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:
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.
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
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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