Question

P10-21 (similar to) |

All techniques, conflicting rankings Nicholson Roofing Materials, Inc., is considering two mutually exclusive projects, each with an initial investment of

$100,000.

The company's board of directors has set a 4-year payback requirement and has set its cost of capital at

9%.

The cash inflows associated with the two projects are shown in the following table:

LOADING...

.

a. Calculate the payback period for each project. Rank the projects by payback period.

b. Calculate the NPV of each project. Rank the project by NPV.

c. Calculate the IRR of each project. Rank the project by IRR.

d. Make a recommendation.

a. The payback period of project A is

nothing

years. (Round to two decimal places.)

1 $30,000 $85,000

2 $30,000 $50,000

3 $30,000 $10,000

4 $30,000 $10,000

5 $30,000 $10,000

6 $30,000 $10,000

Answer #1

a)

Payback period:

Project A:

Payback period of project A = Initial investment / cash flow

Payback period of project A = 100,000 / 30,000

**Payback period of project A = 3.33 years**

Project B:

Cumulative cash flow for year 0 = -100,000

Cumulative cash flow for year 1 = -100,000 + 85,000 = -15,000

Cumulative cash flow for year 2 = -15,000 + 50,000 = 35,000

15,000 / 50,000 = 0.3

**Payback period of project B = 1 + 0.3 = 1.30
years**

**Project B has a better payback period**

b)

NPV:

Project A:

NPV = Present value of cash inflows - present value of cash outflows

NPV = Annuity * [1 - 1 / (1 + r)^{n}] / r - Initial
investment

NPV = 30,000 * [1 - 1 / (1 + 0.09)^{6}] / 0.09 -
100,000

NPV = 30,000 * [1 - 0.596267] / 0.09 - 100,000

NPV = 30,000 * 4.485919 - 100,000

**NPV = $34,577.56**

Project B:

NPV = Present value of cash inflows - present value of cash outflows

NPV = -100,000 + 85,000 / (1 + 0.09)^{1} + 50,000 / (1 +
0.09)^{2} + 10,000 / (1 + 0.09)^{3} + 10,000 / (1 +
0.09)^{4} + 10,000 / (1 + 0.09)^{5} + 10,000 / (1 +
0.09)^{6}

**NPV = $47,333.73**

**Project B has a higher NPV**

c)

IRR:

Project A:

IRR is the rate of return that makes NPV equal to 0:

NPV = 30,000 * [1 - 1 / (1 + R)^{6}] / R - 100,000

Using trial and error method, i.e., after trying various values for R, lets try R as 19.91%

NPV = 30,000 * [1 - 1 / (1 + 0.1991)^{6}] / 0.1991 -
100,000

NPV = 30,000 * [1 - 0.336409] / 0.1991 - 100,000

NPV = 30,000 * 3.332953 - 100,000

NPV = 0

**Therefore, IRR of project A is 19.91%**

Project B:

IRR is the rate of return that makes NPV equal to 0:

NPV = -100,000 + 85,000 / (1 + R)^{1} + 50,000 / (1 +
R)^{2} + 10,000 / (1 + R)^{3} + 10,000 / (1 +
R)^{4} + 10,000 / (1 + R)^{5} + 10,000 / (1 +
R)^{6}

Using trial and error method, i.e.e, after trying various values for R, lets try R as 36.14%

NPV = -100,000 + 85,000 / (1 + 0.3614)^{1} + 50,000 / (1
+ 0.3614)^{2} + 10,000 / (1 + 0.3614)^{3} + 10,000
/ (1 + 0.3614)^{4} + 10,000 / (1 + 0.3614)^{5} +
10,000 / (1 + 0.3614)^{6}

NPV = 0

**Therefore, IRR of project B is 36.14%**

**Project B has a higher IRR**

d)

We would recommend project B

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