Practice Questions
A. Sandra is in the drapery business. She is contemplating the purchase of an automatic
drape-making machine. The machine costs $100,000, and Sandra estimates that it would
save labor costs each year. That will count as a cash inflow. She also assumed the
machine would last 5 years. Because of the risk involved, Sandra’s cost of capital is at 20
percent per year. She will need a payback in three years to justify a purchase.
Year
1
2
3
4
5
Inflow
20,000
35,000
40,000
40,000
40,000
1. Compute the payback period for the machine.
2. Compute the Net Present Value of the machine.
3. Should she buy the machine?
B. Mr. Blochirt is creating a college investment fund for his daughter. He will put in $850
per year for the next 15 years and expects to earn 8% annual rate of return. How much
money will his daughter have when she starts college?
C. How much will you pay for a $20,000 automobile in 10 years if the inflation rate is
20%?
D. A balloon payment of $21,000 on your house is due in 10 years. If you can average
5% interest per year, how much will you have to place into an account today to have the
$21,000 in ten years?
E. Home Security Systems is analyzing the purchase of manufacturing equipment that
will cost $40,000. The annual cash inflows for the next three years will be $18,100. If the
company’s cost of capital is 10%, should they purchase the machine? (Use IRR)
F. X-treme Vitamin Company is considering two investments, both of which cost $10,000. The
cash flows are as follows:
Year
Project
Project
A
B
1
$12,000
10,000
2
8,000
6,000
3
6,000
16,000
a. Which of the two projects should be chosen based on the payback method?
b. Which of the two projects should be chosen based on the net present value method? Assume
a cost of capital of 10 percent.
c. Should a firm normally have more confidence in answer a or answer b?
Answers
A.1.
Investment = 100,000
Inflow in year 1 = 20,000
2 = 35,000
3 = 40,000
4 = 40,000
2.
Year
1
2
3
4
5
In the 4th year, you’ll reach the payback. 20,000 +
35,000 + 40,000 = 95,000, so it’s shortly into year
4 that you’ll reach the 1000,000
Inflow
20,000
35,000
40,000
40,000
40,000
PVIF
0.833
0.694
0.579
0.482
0.402
PV
16,660
24,290
23,160
19,280
16,080
Total Inflows
Outflow
99,470
100,000
Net Present Value = (
530)
3. Do not invest in the machine. The NPV is negative and it will take more than 3 years
to pay back.
B. You are looking for the future value of a series of payments, so this is future
value of an annuity.
Annuity payment = 850
Time = 15 years
Interest = 8% annually
FVA = A x FV IFA
= 850 x 27.152
= $23079.20
C. You’re looking for the value of an amount in the future, so you need to use
Future Value.
PV = 20,000
Interest rate = 20%
Time = 10 years
FV = A x FVif
= 20,000 X 6.192
FV = $123,840
D. You want to know the value today for an amount of money in the future. That is
present value.
FV = 21,000
Interest Rate = 5%
Time = 10 years
PV = A x PVif
= 21000 x .614
= $12,894
E. You are trying to figure out the internal rate of return.
Investment = 40,000
Annuity = 18,000
Time = 3 years
IRR = Investment / Annuity
= 40,000 / 18,100
= 2.210
PVIF of 2.210 for 3 years is 17%
The return is larger than the cost of capital by a substantial amount, so purchase the
machine.
F.
Solution:
X-treme Vitamin Company
a.
Payback Method
Payback for Project A
10,000
 .83 years
12,000
Payback for Project B
10,000
 1 year
10,000
Under the Payback Method, you should select Project A because of the shorter
payback period.
b.
Net Present Value Method
Year
1
2
3
Cash Flow
$12,000
$ 8,000
$ 6,000
Project A
PVIF at 10%
.909
.826
.751
Present Value of Inflows
Present Value of Outflows
Net Present Value
Year
1
2
3
Cash Flow
$10,000
$ 6,000
$16,000
Project B
PVIF at 10%
.909
.826
.751
Present Value of Inflows
Present Value of Outflows
Net Present Value
Present Value
$10,908
$ 6,608
$ 4,506
$22,022
10,000
$12,022
Present Value
$ 9,090
$ 4,956
$12,016
$26,062
10,000
$16,062
Under the net present value method, you should select Project B because of the higher net
present value.
c.
A company should normally have more confidence in answer b because the net present
value considers all inflows as well as the time value of money. The heavy late inflow for
Project B was partially ignored under the payback method.