CHAPTER 7: CAPITAL BUDGETING DECISIONS—PART I

Multiple Choice

d 1. Calculating the payback period for a capital project requires knowing which of the following?
a. Useful life of the project.
b. The company's minimum required rate of return.
c. The project's NPV.
d. The project's annual cash flow.

c 2. The payback criterion for capital investment decisions

a. is conceptually superior to the IRR criterion.
b. takes into consideration the time value of money.
c. gives priority to rapid recovery of cash.
d. emphasizes the most profitable projects.

a 3. Which of the following is NOT relevant in calculating annual net cash flows for an investment?
a. Interest payments on funds borrowed to finance the project.
b. Depreciation on fixed assets purchased for the project.
c. The income tax rate.
d. Lost contribution margin if sales of the product invested in will reduce sales of other products.

c 6. Which of the following events is most likely to reduce the expected NPV of an investment?
a. The major competitor for the product to be manufactured with the machinery being considered for purchase
has been rated "unsatisfactory" by a consumer group.
b. The interest rate on long-term debt declines.
c. The income tax rate is raised by the Congress.
d. Congress approves the use of faster depreciation than was previously available.

b 10. All other things being equal, as cost of capital increases

a. more capital projects will probably be acceptable.
b. fewer capital projects will probably be acceptable.
c. the number of capital projects that are acceptable will change, but the direction of the change is not
determinable just by knowing the direction of the change in cost of capital.
d. the company will probably want to borrow money rather than issue stock.

d 14. The normal methods of analyzing investments

a. cannot be used by not-for-profit entities.
b. do not apply if the project will not produce revenues.
c. cannot be used if the company plans to finance the project with funds already available internally.
d. require forecasts of cash flows expected from the project.

c 17. Which of the following events will increase the NPV of an investment involving a new product?
a. An increase in the income tax rate.
b. An increase in the expected per-unit variable cost of the product.
c. An increase in the expected annual unit volume of the product.
d. A decrease in the expected salvage value of equipment.

a 22. Two new products, X and Y, are alike in every way except that the sales of X will start low and rise throughout
its life, while those of Y will be the same each year. Total volumes over their five-year lives will be the
same, as will selling prices, unit variable costs, cash fixed costs, and investment. The NPV of product X
a. will be less than that of product Y.
b. will be the same as that of product Y.
c. will be greater than that of product Y.
d. none of the above.

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d 23. Which of the following events is most likely to increase the number of investments that meet a company's
acceptance criteria?
a. Top management raises the target rate of return.
b. The interest rate on long-term debt rises.
c. The income tax rate rises.
d. The IRS allows companies to expense purchases of fixed assets, instead of depreciating them over their lives.

c 26. A peso now is worth more than a peso to be received in the future because of
a. inflation.
b. uncertainty.
c. the opportunity cost of waiting.
d. none of the above.

b 30. As the discount rate increases

a. present value factors increase.
b. present value factors decrease.
c. present value factors remain constant.
d. it is impossible to tell what happens to the factors.

a 31. As the length of an annuity increases

a. present value factors increase.
b. present value factors decrease.
c. present value factors remain constant.
d. it is impossible to tell what happens to present value factors.

a 32. The only future costs that are relevant to deciding whether to accept an investment are those that will
a. be different if the project is accepted rather than rejected.
b. be saved if the project is accepted rather than rejected.
c. be deductible for tax purposes.
d. affect net income in the period that they are incurred.

c 34. Which of the following methods FAILS to distinguish between return of investment and return on investment?
a. NPV.
b. IRR.
c. Payback.
d. Book rate of return.

a 38. If Co. X wants to use IRR to evaluate long-term decisions and to establish a cutoff rate of return, X must be
sure the cutoff rate is
a. at least equal to its cost of capital.
b. at least equal to the rate used by similar companies.
c. greater than the IRR on projects accepted in the past.
d. greater than the current book rate of return.

a 39. Which of the following is NOT relevant in calculating net cash flows for Project N?
a. Interest payments on funds that would be borrowed to finance Project N.
b. Depreciation on assets purchased for Project N.
c. The contribution margin the company would lose if sales of the product introduced by Project N will reduce
sales of other products.
d. The income tax rate applicable to the entity.

d 41. If depreciation on a new asset exceeds its savings in cash operating costs, which of the following is true?
a. The project is usually unacceptable.
b. The annual after-tax cash flow on the new asset will be greater than the savings in cash operating costs.
c. The project has a negative NPV.

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 d. All of the above.

b 43. An investment opportunity costing $75,000 is expected to yield net cash flows of $23,000 annually for five
years. The NPV of the investment at a cutoff rate of 14% would be
a. $(3,959).
b. $3,959.
c. $75,000.
d. $78,959.

b 44. An investment opportunity costing $55,000 is expected to yield net cash flows of $22,000 annually for five
years. The payback period of the investment is
a. 0.4 years.
b. 2.5 years.
c. $33,000.
d. some other number.

c 45. An investment opportunity costing $180,000 is expected to yield net cash flows of $53,000 annually for five
years. The IRR of the investment is between
a. 10 and 12%.
b. 12 and 14%.
c. 14 and 16%.
d. 16 and 18%.

b 46. An investment opportunity costing $150,000 is expected to yield net cash flows of $45,000 annually for
five years. The cost of capital is 10%. The book rate of return would be
a. 10%.
b. 20%.
c. 30%.
d. 33.3%.

a 47. An investment opportunity costing $150,000 is expected to yield net cash flows of $36,000 annually for six
years. The NPV of the investment at a cutoff rate of 12% would be
a. $(2,004).
b. $2,004.
c. $150,000.
d. $147,996.

c 48. An investment opportunity costing $100,000 is expected to yield net cash flows of $22,000 annually for seven
years. The payback period of the investment is
a. 0.22 years.
b. 3.08 years.
c. 4.55 years.
d. some other number.

a 49. An investment opportunity costing $200,000 is expected to yield net cash flows of $39,000 annually for eight
years. The IRR of the investment is between
a. 10 and 12%.
b. 12 and 14%.
c. 14 and 16%.
d. 16 and 18%.

b 50. An investment opportunity costing $80,000 is expected to yield net cash flows of $25,000 annually for four
years. The cost of capital is 10%. The book rate of return would be
a. 10.0%.
b. 12.5%.
c. 21.3%.

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 d. 32.0%.

True-False

T 1. Payback period is the length of time it will take a company to recoup its outlay for an investment.

T 2. Discounted cash flow techniques apply to investments that involve either costs only, or both costs and
revenues.

F 3. Cost of capital is the interest rate that a company expects to pay to finance a particular capital investment
project.

F 4. The higher the cost of capital, the higher the present value of future cash inflows.

F 5. If the IRR on a capital project is positive, its NPV will be positive.

T 6. Salvage value is usually ignored in computing the tax depreciation on an investment in depreciable assets.

F 7. IRR can be computed for even cash flows, but not for uneven cash flows.

T 8. If IRR is less than the cost of capital, the NPV will be negative.

F 9. IF NPV is negative, IRR is equal to the cost of capital.

T 10. Payback emphasizes the return of the investment and ignores the return on the investment.

Problems

1. An investment opportunity costing $180,000 is expected to yield net cash flows of $60,000 annually for five
years.

a. Find the NPV of the investment at a cutoff rate of 12%.

b. Find the payback period of the investment.

c. Find the IRR on the investment.

SOLUTION:

a. NPV: $36,300 [(3.605 x $60,000) - $180,000]

b. Payback period: 3 years ($180,000/$60,000)

c. IRR: between 18 % and 20% (3.0 is between 3.127 and 2.991)

2. Tofte is considering the purchase of a machine. Data are as follows:

Cost $100,000
Useful life 10 years
Annual straight-line depreciation $ 10,000
Expected annual savings in cash
operation costs $ 18,000

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 Tofte's cutoff rate is 12% and its tax rate is 40%.

a. Compute the annual net cash flows for the investment.

b. Compute the NPV of the project.

SOLUTION:

a. Annual net cash flows: $14,800 [$18,000 pretax - 40% x ($18,000 - $10,000 depreciation)]

b. NPV: Negative $16,380 [($14,800 x 5.650) - $100,000]

3. Willow Company is considering the purchase of a machine with the following characteristics.

Cost $150,000
Estimated useful life 10 years
Expected annual cash cost savings $35,000

Marquette's tax rate is 40%, its cost of capital is 12%, and it will use straight-line depreciation for the new
machine.

a. Compute the annual after-tax cash flows for this project.

b. Find the payback period for this project.

SOLUTION:

a. Annual cash flows: $27,000 [$35,000 - 40% x ($35,000 - $15,000)]

b. Payback period: 5.56 years ($150,000/$27,000)

4. Bilt-Rite Co. has the opportunity to introduce a new product. Bilt-Rite expects the product to sell for $60 and to
have per-unit variable costs of $40 and annual cash fixed costs of $3,000,000. Expected annual sales volume is
250,000 units. The equipment needed to bring out the new product costs $5,000,000, has a four-year life and no
salvage value, and would be depreciated on a straight-line basis. Bilt-Rite's cost of capital is 10% and its
income tax rate is 40%.

a. Find the increase in annual after-tax cash flows for this opportunity.

b. Find the payback period on this project.

c. Find the NPV for this project.

SOLUTION:

a. Increase in annual cash flows: $1,700,000

Income before taxes, 250,000 x ($60 - $40)

- $3,000,000 - $5,000,000/4 $ 750,000
Income tax (300,000)

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 ----------
Net income $ 450,000
Plus depreciation 1,250,000
----------
Net cash flow $1,700,000
==========

b. Payback period: 2.94 years ($5,000,000/$1,700,000)

c. NPV: $389,000 [($1,700,000 x 3.170) - $5,000,000]

5. An investment opportunity costing $600,000 is expected to yield net cash flows of $120,000 annually for ten
years.

a. Find the NPV of the investment at a cutoff rate of 12%.

b. Find the payback period of the investment.

c. Find the IRR on the investment.

SOLUTION:

a. NPV: $78,000 [(5.650 x $120,000) - $600,000]

b. Payback period: 5 years ($600,000/$120,000)

c. IRR: 15% (5.0 is about halfway between 5.216 and 4.833)

6. Scottso has an investment opportunity costing $300,000 that is expected to yield the following cash flows over
the next six years:

Year One $75,000

Year Two $90,000
Year Three $115,000
Year Four $130,000
Year Five $100,000
Year Six $90,000

a. Find the payback period of the investment.

b. Find the book rate of return of the investment.

c. Find the NPV of the investment at a cutoff rate of 10%.

SOLUTION:

a. Payback period: 3.15 years (75,000 + 90,000 + 115,000 + .15 x 130,000)

b. Book rate of return: 33.3%

Average return: $100,000 ($600,000 total / 6 years)

Depreciation: 50,000 ($30,000 / 6 years)

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 -------
Average income $50,000

Average investment: $300,000 / 2 = $150,000

Book rate of return = $50,000 / 150,000 = 33.3%

c. NPV: $130,530

Cash Factor PV
------ ------ ------
1 75,000 .909 68,175
2 90,000 .826 74,340
3 115,000 .751 86,365
4 130,000 .683 88,790
5 100,000 .621 62,100
6 90,000 .564 50,760
-------
430,530
Investment 300,000
-------
NPV 130,530
======

7. Acme is considering the purchase of a machine. Data are as follows:

Cost $160,000
Useful life 10 years
Annual straight-line depreciation $ ???
Expected annual savings in cash
operation costs $ 33,000

Acme's cutoff rate is 12% and its tax rate is 40%.

a. Compute the annual net cash flows for the investment.

b. Compute the NPV of the project.

c. Compute the IRR of the project.

SOLUTION:

a. Annual net cash flows: $26,200 [$33,000 pretax - 40% x ($33,000 - $16,000 depreciation)]

b. NPV: Negative $11,970 [($26,200 x 5.650) - $160,000]

c. IRR: between 10% and 12% [factor of 6.107 (160,000/26,200) is between 6.145 and 5.650]

8. Scottso has an investment opportunity costing $180,000 that is expected to yield the following cash flows over
the next five years:

Year One $ 30,000

Year Two $ 60,000

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 Year Three $ 90,000
Year Four $ 60,000
Year Five $ 30,000

a. Find the payback period of the investment.

b. Find the book rate of return of the investment.

c. Find the NPV of the investment at a cutoff rate of 12%.

SOLUTION:

a. Payback period: 3.0 years (30,000 + 60,000 + 90,000)

b. Book rate of return: 20%

Average return: $54,000 ($270,000 total / 5 years)

Depreciation: 36,000 ($180,000 / 5 years)
------
Average income $18,000

Average investment: $180,000 / 2 = $90,000

Book rate of return = $18,000 / $90,000 = 20%

c. NPV: $6,930

Cash Factor PV
------ ------ ------
1 30,000 .893 26,790
2 60,000 .797 47,820
3 90,000 .712 64,080
4 60,000 .636 38,160
5 30,000 .567 17,010
-------
193,860
Investment 180,000
-------
NPV 13,860
======

9. Reno Company is considering the purchase of a machine with the following characteristics.

Cost $160,000
Estimated useful life 5 years
Expected annual cash cost savings $56,000
Expected salvage value none

Reno's tax rate is 40%, its cost of capital is 12%, and it will use straight-line depreciation for the new machine.

a. Compute the annual after-tax cash flows for this project.

b. Find the payback period for this project.

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 c. Compute the NPV for this project.

SOLUTION:

a. Annual cash flows: $46,400 [$56,000 - 40% x ($56,000 - 32,000)]

b. Payback period: 3.45 years ($160,000/$46,400)

c. NPV: $7,272 [($46,400 x 3.605) - $160,000]

10. Whitehall Co. has the opportunity to introduce a new product. Whitehall expects the project to sell for $40 and
to have per-unit variable costs of $27 and annual cash fixed costs of $1,500,000. Expected annual sales volume
is 200,000 units. The equipment needed to bring out the new product costs $3,500,000, has a four-year life and
no salvage value, and would be depreciated on a straight-line basis. Whitehall's cutoff rate is 10% and its
income tax rate is 40%.

a. Find the increase in annual after-tax cash flows for this opportunity.

b. Find the payback period on this project.

c. Find the NPV for this project.

SOLUTION:

a. Increase in annual cash flows: $1,100,000

Income before taxes, [200,000 x ($40 - $27)

- $1,500,000 - $3,500,000/4] $ 225,000
Income tax ( 90,000)
----------
Net income $ 135,000
Plus depreciation 875,000
----------
Net cash flow $1,010,000
==========

b. Payback period: 3.47 years ($3,500,000/$1,010,000)

c. NPV: negative $298,300 [($1,010,000 x 3.170) - $3,500,000]

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