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
