# Calculating NPV, IRR, Profitability Index and Payback Period

1. Calculate the net present value and profitability index of a project with a net

investment of $20,000 and expected net cash flows of $3,000 a year for 10 years

if the project's required return is 12 percent. Is the project acceptable?

2. A firm wishes to bid on a contract that is expected to yield the following aftertax

net cash flows at the end of each year:

Year Net Cash Flow

1 $5,000

2 8,000

3 9,000

4 8,000

5 8,000

6 5,000

7 3,000

8 $-1,500

To secure the contract, the firm must spend $30,000 to retool its plant. This

retooling will have no salvage value at the end of the 8 years. Comparable investment

alternatives are available to the firm that earn 12 percent compounded

annually. The depreciation tax benefit from the retooling is reflected

in the net cash flows in the table.

a. Compute the project's net present value.

b. Should the project be adopted?

c. What is the meaning of the computed net present value figure?

6. Two mutually exclusive investment projects have the following forecasted cash

flows:

Year A B

0 $-20,000 $-20,000

1 10,000 0

2 10,000 0

3 10,000 0

4 10,000 60,000

a. Compute the internal rate of return for each project.

b. Compute the net present value for each project if the firm has a 10 percent

cost of capital.

c. Which project should be adopted? Why?

3. A junior executive is fed up with his boss's operating policies. Before leaving

the office of his angered superior, the young man suggests that a well-trained

monkey could handle the trivia assigned to him. Pausing a moment to consider

the import of this closing statement, the boss is seized by the thought

that this must have been in the back of her own mind ever since she hired the

junior executive. She decides to consider replacing the executive with a bright

young baboon. She figures that she could argue strongly to the board that

such "capital deepening" is necessary for the cost-conscious firm. Two days

later, a feasibility study is completed, and the following data are presented to

the president:

? It would cost $12,000 to purchase and train a reasonably alert baboon with

a life expectancy of 20 years.

? Annual expenses of feeding and housing the baboon would be $4,000.

? The junior executive's annual salary is $7,000 (a potential saving if the

baboon is hired).

? The baboon will be depreciated on a straight-line basis over 20 years to a

zero balance.

? The firm's marginal tax rate is 40 percent.

? The firm's current cost of capital is estimated to be 11 percent.

On the basis of the net present value criterion, should the monkey be hired

(and the junior executive fired)?

4. Note the following information on the annual cash flows of two mutually

exclusive projects under consideration by Wang Food Markets, Inc.

Year A B

0 $-30,000 $-60,000

1 10,000 20,000

2 10,000 20,000

3 10,000 20,000

4 10,000 20,000

5 10,000 20,000

Wang requires a 14 percent rate of return on projects of this nature.

a. Compute the NPV of both projects.

b. Compute the internal rate of return on both projects.

c. Compute the profitability index of both projects.

d. Compute the payback period on both projects.

e. Which of the two projects, if either, should Wang accept? Why?

5. Benford, Inc. is planning to open a new sporting goods store in a suburban

mall. Benford will lease the needed space in the mall. Equipment and fixtures

for the store will cost $200,000 and be depreciated over a 5-year period on a

straight-line basis to $0. The new store will require Benford to increase its net

working capital by $200,000 at time 0; thereafter, net working capital balances

are expected to equal 20 percent of the following year's sales. First-year sales

are expected to be $1 million and to increase at an annual rate of 8 percent

over the expected 10-year life of the store. Operating expenses (including

lease payments and excluding depreciation) are projected to equal 70 percent

of sales. The salvage value of the store's equipment and fixtures is anticipated

to be $10,000 at the end of 10 years. Benford's marginal tax rate is 40 percent.

(Note: This problem is the same as Problem 8 in Chapter 10, except for the

following questions.)

a. Calculate the store's net present value, using an 18 percent required return.

b. Should Benford accept the project?

c. Calculate the store's internal rate of return.

d. Calculate the store's profitability index.

Also complete the following Evaluating Risk Problem:

6. Consider a 2-year project with the following information: initial fixed asset investment =

$495,000; straight-line depreciation to zero over the 2-year life; zero salvage value;

selling price =$39; variable costs = $20; fixed costs = $210,000; quantity sold = 150,000

units; tax rate = 31 percent. How sensitive is Operating Cash Flow (OCF) to changes in

quantity sold? State your answer in terms of a dollar amount change (increase or

decrease) in OCF for every additional unit sold.

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Solution:

1. Calculate the net present value and profitability index of a project with a net

investment of $20,000 and expected net cash flows of $3,000 a year for 10 years

if the project's required return is 12 percent. Is the project acceptable?

Solution

Cash flows of $3000 per year are equivalent to ordinary annuity with rate =12% and years =10

Present value factor =5.6502

Present value of cash flows =3000*5.6502=$16950.6

NPV of project=16950-20000= - $3049.4

Profitability index = PV of future cash inflows/ initial outlay

=16950.6/20000

=0.84753

NPV of project is negative and Profitability index is less than 1, project is not acceptable.

2. A firm wishes to bid on a contract that is expected to yield the following after tax

net cash flows at the end of each year:

Year Net Cash Flow

1 $5,000

2 8,000

3 9,000

4 8,000

5 8,000

6 5,000

7 3,000

8 $-1,500

To secure the contract, the firm must spend $30,000 to retool its plant. This

retooling will have no salvage value at the end of the 8 years. Comparable investment

alternatives are available to the firm that earn 12 percent compounded

annually. The depreciation tax benefit from the retooling is reflected

in the net cash flows in the table.

a. Compute the project's net present value.

Year End Cash Flow Present Value at 12%

0 -30000 -30000/(1.12)^0=-30000.00

1 5000 5000/(1.12)^1=4464.29

2 8000 8000/(1.12)^2=6377.55

3 9000 9000/(1.12)^3=6406.02

4 8000 8000/(1.12)^4=5084.14

5 ...

#### Solution Summary

There are six problems related to decission making based upon NPV, IRR, Payback Period and Profitability Index criteria. Step by step method is demonstrated to calculate NPV, PI, IRR or Payback period.