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:
SlumpNormal Boom
$8 million $12 million $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:
SlumpNormalBoom
$8$12$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.Calculate the project's NPV. Is the project a good investment? Explain why
a.Expected cash flow = ($8 million + $12 million + $16 million)/3 = $12 million
- 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 Initial Cash Flow, CoCash Flow in Year 1, C1
1-10,000+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 ?
(1) / /
(2) / /
(3) / /
(4) / /
- Investment 1, because it has the highest NPV.
- 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).
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
- PV(salary) x 0.05 = $38,018.96
Future value = $38,018.96 x (1.08)30 = $382,571.75