Consider the following two mutually exclusive projects: Year Cash Flow (A) Cash
ID: 2738491 • Letter: C
Question
Consider the following two mutually exclusive projects: Year Cash Flow (A) Cash Flow (B) 0 –$220,912 –$16,564 1 28,500 5,875 2 50,000 8,770 3 53,000 13,235 4 399,000 9,669 Whichever project you choose, if any, you require a 6 percent return on your investment. Required: (a) What is the payback period for Project A? (b) What is the payback period for Project B? (c) What is the discounted payback period for Project A? (d) What is the discounted payback period for Project B? (e) What is the NPV for Project A? (f) What is the NPV for Project B ? (g) What is the IRR for Project A? (h) What is the IRR for Project B? (i) What is the profitability index for Project A? (j) What is the profitability index for Project B?
Explanation / Answer
Step-1:
Calculation of payback period for project A:
Formula = Year+ Cost of investment / Initial cash inflow
Years
Project A
Cumulative
Project B
Cumulative
1
$ 1,28,500.00
$ 1,28,500.00
$ 5,875.00
$ 5,875.00
2
$ 2,50,000.00
$ 3,78,500.00
$ 8,770.00
$ 14,645.00
3
$ 3,53,000.00
$ 7,31,500.00
$ 13,235.00
$ 27,880.00
4
$ 43,99,000.00
$ 51,30,500.00
$ 9,669.00
$ 37,549.00
= 2 + $220,912 / $250,000
= 2 + 0.8
= 2.8 years
Step-2:
Calculation of Payback period for project B:
= 3 + $16,564 / $19,110
= 3 + 0.86
= 3.86 years
Step-3:
Calculation of discount payback period:
Years
Cash flow
Present value
Cf * Pv
Cumulative Cf
0
220912
1
$ 2,20,912.00
$ 2,20,912.00
1
$ 1,28,500.00
0.9433
$ 1,21,214.00
$ 99,698.00
2
$ 2,50,000.00
0.8899
$ 2,22,475.00
$ 1,22,777.00
3
$ 3,53,000.00
0.8396
$ 2,96,378.00
4
$ 43,99,000.00
0.792
$ 34,84,008.00
Discount Payback period = 1.45 years
Step-4:
Years
Cash flow
Pv
Cf * Pv
Cumulative Cf
0
16564
1
16564
16564
1
$ 5,875.00
0.9433
$ 5,542.00
$ 11,022.00
2
$ 8,770.00
0.8899
$ 7,804.00
$ 3,218.00
3
$ 13,235.00
0.8396
$ 11,112.00
7894
4
$ 9,669.00
0.792
$ 7,658.00
Discount Payback period:
= 2.29years.
Step-5:
Years
Cash flow
Present value
1
$ 1,28,500.00
121226.42
2
$ 2,50,000.00
222499.11
3
$ 3,53,000.00
296385.61
4
$ 43,99,000.00
3484420.02
Net present value
=$3,903,619.
Step-6:
Years
Cash flow
Present value
1
$ 5,875.00
$ 5,542.00
2
$ 8,770.00
$ 7,804.00
3
$ 13,235.00
$ 11,112.00
4
$ 9,669.00
$ 7,658.00
Net present value
= 15554.83
Years
Project A
Cumulative
Project B
Cumulative
1
$ 1,28,500.00
$ 1,28,500.00
$ 5,875.00
$ 5,875.00
2
$ 2,50,000.00
$ 3,78,500.00
$ 8,770.00
$ 14,645.00
3
$ 3,53,000.00
$ 7,31,500.00
$ 13,235.00
$ 27,880.00
4
$ 43,99,000.00
$ 51,30,500.00
$ 9,669.00
$ 37,549.00