Question

(1)Your firm has identified three potential investment projects. The projects and their cash flows
are shown here
(Project Cash Flow Today ($) Cash Flow in One Year ($))
A -10- 20
B 5 -5
C 20 -10
Suppose all cash flows are certain and the risk-free interest rate is 10%.
a. What is the NPV of each project?
b. If the firm can choose only one of these projects, which should it choose?
c. If the firm can choose any two of these projects, which should it choose?

2)You run a construction firm. You have just won a contract to construct a government office
building. It will take one year to construct it, requiring an investment of $10 million today and
$5 million in one year. The government will pay you $20 million upon the building’s comple-
tion. Suppose the cash flows and their times of payment are certain, and the risk-free interest
rate is 10%.
a. What is the NPV of this opportunity?
b. How can your firm turn this NPV into cash today?
3)Your daughter is currently eight years old. You anticipate that she will be going to college in 10
years. You would like to have $100,000 in a savings account to fund her education at that time.
If the account promises to pay a fixed interest rate of 3% per year, how much money do you
need to put into the account today to ensure that you will have $100,000 in 10 years?
4)Your grandfather put some money in an account for you on the day you were born. You are now
18 years old and are allowed to withdraw the money for the first time. The account currently
has $3996 in it and pays an 8% interest rate.
a. How much money would be in the account if you left the money there until your 25th birthday?
b. What if you left the money until your 65th birthday?
c. How much money did your grandfather originally put in the account?
5)Suppose you receive $100 at the end of each year for the next three years.
a. If the interest rate is 8%, what is the present value of these cash flows?
b. What is the future value in three years of the present value you computed in (a)?
c. Suppose you deposit the cash flows in a bank account that pays 8% interest per year. What
is the balance in the account at the end of each of the next three years (after your deposit is
made)? How does the final bank balance compare with your answer in (b)?
6)The British government has a consol bond outstanding paying £100 per year forever. Assume
the current interest rate is 4% per year.
a. What is the value of the bond immediately after a payment is made?
b. What is the value of the bond immediately before a payment is made?
7)You are 25 years old and decide to start saving for your retirement. You plan to save $5000 at
the end of each year (so the first deposit will be one year from now), and will make the last
deposit when you retire at age 65. Suppose you earn 8% per year on your retirement savings.
a. How much will you have saved for retirement?
b. How much will you have saved if you wait until age 35 to start saving (again, with your first
deposit at the end of the year)?
8)You are thinking of building a new machine that will save you $1000 in the first year. The
machine will then begin to wear out so that the savings decline at a rate of 2% per year forever.
What is the present value of the savings if the interest rate is 5% per year?
9)You are running a hot Internet company. Analysts predict that its earnings will grow at 30% per
year for the next five years. After that, as competition increases, earnings growth is expected to
slow to 2% per year and continue at that level forever. Your company has just announced earn-
ings of $1,000,000. What is the present value of all future earnings if the interest rate is 8%?
(Assume all cash flows occur at the end of the year.)

Answer 1

1.

Project	Cash Flow Today ($) (T=0)	Cash Flow in One Year ($)(T=1)
A	-10	-20
B	5	-5
C	20	-10

Risk Free Interest rate = 10%

a. NPV

Project A

NPV = -10-20(P/F,10%,1)

NPV = -10 - 20*0.9091 = -10-18.182 = -$28.182

Project B

NPV = 5 - 5(P/F,10%,1)

NPV = 5 - 5*0.9091 = 5-4.5455 = $0.4545

Project C

NPV = 20 -10(P/F,10%,1)

NPV = 20 -10*0.9091 = 20-9.091 = $10.909

b. NPV(C) >NPV(B)>NPV(A)

In order to choose only one project then Project C should be chosen as its NPV is positive and highest

c. In order to choose two projects then Project C and B should be chosen as there NPV is positive.