Quantitative Methods 【Reading 6】Sample capital, following, budgeting, project

andytrader

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

andytrader

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

C) opportunity cost of capital for 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.

andytrader

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) 15%.

B) 25%.

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%.

andytrader

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) $19,113.

B) $63,000.

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.

andytrader

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) 13.20%; $1,567.

B) 17.97%; $5,844.

C) 5.56%; −$3,180.

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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

andytrader

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) 7.01%; −$53,765.

B) 13.99%; $166,177.

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.

andytrader

Calabash Crab House is considering an investment in mutually exclusive kitchen-upgrade projects with the following cash flows:

	Project A	Project B
Initial Year	-$10,000	-$9,000
Year 1	2,000	200
Year 2	5,000	-2,000
Year 3	8,000	11,000
Year 4	8,000	15,000

Assuming Calabash has a 12.5% cost of capital, which of the following investment decisions is most appropriate?

A) Accept Project A because its internal rate of return is higher than that of Project B.

B) Accept Project B because its net present value is higher than that of Project A.

C) Accept both projects because they both have positive net present values.

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When net present value (NPV) and internal rate of return (IRR) give conflicting project rankings, NPV is the most appropriate method for deciding between mutually exclusive projects. Here, the NPV of project A is $6,341 and the NPV of Project B is $6,688. Both NPVs are positive, so Calabash should select the Project B because of its higher NPV.

andytrader

The internal rate of return (IRR) method and net present value (NPV) method of project selection will always provide the same accept or reject decision when:

A) the projects are independent.

B) the projects are mutually exclusive.

C) up-front project costs are under $1.0 million.

If a project’s IRR exceeds the cost of capital, the project’s NPV will be positive. The only way in which accepting a positive NPV project would reduce firm value is if its selection precludes selection of a project that would have enhanced firm value to a greater extent (i.e., had a higher NPV). IRR and NPV method accuracy do not depend upon project duration or costs.

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Sarah Kelley, CFA, is analyzing two mutually exclusive investment projects. Kelley has calculated the net present value (NPV) and internal rate of return (IRR) for each project:

Project 1: NPV = $230; IRR = 15%
Project 2: NPV = $4,000; IRR = 6%

Kelley should make which of the following recommendations concerning the two projects?

A) Accept Project 1 only.

B) Accept both projects.

C) Accept Project 2 only.

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Because the investment projects are mutually exclusive, only one project can be chosen. The NPV and IRR criteria are giving conflicting project rankings. When decision criteria conflict, always use the NPV criteria because NPV evaluates projects using an appropriate discount rate, the weighted average cost of capital. The IRR may not be a market rate, therefore future cash flows associated with the project may not be capable of earning a rate of return equal to the IRR.

andytrader

Which of the following is least likely a problem associated with the internal rate of return (IRR) method for making investment decisions?

A) An investment project may have more than one internal rate of return.

B) The IRR method determines the discount rate that sets the net present value of a project equal to zero.

C) IRR and NPV criteria can give conflicting decisions for mutually exclusive projects.

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The IRR method equates an investment’s present value of inflows to its present value of outflows. The IRR by definition is the discount rate that sets the net present value of a project equal to zero. Therefore, the decision rule for independent projects is as follows: if the IRR is above the firm’s cost of capital, the project should be accepted, and if the IRR is below the cost of capital, the project should be rejected.