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1. For an outlay of $8 million you can purchase a tanker load of bucolic acid delivered
in Rotterdam one year hence. Unfortunately the net cash flow from selling the tanker load
will be very sensitive to growth rate of the world economy:
Slump
$8 million
Normal
$12 million
Boom
$16 million
a. What is the expected cash flow? Assume the three outcomes for the economy are
equally likey.
b. What is the expected rate of return on the investment in the project?
c. One share of stock Z is selling for $10. The stock has the following payoffs after one
year:
Slump
$8
Normal
$12
Boom
$16
Calculate the expected rate of return offered by stock Z. Explain why this is the
opportunity cost of capital for your bucolic acid project.
d.
a.
Calculate the project's NPV. Is the project a good investment? Explain why
Expected cash flow = ($8 million + $12 million + $16 million)/3 = $12 million
b. Expected rate of return = ($12 million/$8 million) – 1 = 0.50 = 50%
c. Expected cash flow = ($8 + $12 + $16)/3 = $12
Expected rate of return = ($12/$10) – 1 = 0.20 = 20%
The net cash flow from selling the tanker load is the same as the
payoff from one million shares of Stock Z in each state of the world
economy. Therefore, the risk of each of these cash flows is the same.
d. NPV = $8,000,000 + ($12,000,000/1.20) = +$2,000,000
The project is a good investment because the NPV is positive.
Investors would be prepared to pay as much as $10,000,000 for the
project, which costs $8,000,000.
2. Calculate the NPV and rate of return of each of the following investment . The
opportunity cost of capital is 20 percent for all four investments.
Investment
1
Initial Cash Flow, Co
-10,000
Cash Flow in Year 1, C1
+18,000
2
- 5,000
+ 9,000
3
-5,000
+ 5,700
4
-2,000
+ 4,000
a. Which investment is most valuable?
b. Suppose each investment would require use of the same parcel of land. Therefore you
can take only one. Which one ?
Investment
NPV
18,000
 $5,000
1.20
Return
18,000  10,000
 0.80  80.0%
10,000
(1)
 10,000 
(2)
 5,000 
9,000
 $2,500
1.20
9,000  5,000
 0.80  80.0%
5,000
(3)
 5,000 
5,700
 $250
1.20
5,700  5,000
 0.14  14.0%
5,000
(4)
 2,000 
4,000
 $1,333.33
1.20
4,000  2,000
 1.00  100.0%
2,000
a.
Investment 1, because it has the highest NPV.
b.
Investment 1, because it maximizes shareholders’ wealth.
3. What is the VP of $100 received in:
a. Year 10 (at a discounted rate of 1 percent).
b. Year 10 (at a discounted rate of 13 percent).
c. Year 15 (at a discounted rate of 25 percent).
d. Each of the years 1 through 3 (at a discount rate of 12 percent).
a.
PV = $100/1.0110 = $90.53
b.
PV = $100/1.1310 = $29.46
c.
PV = $100/1.2515 = $ 3.52
d.
PV = $100/1.12 + $100/1.122 + $100/1.123 = $240.18
4. Mike Polanski is 30 years of age and his salary next year will be $40,000. Mike
forecasts that his salary will increase at a steady rate of 5 percent per annum until his
retirement at age 60.
a. If he discount rate is 8 percent, what is the PV of these future salary payments?
b. If Mike saves 5 percent of his salary each year and invests these savings at an interest
rate of 8 percent, how much will he have saved by age 60?
c. If Mike plan to spend these savings in the even amount over the subsequent 20 years
how much can he spend each year?
a.
Let St = salary in year t
30
PV  
t 1
30

t 1
St

(1.08) t
30

t 1
(40,000/1. 05)

(1.08 / 1.05) t
40,000 (1.05) t 1
(1.08) t
30

t 1
38,095.24
(1.0286) t
 1

1
 38,095.24  

 $760,379.2 1
30 
 0.0286 0.0286  (1.0286) 
b.
PV(salary) x 0.05 = $38,018.96
Future value = $38,018.96 x (1.08)30 = $382,571.75
c.
1

1
PV  C   
t 
 r r  (1  r) 
 1

1
$382,571.7 5  C  

20 
 0.08 0.08  (1.08) 
C  $382,571.7 5
 1

1

  $38,965.78

 0.08 0.08  (1.08) 20 