Homework Answers
| A | B | |||
| year | cash flows | cumulative cash flow | cash flow | cumulative cash flow |
| 1 | 50000 | 50000 | 90000 | 90000 |
| 2 | 90000 | 140000 | 90000 | 180000 |
| 3 | 150000 | 290000 | 90000 | 270000 |
| 4 | 110000 | 400000 | 90000 | 360000 |
| 5 | - | - | 90000 | 450000 |
a) Payback period:
- For machine A, cost is 220000/-.which falls somewhere in 3rd year. So, (220,000-140000)/(290000-140000)*12 months => 6.4 or 7 months. Hence, 2 year, 7 months.
- For machine B, cost is 250000/-.which falls somewhere in 3rd year. So, (250,000-180000)/(270000-180000)*12 months => 9.3 or 9 months. Hence, 2 year, 9 months.
b)
| A | |
| year | cash flows |
| 1 | 50000 |
| 2 | 90000 |
| 3 | 150000 |
| 4 | 110000 |
| 5 | 20000 |
| TOTAL | 420000 |
ARR = Average profit after depreciation/Average investment*100
= [(420000-(220,000-20000))/5]/220000*100 = 20%
c)
| A | B | |||||
| year | cash flows | Discounted factor @ 14% | Discounted cashflows | cash flow | Discount factor @ 14% | discounted cashflows |
| 0 | -220000 | 1.00 | -220000 | -250000 | 1.00 | -250000 |
| 1 | 50000 | 0.877193 | 43859.65 | 90000 | 0.877193 | 78947.37 |
| 2 | 90000 | 0.769468 | 69252.08 | 90000 | 0.769468 | 69252.08 |
| 3 | 150000 | 0.674972 | 101245.7 | 90000 | 0.674972 | 60747.44 |
| 4 | 110000 | 0.59208 | 65128.83 | 90000 | 0.59208 | 53287.22 |
| 5 | 20000 | 0.519369 | 10387.37 | 90000 | 0.519369 | 46743.18 |
| NPV | 69873.66 | NPV | 58977.29 | |||
since NPV of machine A is better, its advisable.
d) IRR of machine B:
since we kmow thw machine B yields NPV of 58977.29 @ 14% discount rate, we will use higher rate say 25% to compute its IRR (as guess).
| Year | cash flow | Discount rate @ 25% | discounted cashflows |
| 0 | -250000 | 1.0 | -250000 |
| 1 | 90000 | 0.8 | 72000 |
| 2 | 90000 | 0.64 | 57600 |
| 3 | 90000 | 0.512 | 46080 |
| 4 | 90000 | 0.4096 | 36864 |
| 5 | 90000 | 0.32768 | 29491.2 |
| NPV | -7964.80 |
So, IRR = Ra + (NPVa)/(NPVa+NPVb)/(Ra-Rb)
where Ra = 14%, Rb= 25%
= 14% + [ 58977/ (58977+7964.8) * (25-11) ] ie = 23.44%
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