All techniques — Decision among mutually exclusive investments Pound Industries
ID: 2788082 • Letter: A
Question
All techniques—Decision among mutually exclusive investmentsPound Industries is attempting to select the best of three mutually exclusive projects. The initial investment and after-tax cash inflows associated with these projects are shown in the following table.
a.Calculate the payback period for each project. So, what is the payback period of project A,B, and C.
b.Calculate the net present value (NPV) of each project, assuming that the firm has a cost of capital equal to 12%. What is the NPV for project A,B,C?
c.Calculate the internal rate of return (IRR) for each project. What is the IRR for each project A,B,C?
d.Indicate which project you would recommend. Would you recommend project A, B, or C?
Cash flows
Project A
Project B
Project C
Initial investment (CF)
$30,000
$70,000
$70,000
t=1to 5
$10,000
$22,000
$23,000
Cash flows
Project A
Project B
Project C
Initial investment (CF)
$30,000
$70,000
$70,000
Cash inflows (CF),t=1to 5
$10,000
$22,000
$23,000
Explanation / Answer
a) Payback period means at what time the cash inflows from a project will recover the cash outflows/ Initial investment. In our case, since the cash inflows are constant, we will get the payback period by dividing the initial investment with the yearly cash inflows -
Project A = $30000 / $10000 per year = 3 years
Project B = $70000 / $22000 per year = 3.182 years
Project C = $70000 / $23000 per year = 3.043 years
b) To compute NPV, multiply the yearly cash inflows by the Cumulative Present value factor (CPVF) @12% for 5 years and deduct the initial investment -
NPV = Cash Inflows per year x CPVF (12%, 5) - Initial Investment
Project A = $10,000 x 3.60477620228 - $30,000 = $6,047.76
Project B = $22,000 x 3.60477620228 - $70,000 = $9,305.08
Project C = $23,000 x 3.60477620228 - $70,000 = $12,909.85
c) IRR is the rate at which Initial investement would be equal to the present value of cash inflows from the project. So, we have -
Cash Inflows x CPVF(IRR, 5) = Initial investment
Project A
10000 x CPVF(IRR, 5) = 30000
Or, CPVF(IRR, 5) = 3
Now, we look for this value in the CPVF table. We have -
At 19%, CPVF = 3.0576
At 20%, CPVF = 2.9906
IRR is between these two rate, so we need to interpolate -
Difference required (if we move from 19%) = 3.0576 - 3 = 0.0576
Total Difference (between 19% & 20%) = 3.0576 - 2.9906 = 0.067
IRR = Lower rate + Difference in rates x Difference required / Total Difference
IRR = 19% + 1% x 0.0576 / 0.067 = 19.86% (Their can be minimal difference of rouding off as I am solving upto four digits of CPVF)
Project B
22000 x CPVF (IRR, 5) = 70000
Or, CPVF (IRR, 5) = 3.1818
We look for this value in the CPVF table -
At 17%, CPVF = 3.1993
At 18%, CPVF = 3.1272
Difference required = 3.1993 - 3.1818 = 0.0175
Total Difference = 3.1993 - 3.1272 = 0.0721
IRR = 17% + 1% x 0.0175 x 0.0721 = 24.27%
Project C
23000 x CPVF (IRR, 5) = 70000
Or, CPVF (IRR, 5) = 3.0435
We look for this value in the CPVF table -
At 19%, CPVF = 3.0576
At 20%, CPVF = 2.9906
Difference required = 3.0576 - 3.0435 = 0.0141
Total Difference = 3.0576 - 2.9906 = 0.067
IRR = Lower rate + Difference in rates x Difference required / Total Difference
IRR = 19% + 1% x 0.0141 / 0.067 = 19.21%
d) IRR rule - Higher the IRR, the better is the project
NPV rule - Higher the IRR, the better is the project
As per the NPV rule, Project C is more desirable and as per the IRR rule, Project B is more desirable. However, if we have to choose one, I would choose Project C, as its NPV is highest and also has an adequate IRR is between the two other projects.