Capital Budgeting

CAPITAL BUDGETING
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Problem A

Fargo Corp is considering the purchase of a new piece of

equipment. The equipment costs $50,000, and will have a
salvage value of $5,000 after nine years. Using the new piece of
equipment will increase Fargo's annual cash flows by $6,000.
Fargo has a hurdle rate of 12%.

a. How much is Fargo's annual depreciation will on the

equipment?
b. What is Fargo's projected annual increase in net income?
c. What is the accounting rate of return for purchasing the new
piece of equipment?
d. Based on financial factors, should Fargo purchase the new
equipment? Why or why not?
a. $5,000 = ($50,000 - $5,000)/9
b. $1,000 = $6,000 - $5,000
c. 2% = $1,000/$50,000
d. No; the accounting rate of return of 2% is greater than the hurdle rate of 12%.

Problem B

Fire Corp is considering the purchase of a new piece of

equipment. The equipment costs $50,000, and will have a
salvage value of $5,000 after nine years. Using the new piece of
equipment will increase Fire's annual cash flows by $6,000.

a. What is the payback period for the new piece of equipment?

b. Suppose that the increase in cash flows were $10,000 in the
first year, then decreased by $1,000 each year over the life of the
equipment. What is the payback period for the equipment?
a. 8.33 years = $50,000/$6,000
b. 7.33 years: $50,000 - $10,000 - $9,000 - $8,000 - $7,000 - $6,000 - $5,000 - $4,000 = $1,000 left to be paid off in
year 8, when $3,000 is earned. 7 + $1,000/$3,000 = 7.33 years

Problem C

Dobson Corp is considering the purchase of a new piece of

equipment. The cost savings from the equipment would result in
an annual increase in net income of $50,000. The equipment will
have an initial cost of $500,000 and have an 8 year life. There is
no salvage value of the equipment. The hurdle rate is 10%.
Ignore income taxes. Calculate the following:

a. Accounting rate of return

b. Payback period
a. 10% = $50,000/$500,000
b. 4.44 years = $500,000/($50,000 + [($500,000 - $0)/8])

Problem D

Grady Corp is considering the purchase of a new piece of

equipment. The equipment costs $50,000, and will have a
salvage value of $5,000 after nine years. Using the new piece of
equipment will increase Grady's annual cash flows by $6,000.
Grady has a hurdle rate of 12%.
a. What is the present value of the increase in annual cash
flows?
b. What is the present value of the salvage value?
c. What is the net present value of the equipment purchase?
d. Based on financial factors, should Grady purchase the
equipment? Why?
a. $31,969.20 = $6,000 × 5.3282
b. $1,803 = $5,000 × 0.3606
c. ($16,227.80) = $31,969.20 + $1,803 - $50,000
d. No; the net present value is negative.

Problem E

Cloud Corp. is considering the purchase of a new piece of equipment. The equipment costs $30,000, and will have a
salvage value of $4,000 after nine years. Using the new piece of equipment will increase Cloud's annual cash flows
by $6,000. Cloud has a hurdle rate of 12%.

a. What is the net present value?

b. What would the net present value be with a 15% hurdle rate?
c. Based on the NPV calculations, in what range would the equipment's internal rate of return fall?

Answer already given for letter c:

Compare the net present value when using the 12% hurdle rate (this will yield an NPV of a positive amount) with
the net present value using a hurdle rate of 15% (this will yield an NPV with a positive amount). Since the IRR will
yield a zero NPV, the range of the IRR in this problem is between 12% and 15%. Remember that as the hurdle rate
increases, the NPV will decrease. You can apply this analysis of the IRR to upcoming problems that does not need
an interpolation nor a table. (in this case, the range where the IRR would fall was being asked.) Again the answer for
letter c is the IRR is between 12% and 15%.

a. $3,411.60 = ($6,000 × 5.3282) + ($4,000 × 0.3606) - $30,000

b. ($233.20) = ($6,000 × 4.7716) + ($4,000 × 0.2843) - $30,000
c. IRR is between 12% and 15% (14.79%)

Problem F

Mindy Corp is considering the purchase of a new piece of

equipment. The cost savings from the equipment would result in
an annual increase in net income after tax of $50,000. The
equipment will have an initial cost of $500,000 and have an 8
year life. The equipment has no salvage value. The hurdle rate is
10%. Answer the following:

a. What is the net present value?

b. What would the net present value be with a 15% hurdle rate?
c. Based on the NPV calculations, in what range would the
equipment's internal rate of return fall?

a. $100,176 = ($50,000 + [($500,000 - $0)/8]) × 5.3349 -

$500,000
b. $4,821 = ($50,000 + [($500,000 - $0)/8]) × 4.4873 - $500,000
c. IRR is greater than 15% (15.29%)
Problem G

Grove Corp is considering the purchase of a new piece of

equipment. The cost savings from the equipment would result in
an annual increase in net income of $200,000. The equipment
will have an initial cost of $1,200,000 and have an 8 year life.
The salvage value of the equipment is estimated to be $200,000.
The hurdle rate is 10%. Ignore income taxes. Answer the
following:

a. What is the accounting rate of return?

b. What is the payback period?
c. What is the net present value?
d. What would the net present value be with a 15% hurdle rate?
e. Based on the NPV calculations, in what range would the
equipment's internal rate of return fall?
a. 16.67% = $200,000/$1,200,000
b. 3.7 years = $1,200,000/($200,000 + [($1,200,000 - $200,000)/8])
c. $627,142.50 = {($200,000 + [($1,200,000 - $200,000)/8]) × 5.334} + ($200,000 × .4665) - 1,200,000
d. $323,752.50 = {($200,000 + [($1,200,000 - $200,000)/8]) × 4.4873} + ($200,000 × .3269) - 1,200,000
e. IRR is greater than 15% (22.47%)
Problem H

Briar Corp is considering the purchase of a new piece of

equipment. The cost savings from the equipment would result in
an annual increase in cash flow of $200,000. The equipment will
have an initial cost of $1,200,000 and have an 8 year life. The
salvage value of the equipment is estimated to be $200,000. The
hurdle rate is 8%. Ignore income taxes. Answer the following:

a. What is the accounting rate of return?

b. What is the payback period?
c. What is the net present value?
d. What would the net present value be with a 12% hurdle rate?
e. Based on the NPV calculations, in what range would the
equipment's internal rate of return fall?
a. 6.25% = ($200,000 - [($1,200,000 - $200,000)/8])/$1,200,000
b. 6 years = $1,200,000/$200,000
c. $57,380 = ($200,000 × 5.7466) + ($200,000 × .5403) - 1,200,000
d. ($125,700) = ($200,000 × 4.9676) + ($200,000 × .4039) - 1,200,000
e. IRR is between 8% and 12% (9.15%)

Problem I

Emerson Corp is trying to decide whether to lease or purchase a

piece of equipment needed for the next five years. The
equipment would cost $500,000 to purchase, and maintenance
costs would be $20,000 per year. After five years, Emerson
estimates it could sell the equipment for $100,000. If Emerson
leases the equipment, it would pay $150,000 each year, which
would include all maintenance costs. Emerson's hurdle rate is
12%.

a. What is the net present value of the cost of purchasing the

equipment?
b. What is the net present value of the cost of leasing the
equipment?
c. Based on financial factors, should Emerson purchase or lease
the equipment? Why?
a. $515,356 = $500,000 + ($20,000 × 3.6048) - ($100,000 × 0.5674)
b. $540,720 = $150,000 × 3.6048
c. Purchase; the net present value of the cost is lower.
Problem J

115. Norwood, Inc., which has a hurdle rate of 12%, is considering three different independent investment
opportunities. Each project has a seven-year life. The annual cash flows and initial investment for each of
the projects are as follows:
 a. What is the present value of the annual cash flows for each of the three projects?
b. What is the net present value of each of the projects?
c. What is the profitability index of each of the projects?
d. In what order should Norwood prioritize investment in the projects?

a. A $600,003 = $131,470 × 4.5638; B $550,029 = $120,520 × 4.5638; C $500,010 = $109,560 × 4.5638

b. A $280,003 = $600,003 - $320,000; B $250,029 = $550,029 - $300,000; C $270,010 = $500,010 -
$230,000
c. A 1.88 = $600,003/$320,000; B 1.83 = $550,029/$300,000; C 2.17 = $500,010/$230,000
d. C, A, B

Feedback: Net present value is calculated by discounting the annual cash flows and subtracting the initial
investment. Profitability index = Present value of future cash flows/Initial investment. Investment in
projects should be prioritized by their profitability indexes.

Problem K

Cortland Corp is considering the purchase of a new piece of equipment. The cost savings from the equipment would
result in an annual increase in net cash flows of $100,000. The equipment will have an initial cost of $400,000 and
have a 5 year life. If the salvage value of the equipment is estimated to be $75,000, what is the annual net income?
Ignore income taxes.
Depreciation = ($400,000 - $75,000)/5 = $65,000. Annual net cash flow $100,000 - Depreciation $65,000 = Annual
net income $35,000.

Problem L

Fletcher Corp is considering the purchase of a new piece of equipment. The equipment will have an initial cost of
$400,000, a 5 year life, and a salvage value of $75,000. If the accounting rate of return for the project is 10%, what
is the annual increase in net cash flow? Ignore income taxes.
Depreciation = ($400,000 - $75,000)/5 = $65,000. Net income = $400,000 × 10% = $40,000. Annual increase in net
cash flow = $65,000 + $40,000 = $105,000.

Problem M

Wright Corp is considering the purchase of a new piece of equipment, which would have an initial cost of
$1,000,000 and a 5 year life. There is no salvage value for the equipment. The increase in cash flow each year of the
equipment's life would be as follows:

What is the payback period?

$1,000,000 - $375,000 - $350,000 = $275,000 to be paid back after year 2. Fraction of year 3 to pay it back =
$275,000/$285,000 = .96. Payback period = 2 + .96 = 2.96 years.
Problem N

Patterson Corp is considering the purchase of a new piece of equipment, which would have an initial cost of
$500,000, a 7 year life, and $150,000 salvage value. The increase in net income each year of the equipment's life
would be as follows:

What is the payback period?

Annual depreciation = ($500,000 - $150,000)/7 = $50,000, so annual cash flows will equal the net income each year
plus $50,000. $500,000 - $149,000 - $141,000 - $139,000 = $71,000 to be paid back after year 3. Fraction of year 4
to pay it back = $71,000/$128,000 = .55. Payback period = 3 + .55 = 3.55 years.

Problem O

Grace Corp, whose required rate of return is10%, is considering the purchase of a new piece of equipment. The
internal rate of return of the project, which has a life of 8 years, is 12%. The project would have Answer: D

A. an accounting rate of return greater than

10%.

B. a payback period more than 8

years.

C. a net present value of

zero.

D. a net present value greater than

zero.

Problem P

Newport Corp is considering the purchase of a new piece of equipment. The cost savings from the equipment would
result in an annual increase in cash flow of $200,000. The equipment will have an initial cost of $900,000 and have
a 6 year life. There is no salvage value for the equipment. If the hurdle rate is 10%, what is the internal rate of
return? Ignore income taxes.

A. between 6% and
8%
B. between 8% and
10%

C. between 10% and

12%

D. less than
zero

The net present value at 10% is ($200,000 × 4.3553) - $900,000 = ($28,940), so the internal rate of return is
less than 10% since NPV is negative. The net present value at 8% is ($200,000 × 4.6229) - $900,000 =
$24,580, so the internal rate of return is more than 8% since NPV is positive.

Problem Q

Frank Inc. is trying to decide whether to lease or purchase a

piece of equipment needed for the next ten years. The equipment
would cost $45,000 to purchase, and maintenance costs would
be $5,000 per year. After ten years, Frank estimates it could sell
the equipment for $20,000. If Frank leased the equipment, it
would pay a set annual fee that would include all maintenance
costs. Frank has determined after a net present value analysis
that at its hurdle rate of 10%, it would be better off by $5,700 if
it buys the equipment. What would the approximate annual cost
be if Frank were to lease the equipment?
NPV to buy = $45,000 + ($5,000 × 6.1446) - ($20,000 × 0.3855) = $68,013. NPV to lease = $68,013 + $5,700 =
$73,713. Annual lease cost = $73,713/6.1446 = $11,996.
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