Homework Answers
a) Program A is preferrable at 10% MARR
MARR at 10% is Year 0 =1, Year 1= 1/1.1 = 0.9091, Year 2 = 0.9091/1.1 = 0.8264, Year 3 = 0.8264/1.1 = 0.7531, Year 4 = 0.7531/1.1 = 0.683, Year 5 = 0.683/1.1 = 0.6209
Program A Net Present Value of Cash Inflow
| Year | Cash Inflow (A) | Discounting Factor (B) | Net Present Value of Cash Flow (A X B) | Equation |
| 0 | -10000 | 1.0000 | -10,000 | =-10000 X 1 |
| 1 | 4000 | 0.9091 | 3,636 | =4000 X 0.9091 |
| 2 | 4000 | 0.8264 | 3,306 | =4000 X 08264 |
| 3 | 4000 | 0.7513 | 3,005 | =4000 X 0.7531 |
| 4 | 4000 | 0.6830 | 2,732 | =4000 X 0.6830 |
| 5 | 4000 | 0.6209 | 2,484 | =4000 X 0.6209 |
| Total | 5,163 |
Program B Net Present Value of Cash Inflow
| Year | Cash Inflow (A) | Discounting Factor (B) | Net Present Value of Cash Flow (A X B) | Equation |
| 0 | -10000 | 1.0000 | -10,000 | =-10000 X 1 |
| 1 | 10000 | 0.9091 | 9,091 | =10000 X 0.9091 |
| 2 | 2000 | 0.8264 | 1,653 | =2000 X 08264 |
| 3 | 2000 | 0.7513 | 1,503 | =2000 X 0.7531 |
| 4 | 2000 | 0.6830 | 1,366 | =2000 X 0.6830 |
| 5 | 2000 | 0.6209 | 1,242 | =2000 X 0.6209 |
| Total | 4,854 |
Thus, net present value of Cash inflow of Program A ($5163) > Program B ($4854).
b) Program B is preferable at MARR of 20%
MARR at 20% is Year 0 =1, Year 1= 1/1.2 = 0.8333, Year 2 = 0.8333/1.2 = 0.6944, Year 3 = 0.6944/1.2 = 0.5787, Year 4 = 0.5787/1.2 = 0.4823, Year 5 = 0.4823/1.2 = 0.4019
Program A Net Present Value of Cash Inflow
| Year | Cash Inflow (A) | Discounting Factor (B) | Net Present Value of Cash Flow (A X B) | Equation |
| 0 | -10000 | 1.0000 | -10,000 | =-10000 X 1 |
| 1 | 4000 | 0.8333 | 3,333 | =4000 X 0.8333 |
| 2 | 4000 | 0.6944 | 2,778 | =4000 X 0.6944 |
| 3 | 4000 | 0.5787 | 2,315 | =4000 X 0.5787 |
| 4 | 4000 | 0.4823 | 1,929 | =4000 X 0.4823 |
| 5 | 4000 | 0.4019 | 1,608 | =4000 X 0.4019 |
| Total | 1,962 |
Program B Net Present Value of Cash Inflow
| Year | Cash Inflow (A) | Discounting Factor (B) | Net Present Value of Cash Flow (A X B) | Equation |
| 0 | -10000 | 1.0000 | -10,000 | =-10000 X 1 |
| 1 | 10000 | 0.8333 | 8,333 | =10000 X 0.8333 |
| 2 | 2000 | 0.6944 | 1,389 | =2000 X 0.6944 |
| 3 | 2000 | 0.5787 | 1,157 | =2000 X 0.5787 |
| 4 | 2000 | 0.4823 | 965 | =2000 X 0.4823 |
| 5 | 2000 | 0.4019 | 804 | =2000 X 0.4019 |
| Total | 2,648 |
Thus, net present value of Cash inflow of Program B ($2648) > Program A ($1962).
c) Graph of Program A
Program A Table-
| Year | I = 0% | I = 10% | I = 20% | I = 30% |
| 0 | -10000 | -10,000 | -10,000 | -10,000 |
| 1 | 4000 | 3,636 | 3,333 | 3,077 |
| 2 | 4000 | 3,306 | 2,778 | 2,367 |
| 3 | 4000 | 3,005 | 2,315 | 1,821 |
| 4 | 4000 | 2,732 | 1,929 | 1,401 |
| 5 | 4000 | 2,484 | 1,608 | 1,077 |
| Total | 10,000 | 5,163 | 1,962 | -258 |
Program B graph
Program B Data
| Year | I = 0% | I = 10% | I = 20% | I = 30% |
| 0 | -10000 | -10,000 | -10,000 | -10,000 |
| 1 | 10000 | 9,091 | 8,333 | 7,692 |
| 2 | 2000 | 1,653 | 1,389 | 1,183 |
| 3 | 2000 | 1,503 | 1,157 | 910 |
| 4 | 2000 | 1,366 | 965 | 700 |
| 5 | 2000 | 1,242 | 804 |
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2) Two mutually exclusive design alternatives are being considered, with each one having a useful life of 10 years. The estimated sales and cost data for each alternative are shown. Annual revenues are based on the number of units sold and the selling price. Annual expenses are based on the fixed and variable costs. If the MARR is 20% per year, determine which alternative is preferable based on the PW Method. 12 Investment cost Units to be sold each year...
2) Two mutually exclusive design alternatives are being considered, with each one having a useful life of 10 years. The estimated sales and cost data for each alternative are shown. Annual revenues are based on the number of units sold and the selling price. Annual expenses are based on the fixed and variable costs. If the MARR is 20% per year, determine which alternative is preferable based on the PW Method. 12 Investment cost Units to be sold each year...
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ANNUAL WORTH Analysis
Two mutually exclusive design alternatives are being considered. The estimated cash flows for each alternative are given in the following table with MARR = 10% per year. Suggest your recommendation by using multiple attribute annual worth AW analysis. Design A Design B Investment cost (RM) 28,000 55,000 One-off expenses 10,000 13,000 In year 4 (RM) Annual revenues (RM) 22,000 28,000 Market value (RM) 6,000 8,000 Useful life 10 years 6 years
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