra year. The return would hav
! Forgot to subtract out debt (-1)
Did not compute annual return (-0.5 to -1)
forgot the (1.03)
l using market value of firm (-1.5 to -2)
ble
btracted out new debt of 40%… and used 15 million shares.
tible since moving to a 40% debt ratio will reduce the number of shares outstanding.
assuming that voting stockholders get the entire value of control in this case…
! If you use (1+g) in the equation, your book value is slightly smaller (483 million)
Common errors

1. Depreciated market value of old firm rather than book value (-2)
2. Computed tax savings using (1-t) instead of t (-1)
3. Mistakes in present value calcualtion (-1/2 to -1)
! The change in stock price should reflect the difference between what was paid and what you get as
The stock price prior to the change was $12.50…. The new stock price you compute should reflect th
! Used only first 10 years of cashflows (why?)
Used 20 years instead of 10 years
each year

ve been 15.1%.

s synergy benefits
he fact that they overpaid….

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- Spring '11
- RichardM.Levine
- Cost Of Capital, Valuation, Mathematical finance, Return on capital