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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Landen, Inc. uses several methods to evaluate capital projects. An appropriate decision rule for Landen would be to invest in a project if it has a positive:

A) profitability index (PI).

B) net present value (NPV).

C) internal rate of return (IRR).

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The decision rules for net present value, profitability index, and internal rate of return are to invest in a project if NPV > 0, IRR > required rate of return, or PI > 1.

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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 NPV and IRR.

NPV

IRR

A) $243 20%

B) $883 15%

C) $883 20%

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To determine the NPV, enter the following:
PV of $3,000 in year 1 = $2,727, PV of $2,000 in year 2 = $1,653, PV of $2,000 in year 3 = $1,503. NPV = ($2,727 + $1,653 + $1,503) ? $5,000 = 883.

You know the NPV is positive, so the IRR must be greater than 10%. You only have two choices, 15% and 20%. Pick one and solve the NPV. If it is not close to zero, then you guessed wrong; select the other one.

[3000 ÷ (1 + 0.2)1 + 2000 ÷ (1 + 0.2)2 + 2000 ÷ (1 + 0.2)3] ? 5000 = 46 This result is closer to zero (approximation) than the $436 result at 15%. Therefore, the approximate IRR is 20%.

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Which of the following statements about the payback period is FALSE?

A) The payback period provides a rough measure of a project's liquidity and risk.

B) The payback method considers all cash flows throughout the entire life of a project.

C) The payback period is the number of years it takes to recover the original cost of the investment.

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The payback period does not take any cash flows after the payback point into consideration.

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The Seattle Corporation has been presented with an investment opportunity which will yield cash flows of $30,000 per year in years 1 through 4, $35,000 per year in years 5 through 9, and $40,000 in year 10. This investment will cost the firm $150,000 today, and the firm's cost of capital is 10%. The payback period for this investment is closest to:

A) 5.23 years.

B) 6.12 years.

C) 4.86 years.

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Years	0	1	2	3	4	5
Cash Flows	-$150,000	$30,000	$30,000	$30,000	$30,000	$35,000

$150,000
120,000	(4 years)(30,000/year)
$30,000

With $30,000 unrecovered cost in year 5, and $35,000 cash flow in year 5; $30,000 / $35,000 = 0.86 years

4 + 0.86 = 4.86 years

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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

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The process of evaluating and selecting profitable long-term investments consistent with the firm’s goal of shareholder wealth maximization is known as:

A) financial restructuring.

B) capital budgeting.

C) monitoring.

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In the process of capital budgeting, a manager is making decisions about a firm’s earning assets, which provide the basis for the firm’s profit and value. Capital budgeting refers to investments expected to produce benefits for a period of time greater than one year. Financial restructuring is done as a result of bankruptcy and monitoring is a critical assessment aspect of capital budgeting.

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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