For the following two projects, determine the Payback Period Discounted Payback
ID: 2793210 • Letter: F
Question
For the following two projects, determine the
Payback Period
Discounted Payback
Net Present Value
Profitability Index (Benefit-Cost Ratio)
Internal Rate of Return
Modified Internal Rate of Return
Project A
Project B
Year
Net Income
Cash Flow
Net Income
Cash Flow
0
(15,000)
(19,000)
1
5,000
6,000
3,000
4,000
2
5,000
6,000
5,000
6,000
3
5000
6,000
7,000
8,000
4
5,000
6,000
11,000
12,000
Risk Index
1.80
.60
The firm’s cost of capital ko is 15% and the risk free rate Rf is 10%. The firm assesses risk and assigns a risk index to determine a risk adjusted discount rate. An index of 1.0 would be assigned to an average risk project.
To determine risk adjusted rates the firm uses the following equation:
Risk Adjusted Rate (RADR) = Rf + [Risk Index (ko – Rf)
Task: Rank the projects in accordance with each method of analysis.
Project A
Project B
Year
Net Income
Cash Flow
Net Income
Cash Flow
0
(15,000)
(19,000)
1
5,000
6,000
3,000
4,000
2
5,000
6,000
5,000
6,000
3
5000
6,000
7,000
8,000
4
5,000
6,000
11,000
12,000
Risk Index
1.80
.60
Explanation / Answer
Project A Year Cash Flow PV F at 19% PV at 19% Cum.P/Back(Ordinary P/B) Cum. Disc.payback 0 -15,000 1 -15000 -15,000 -15000 1 6,000 0.84034 5042 -9,000 -9958 2 6,000 0.70616 4237 -3,000 -5721 3 6,000 0.59342 3560 3,000 -2160 4 6,000 0.49867 2992 9,000 832 NPV 9,000 832 IRR 22% MIRR 21% Ordinary Payback period=2+(3000/6000)= 2.5 years Discounted payback period=3+(2160/2992)= 3.72 years Profitability Index (Benefit-Cost Ratio) 832/15000= 5.55% Project B Year Cash Flow PV F at 13% PV at 13% Cum.P/Back(Ordinary P/B) Cum. Disc.payback 0 -19,000 1 -19000 -19,000 -19000 1 4,000 0.88496 3540 -15,000 -15460 2 6,000 0.78315 4699 -9,000 -10761 3 8,000 0.69305 5544 -1,000 -5217 4 12,000 0.61332 7360 11,000 2143 NPV 11,000 2143 IRR 17% MIRR 16% Ordinary Payback period=3+(1000/12000)= 2.08 years Discounted payback period=3+(5217/7360)= 3.71 years Profitability Index (Benefit-Cost Ratio) 2143/19000= 11.28% Project A Project B Ranking Payback Period 2.5 2.08 Project A Discounted Payback 3.72 3.71 Project A Net Present Value 832 2143 Project B Profitability Index (Benefit-Cost Ratio) 5.55% 11.28% Project B Internal Rate of Return 22% 17% Project A Modified Internal Rate of Return 21% 16% Project A For MIRR , cost of capital 15% is the Finance rate & the respective risk-adjusted rate ,ie. 19% & 13% are taken as the re-investment rate
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