Reading 44: Capital Budgeting LOSd习题精选 single, 2010, discounted, following, including

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LOS d: Calculate and interpret the results using each of the following methods to evaluate a single capital project: net present value (NPV), internal rate of return (IRR), payback period, discounted payback period, and profitability index (PI).

Edelman Enginenering is considering including an overhead pulley system in this year's capital budget. The cash outlay for the pully system is $22,430. The firm's cost of capital is 14%. After-tax cash flows, including depreciation are $7,500 for each of the next 5 years. 

Calculate the internal rate of return (IRR) and the net present value (NPV) for the project, and indicate the correct accept/reject decision.

NPV

IRR

Accept/Reject

A) $3,318 20% Accept

B) $15,070 14% Accept

C) $15,070 14% Reject

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Using the cash flow keys:
CF0 = -22,430; CFj = 7,500; Nj = 5; Calculate IRR = 20%
I/Y = 14%; Calculate NPV = 3,318

Because the NPV is positive, the firm should accept the project.

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A company is considering the purchase of a copier that costs $5,000. Assume a cost of capital of 10 percent and the following cash flow schedule:

• Year 1: $3,000
• Year 2: $2,000
• Year 3: $2,000

Determine the project's payback period and discounted payback period.

Payback Period

Discounted Payback Period

A) 2.0 years 2.4 years

B) 2.0 years 1.6 years

C) 2.4 years 1.6 years

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Regarding the regular payback period, after 1 year, the amount to recover is $2,000 ($5,000 - $3,000). After the second year, the amount is fully recovered.

The discounted payback period is found by first calculating the present values of each future cash flow. These present values of future cash flows are then used to determine the payback time period.

3,000 / (1 + .10)¹ = 2,727

2,000 / (1 + .10)² = 1,653 

2,000 / (1 + .10)³ = 1,503.

Then:

5,000 - (2,727 + 1,653) = 620

620 / 1,503 = .4.

So, 2 + 0.4 = 2.4.

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An analyst has gathered the following data about a company with a 12% cost of capital:

	Project A	Project B
Cost	$15,000	$25,000
Life	5 years	5 years
Cash inflows	$5,000/year	$7,500/year

Projects A and B are mutually exclusive. What should the company do?

A) Reject A, Accept B.

B) Accept A, Reject B.

C) Reject A, Reject B.

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For mutually exclusive projects accept the project with the highest NPV. In this example the NPV for Project A (3,024) is higher than the NPV of Project B (2,036). Therefore accept Project A and reject Project B.

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If the projects are independent, what should the company do?

A) Reject A, Reject B.

B) Accept A, Reject B.

C) Accept A, Accept B.

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Project A: N = 5; PMT = 5,000; FV = 0; I/Y = 12; CPT → PV = 18,024; NPV for Project A = 18,024 ? 15,000 = 3,024.

Project B: N = 5; PMT = 7,500; FV = 0; I/Y = 12; CPT → PV = 27,036; NPV for Project B = 27,036 ? 25,000 = 2,036.

For independent projects the NPV decision rule

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Tapley Acquisition, Inc., is considering the purchase of Tangent Company. The acquisition would require an initial investment of $190,000, but Tapley's after-tax net cash flows would increase by $30,000 per year and remain at this new level forever. Assume a cost of capital of 15%. Should Tapley buy Tangent?

A) No, because k > IRR.

B) Yes, because the NPV = $10,000.

C) Yes, because the NPV = $30,000.

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This is a perpetuity.

PV = PMT / I = 30,000 / 0.15 = 200,000

200,000 ? 190,000 = 10,000

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Which of the following statements about the discounted payback period is least accurate? The discounted payback:

A) frequently ignores terminal values.

B) period is generally shorter than the regular payback.

C) method can give conflicting results with the NPV.

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The discounted payback period calculates the present value of the future cash flows. Because these present values will be less than the actual cash flows it will take a longer time period to recover the original investment amount.

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Which of the following statements about NPV and IRR is least accurate?

A) For independent projects if the IRR is > the cost of capital accept the project.

B) The NPV method assumes that all cash flows are reinvested at the cost of capital.

C) For mutually exclusive projects you should use the IRR to rank and select projects.

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For mutually exclusive projects you should use NPV to rank and select projects.

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A company is considering a $10,000 project that will last 5 years.

• Annual after tax cash flows are expected to be $3,000
• Target debt/equity ratio is 0.4
• Cost of equity is 12%
• Cost of debt is 6%
• Tax rate 34%

What is the project's net present value (NPV)?

A) -$1,460.

B) +$1,460.

C) $+1,245

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First, calculate the weights for debt and equity

w_d + w_e = 1

w_e = 1 ? w_d

w_d /  w_e = 0.40

w_d = 0.40 × (1 ? w_d)

w_d = 0.40 ? 0.40w_d

1.40w_d = 0.40

w_d = 0.286, w_e = 0.714

Second, calculate WACC

WACC = (w_d × k_d) × (1 ? t) + (w_e × k_e) = (0.286 × 0.06 × 0.66) + (0.714 × 0.12) = 0.0113 + 0.0857 = 0.0970

Third, calculate the PV of the project cash flows

N = 5, PMT = -3,000, FV = 0, I/Y = 9.7, CPT → PV = 11,460

And finally, calculate the project NPV by subtracting out the initial cash flow

NPV = $11,460 ? $10,000 = $1,460

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Lincoln Coal is planning a new coal mine, which will cost $430,000 to build, with the expenditure occurring next year. The mine will bring cash inflows of $200,000 annually over the subsequent seven years. It will then cost $170,000 to close down the mine over the following year. Assume all cash flows occur at the end of the year. Alternatively, Lincoln Coal may choose to sell the site today. What minimum price should Lincoln set on the property, given a 16% required rate of return?

A) $325,859.

B) $280,913.

C) $376,872.

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The key to this problem is identifying this as a NPV problem even though the first cash flow will not occur until the following year. Next, the year of each cash flow must be property identified; specifically: CF₀ = $0; CF₁ = -430,000; CF_2-8 = +$200,000; CF₉ = -$170,000. One simply has to discount all of the cash flows to today at a 16% rate. NPV = $280,913.

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A firm is considering a $5,000 project that will generate an annual cash flow of $1,000 for the next 8 years. The firm has the following financial data:

• Debt/equity ratio is 50%.
• Cost of equity capital is 15%.
• Cost of new debt is 9%.
• Tax rate is 33%.

Determine the project's net present value (NPV) and whether or not to accept it.

NPV

Accept / Do not accept

A) -$33 Do not accept

B) +$33 Accept

C) +$4,968 Accept

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First, calculate the weights for debt and equity

d + w_e = 1

d = 0.50W_e

e + W_e = 1

d = 0.333, w_e = 0.667

Second, calculate WACC

WACC = (w_d × k_d) × (1 ? t) + (w_e × k_e) = (0.333 × 0.09 × 0.67) + (0.667 × 0.15) = 0.020 + 0.100 = 0.120

Third, calculate the PV of the project cash flows

N = 8, PMT = -1,000, FV = 0, I/Y = 12, CPT PV = 4,967

And finally, calculate the project NPV by subtracting out the initial cash flow

NPV = $4,967 ? $5,000 = -$33

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A firm is considering a $200,000 project that will last 3 years and has the following financial data:

• Annual after-tax cash flows are expected to be $90,000.
• Target debt/equity ratio is 0.4.
• Cost of equity is 14%.
• Cost of debt is 7%.
• Tax rate is 34%.

Determine the project's payback period and net present value (NPV).

Payback Period

NPV

A) 2.43 years $18,716

B) 2.22 years $18,716

C) 2.22 years $21,872

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Payback Period

$200,000 / $90,000 = 2.22 years

NPV Method

First, calculate the weights for debt and equity

w_d + w_e = 1
w_e = 1 ? w_d
w_d / w_e = 0.40
w_d = 0.40 × (1 ? w_d)
w_d = 0.40 ? 0.40w_d
1.40w_d = 0.40
w_d = 0.286, w_e = 0.714

Second, calculate WACC

WACC = (w_d × k_d) × (1 ? t) + (w_e × k_e) = (0.286 × 0.07 × 0.66) + (0.714 × 0.14) = 0.0132 + 0.100 = 0.1132

Third, calculate the PV of the project cash flows

90 / (1 + 0.1132)¹ + 90 / (1 + 0.1132)² + 90 / (1 + 0.1132)³ = $218,716

And finally, calculate the project NPV by subtracting out the initial cash flow

NPV = $218,716 ? $200,000 = $18,716