consider a project with $150,000 initial cost (year 0), cash inflows of $45,200 per year for 5 years (end of each year), and a discount rate of 10%. What is the (straight) payback period?
- a) 3.7 years b) 3.3 years c) 3 years d) 4.2 years
#4 Given your answer in the last question and that you want to use the payback rule with a cutoff period of 3 years, would you accept the project?
- a) Accept b) Reject
#5 What is the discounted payback period if the opportunity cost of capital (OCC) is 10%?
- a) 3 years b) 3.3 years c) 3.7 years d) 4.2 years
#6 What’s the profitability index of the project in the previous question, if the opportunity cost of capital is 10%?
- a) 0.21 b) 0.14 c) 0.12 d) 0.18
Answer
We have been provided with the information as follow
| Initial Cost | 150,000 |
| Cash inflow for 5 year | 42500 |
| Discount Rate rate | 10 |
Now we will calculate NPV as follow
| Year | Cash Flow |
Pv Factor @10% |
Prasent Value |
| 0 | -150,000 | 1 | -150000 |
| 1 | 42500 | 0.909091 | 38636.36 |
| 2 | 42500 | 0.826446 | 35123.97 |
| 3 | 42500 | 0.751315 | 31930.88 |
| 4 | 42500 | 0.683013 | 29028.07 |
| 5 | 42500 | 0.620921 | 26389.16 |
| 11108.44 |
Since NPV = $ 11,108.44 accept the project
Answer 4 : a) Accept
Payback period is as follow
| Year | Cash Flow |
Incremental Cash Flow |
| 0 | -150,000 | -150,000 |
| 1 | 42500 | -107,500 |
| 2 | 42500 | -65,000 |
| 3 | 42500 | -22,500 |
| 4 | 42500 | 20,000 |
| 5 | 42500 | 62,500 |
In the 4 th year company receive 42500 but he needs only 22500 to recover so days will be calculated as follow
=22500*12/42500
=0.7 year
Payback period = 3.7 yaers
Now we will calculate discounted Payback as follow
| Year | Cash Flow |
Pv Factor @10% |
Prasent Value |
|
| 0 | -150,000 | 1 | -150000 | -150,000 |
| 1 | 42500 | 0.909090909 | 38636.36 | -111,364 |
| 2 | 42500 | 0.826446281 | 35123.97 | -76,240 |
| 3 | 42500 | 0.751314801 | 31930.88 | -44,309 |
| 4 | 42500 | 0.683013455 | 29028.07 | -15,281 |
| 5 | 42500 | 0.620921323 | 26389.16 | 11,108 |
In the 5th year company receive 26389.16 but he needs only 15,281 to recover so days will be calculated as follow
=15281*12/26389.16
=0.2year
Payback period = 4.2 years
Prfitabelity Index = PV of future cash Flow / Initial Investment
=11,108 /150,000
=0.074056
=0.074
