Consider the following two mutually exclusive projects: Year Cash Flow (A) Cash
ID: 2613188 • Letter: C
Question
Consider the following two mutually exclusive projects: Year Cash Flow (A) Cash Flow (B) 0 –$ 341,000 –$ 51,000 1 54,000 24,900 2 74,000 22,900 3 74,000 20,400 4 449,000 15,500 Whichever project you choose, if any, you require a 15 percent return on your investment. a-1 What is the payback period for each project? hat is the discounted payback period for each project? What is the NPV for each project?What is the IRR for each project?
What is the profitability index for each project?
What is the profitability index for each project?
Explanation / Answer
Part A)
Payback period is the period within the investment made by the company is expected to be realized with the use of cash inflows generated from the project.
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Project A:
The initial investment of $341,000 will be recovered as follows:
Year 1 = $54,000, Year 2 = $74,000, Year 3 = $74,000 and the balance of $139,000 between Year 3 and Year 4
The payback period can be calculated with the use of following formula:
Payback Period = Year (s) Upto Which Partial Recovery is Made + Balance/Cash Flow of the Year in which Full Recovery is Made
Payback Period = 3 + 139,000/449,000 = 3.31 Years
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Project B:
The initial investment of $51,000 will be recovered as follows:
Year 1 = $24,900, Year 2 = $22,900 and the balance of $2,200 between Year 2 and Year 3
The payback period can be calculated with the use of following formula:
Payback Period = Year (s) Upto Which Partial Recovery is Made + Balance/Cash Flow of the Year in which Full Recovery is Made
Payback Period = 2 + 2,200/20,400 = 2.11 years
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Part B)
Payback period is the period within the investment made by the company is expected to be realized with the use of discounted cash inflows generated from the project.
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Project A:
The initial investment of $341,000 will be recovered as follows:
Year 1 = $46,956.52, Year 2 = $55,954.63, Year 3 = $48,656.20 and the balance of $189,432.65 between Year 3 and Year 4
The discounted payback period can be calculated with the use of following formula:
Discounted Payback Period = Year (s) Upto Which Partial Recovery is Made + Balance/Discounted Cash Flow of the Year in which Full Recovery is Made
Discounted Payback Period = 3 + 189,432.65/256,717.21 = 3.74 Years
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Project B:
The initial investment of $51,000 will be recovered as follows:
Year 1 = $21,652.17, Year 2 = $17,315.69 and the balance of $12,032.14 between Year 2 and Year 3
The discounted payback period can be calculated with the use of following formula:
Discounted Payback Period = Year (s) Upto Which Partial Recovery is Made + Balance/Discounted Cash Flow of the Year in which Full Recovery is Made
Discounted Payback Period = 2 + 12032.14/13413.33 = 2.90 Years
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Part C)
NPV is the difference between the present value of cash inflows and cash outflows. The formula for calculating NPV is:
NPV = Cash Flow Year 0 + Cash Flow Year 1/(1+Discount Rate)^1 + Cash Flow Year 2/(1+Discount Rate)^2 + Cash Flow Year 3/(1+Discount Rate)^3 + Cash Flow Year 4/(1+Discount Rate)^4
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Project A:
NPV = -341,000 + 54,000/(1+15%)^1 + 74,000/(1+15%)^2 + 74,000/(1+15%)^3 + 449,000/(1+15%)^4 = $67,284.56
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Project B:
NPV = -51,000 + 24,900/(1+15%)^1 + 22,900/(1+15%)^2 + 20,400/(1+15%)^3 + 15,500/(1+15%)^4 = $10,243.37
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Part D)
IRR is the minimum acceptable rate of return from a project. Below this rate, the project will not be accepted. The IRR can be calculated with the use of IRR function of EXCEL/Financial Calculator. The basic formula for calculating IRR is:
NPV = 0 = Cash Flow Year 0 + Cash Flow Year 1/(1+Discount Rate)^1 + Cash Flow Year 2/(1+Discount Rate)^2 + Cash Flow Year 3/(1+Discount Rate)^3 + Cash Flow Year 4/(1+Discount Rate)^4
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Project A:
IRR = 21.60%
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Project B:
IRR = 25.44%
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Part D)
Profitability Index is the ratio of present value of cash inflows and initial investment. It can be calculated with the use of following formula:
Profitability Index = Present Value of Cash Inflows/Initial Investment
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Project A:
Present Value of Cash Inflows = 54,000/(1+0.15)^1 + 74,000/(1+0.15)^2 + 74,000/(1+0.15)^3 + 449,000/(1+0.15)^4 = $408,284.56
Profitability Index = 408,284.56/341,000 = 1.20
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Project B:
Present Value of Cash Inflows = 24,900/(1+0.15)^1 + 22,900/(1+0.15)^2 + 20,400/(1+0.15)^3 + 15,500/(1+0.15)^4 = $61,243.37
Profitability Index = 61,243.37/51,000 = 1.20
Year Cash Flows Discounted Cash Flows 1 54,000 46,956.52 2 74,000 55,954.63 3 74,000 48,656.20 4 449,000 256,717.21