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# Net present value, payback, IRR, and accounting rate of return

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Consider the following two mutually exclusive projects, each of which requires an initial investment of \$100,000 and has no salvage value. The organization, which has a cost of capital of 15%, must choose one or the other (see attached)
Cash Inflows (End of year)
Year Project A Project B
1 \$30,000 \$0
2 \$30,000 \$20,000
3 \$30,000 \$20,000
4 \$30,000 \$50,000
5 \$30,000 \$90,000

a. compute the payback period of these projects. Using the payback criterion, which project is more desirable?
b. Compute the net present value of these two projects. Using the net present value criterion, which project is more desirable?

c. What do you think about the idea of using the payback period to adjust for risk?
d. How do you think about the idea of using the payback period to adjust for risk?
e. Compute the internal rate of return for each project
f. Assuming the straight-line depreciation is used to compute income, compute the accounting rate of return for these two projects

g. What do you think of the accounting rate of return criterion?

#### Solution Preview

Consider the following two mutually exclusive projects, each of which requires an initial investment of \$100,000 and has no salvage value.  The organization, which has a cost of capital of 15%, must choose one or the other (see attached)

Cash Inflows (End of year)
Year Project A Project B
1 \$30,000 \$0
2 \$30,000 \$20,000
3 \$30,000 \$20,000
4 \$30,000 \$50,000
5 \$30,000 \$90,000

a. compute the payback period of these projects. Using the payback criterion, which project is more desirable?

Payback Period

Payback period is the number of years in which the initial investment is recouped
Payback = Year before full recovery + (unrecovered cost at start of year/Cash Flow during year)

Project A

Year Cash flow Cumulative cash flow

0 (\$100,000) (\$100,000)
1 \$30,000 -\$70,000
2 \$30,000 -\$40,000
3 \$30,000 -\$10,000
4 \$30,000 \$20,000 Payback period= 3.33 years
5 \$30,000 \$50,000 =3 + 10000 / 30000
\$50,000

Payback period= 3.33 years

Project B

Year Cash flow Cumulative cash flow

0 (\$100,000) (\$100,000)
1 \$0 -\$100,000
2 \$20,000 -\$80,000
3 \$20,000 -\$60,000
4 \$50,000 -\$10,000
5 \$90,000 \$80,000 Payback period= 4.11 years
\$80,000 =4 + 10000 / 90000

Payback period= 4.11 years

Project A is better from payback period criterion

b. Compute the net present value of these two projects. Using the net present value ...

#### Solution Summary

The solution provides answers to a capital budgeting problem and calculates Net present value, payback, IRR, and accounting rate of return

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