Solutions to Quiz 3: Spring 1998
1. The inputs are as follows:
S = 25 (1-.6)(1.05)/ (.10 - .05) =
315
; (300 if $25 mil is assumed to be EBIT next year)
K = 500
r = 7%
t = 3 years (Equally Weighted average of 2 and 4 year durations)
s
2
= 0.5
2
(.25)
2
+
0.5
2
(.40)
2
+ 2 (.5) (.5) (.5) (.25) (.4) = 0.0806
2
. Company B’s reserves will be more valuable.
To value the oil reserves as an option
Input
Company A
Company B
S
1000 * (24-6)/(1+y)
2
1000 * (24-4)/(1+y)
2
K
1000* 10
1000* 12
t
15
15
If we assume that y = 1/15 = 0.06667 and r = 7%, the value of oil reserves as options can be graphed as follows:

Value of Oil Reserves as an Option
0
1000
2000
3000
4000
5000
6000
7000
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
70.00%
80.00%
90.00%
100.00%
Standard Deviation in Oil Prices
Company A
Company B
In other words, the present value effect on the value of S is dominated by the option effect (which is captured in the variance. That is why
the difference gets narrower as the standard deviation in oil prices decreases; the actual standard deviation in oil prices is about 30%)
The next graph shows the value of the options as a function of the dividend yield.

Value of Oil Reserves as Option
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
0%
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
Dividend Yield = Annual CF/Value of Reserves
Company A
Company B
Again, the value of company B’s reserves are greater than company A’s reserves but the difference narrows as the yield increases.
[Since there is sufficient ambiguity in the problem and there is an outside chance that company A’s reserves could be worth more, I gave 2
points for those who picked (a) or (d).
2B. The value of oil is higher (increasing S) and the variance is lower. The net effect can be positive or negative.
3a. The variance is lower but the value of the project will go up. The net effect will almost certainly be positive, but I gave credit to those
who said it was uncertain.

3b. The value of the option will increase.
3c. The variance may increase but the value effect will be negative. The net effect again will almost certainly be negative, but I gave full
credit for those who picked uncertain.
3d. The interest rate increase will have a positive effect but it will lower the present value of the project, thus lowering value. The net effect
is likely to be negative, but I gave full credit for
uncertain.

Solution to Quiz 3: Fall 1998
Problem 1
Adjusted pre-tax operating income = $ 10 million - $ 1.5 million =
$
8.50
Adjusted after-tax operating income = $ 8.5 million (1-.40) =
$
5.10 (I also gave
Firm Value = 5.1(1.05)/(.09-.05) =
$
133.88
full credit
Illiquidity Discount = .30 - .04 (ln(100) =
11.58%
if you did not
Firm Value after Illiquidity Discount = 133.88 (1-.1158) =
$
118.37 use (1+g))
Problem 2
a. Net present value of the project = $ 30 - $ 40 = - $ 10 million
b. Inputs
S = Present Value of Net Revenues =
$ 30 million
K = Cost of televising the Olympics =
$ 40 million
t = Time until Olympics =
2 years
r = Riskless rate =
5%
Variance in value =
0.09
y = Cost of delay =
0
d1=
-0.2302
N(d1) =
0.409
d2 =
-0.6545
N(d2) =
0.2564
Value of the Rights = 30 (0.409) - 40 exp (-0.05)(2) (.2564) =
2.99
($2.71 mil
c. Range of Probability that rights are profitable = 0.2564 - 0.4090
wit approx
N(d))

Solution to Spring 1999 Quiz
Problem 1
VS = AT Operating Margin * (1- Reinvestment Rate) * (1 + g)/(WACC - g)
Reinvestment Rate = g / ROC = g / (AT Operating Margin * Sales/Capital)
Let the margin for Generic Office be x,
VS for Generic Office = 1.5 = x (1-.05/2x)(1.05)/(.10-.05)
Solve for x,
x = (1.5*.05+(.05/2)*1.05)/1.05

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- Finance, Variance, Cost Of Capital, Net Present Value, Mathematical finance, Sales/ Capital