Reading 6: Discounted Cash Flow Applications-LOS a 习题精选 2011, net, investment, budgeting, interpret

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Session 2: Quantitative Methods: Basic Concepts
Reading 6: Discounted Cash Flow Applications

LOS a: Calculate and interpret the net present value (NPV) and the internal rate of return (IRR) of an investment.

 

 

The capital budgeting director of Green Manufacturing is evaluating a laser imaging project with the following characteristics:

• Cost: $150,000
• Expected life: 3 years
• After-tax cash flows: $60,317 per year
• Salvage value: $0

If Green Manufacturing’s cost of capital is 11.5%, what is the project’s internal rate of return (IRR)?

A) 13.6%.

B) $3,875.

C) 10.0%.

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Since we are seeking the IRR, the answer has to be in terms of a rate of return, this eliminates the option not written in a percentage.

Since they payments (cash flows) are equals, we can calculate the IRR as: N = 3; PV = 150,000; PMT = 60,317; CPT → I/Y = 9.999

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In order to calculate the net present value (NPV) of a project, an analyst would least likely need to know the:

A) timing of the expected cash flows from the project.

B) opportunity cost of capital for the project.

C) internal rate of return (IRR) of the project.

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The NPV is calculated using the opportunity cost, discount rate, expected cash flows, and timing of the expected cash flows from the project. The project’s IRR is not used to calculate the NPV.

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An investment with a cost of $5,000 is expected to have cash inflows of $3,000 in year 1, and $4,000 in year 2. The internal rate of return (IRR) for this investment is closest to:

A) 25%.

B) 15%.

C) 30%.

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The IRR is the discount rate that makes the net present value of the investment equal to 0.

This means -$5,000 + $3,000 / (1 + IRR) + $4,000 / (1 + IRR)² = 0

One way to compute this problem is to use trial and error with the existing answer choices and choose the discount rate that makes the PV of the cash flows closest to 5,000.

$3,000 / (1.25) + $4,000 / (1.25)² = 4,960.

Alternatively: CFO = -5,000; CF1 = 3,000; CF2 = 4,000; CPT → IRR = 24.3%.

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The estimated annual after-tax cash flows of a proposed investment are shown below:

Year 1: $10,000
Year 2: $15,000
Year 3: $18,000

After-tax cash flow from sale of investment at the end of year 3 is $120,000

The initial cost of the investment is $100,000, and the required rate of return is 12%. The net present value (NPV) of the project is closest to:

A) $63,000.

B) $19,113.

C) -$66,301.

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10,000 / 1.12 = 8,929

15,000 / (1.12)² = 11,958

138,000 / (1.12)³ = 98,226

NPV = 8,929 + 11,958 + 98,226 ? 100,000 = $19,113

Alternatively: CFO = -100,000; CF1 = 10,000; CF2 = 15,000; CF3 = 138,000; I = 12; CPT → NPV = $19,112.

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Fisher, Inc., is evaluating the benefits of investing in a new industrial printer. The printer will cost $28,000 and increase after-tax cash flows by $8,000 during each of the next five years. What are the respective internal rate of return (IRR) and net present value (NPV) of the printer project if Fisher’s required rate of return is 11%?

A) 17.97%; $5,844.

B) 5.56%; ?$3,180.

C) 13.20%; $1,567.

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IRR Keystrokes: CF₀ = -$28,000; CF₁ = $8,000; F₁ = 5; CPT → IRR = 13.2%.

NPV Keystrokes: CF₀ = -$28,000; CF₁ = $8,000; F₁ = 5; I = 11; CPT → NPV = 1,567.

Since cash flows are level, an alternative is:
IRR:  N = 5; PMT = 8,000; PV = -28,000; CPT → I/Y = 13.2%.
NPV:  I/Y = 11; CPT → PV = -29,567 + 28,000 = 1,567

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The financial manager at Genesis Company is looking into the purchase of an apartment complex for $550,000. Net after-tax cash flows are expected to be $65,000 for each of the next five years, then drop to $50,000 for four years. Genesis’ required rate of return is 9% on projects of this nature. After nine years, Genesis Company expects to sell the property for after-tax proceeds of $300,000. What is the respective internal rate of return (IRR) and net present value (NPV) on this project?

A) 13.99%; $166,177.

B) 7.01%; ?$53,765.

C) 6.66%; ?$64,170.

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IRR Keystrokes: CF₀ = -$550,000; CF₁ = $65,000; F₁ = 5; CF₂ = $50,000; F₂ = 3; CF₃ = $350,000; F₃ = 1.

NPV Keystrokes: CF₀ = -$550,000; CF₁ = $65,000; F₁ = 5; CF₂ = $50,000; F₂ = 3; CF₃ = $350,000; F₃ = 1.

Compute NPV, I = 9.

Note: Although the rate of return is positive, the IRR is less than the required rate of 9%.  Hence, the NPV is negative.