Consider the following projects: CASH FLOWS ($) PROJECT C_0 C_1 C_2 C_3 C_4 C_5
ID: 2669362 • Letter: C
Question
Consider the following projects:
CASH FLOWS ($)
PROJECT C_0 C_1 C_2 C_3 C_4 C_5
A -1000 +1000 0 0 0 0
B -2000 +1000 +1000 +4000 +1000 +1000
C -3000 +1000 +1000 0 +1000 +1000
If the opportunity cost of capital is %10, which projects have a positive NPV?
Calculate the payback period for each project.
Which project(s) would a firm using the payback rule accept if the cutoff period were three years?
Calculate the discounted payback period for each period.
Which project(s) would a firm using the discounted payback rule accept if the cutoff period were three years?
Explanation / Answer
For project A:
Pay back period means the period at which all earnings are pay back itself is known as payback period.
Year
Cash flows($)
Cumulative cash flows($)
0
-1,000
-1,000
1
1000
0
2
0
3
0
4
0
5
0
Here, the cash flow is payback at the end of the 1st year. Therefore payback period is 1 year.
For project B:
Year
Cash flows($)
Cumulative cash flows($)
0
-2,000
-2,000
1
1,000
-1,000
2
1,000
0
3
4,000
4
1,000
5
1,000
The cash flows are payback itself at the end of the 2nd year. Therefore, Payback period is 2 years.
For project C:
Year
Cash flows($)
Cumulative cash flows($)
0
-3,000
-3,000
1
1,000
-2,000
2
1,000
-1,000
3
0
-1,000
4
1,000
0
5
1,000
Year
Cash flows($)
Present value factor at 10%
Discounted cash flows($)
Cumulative DCF
0
-1,000
1
-1,000
-1,000
1
1,000
0.9091
909.1
-91
2
0
0.8264
0
-91
3
0
0.7513
0
-91
4
0
0.6830
0
-91
5
0
0.6290
0
-91
For this project there is no payback period. Because there are no cash flows to payback.
For Project B:
Year
Cash flows($)
Present value factor at 10%
Discounted cash flows($)
Cumulative DCF
0
-2,000
1
-1,000
-1,000
1
1,000
0.9091
909.1
-91
2
1,000
0.8264
826.4
736
3
4,000
0.7513
3005.2
3,741
4
1,000
0.6830
683
4,424
5
1,000
0.6290
629
5,053
Year before recovery is = 2.
Remaining Years = (826.4 – 736)/826.4
= 0.11
Payback period is 2.11 years.
For project C:
Year
Cash flows($)
Present value factor at 10%
Discounted cash flows($)
Cumulative DCF
0
-3,000
1
-1,000
-3,000
1
1,000
0.9091
909.1
-2,091
2
1,000
0.8264
826.4
-1,265
3
0
0.7513
0
-1,265
4
1,000
0.6830
683
-582
5
1,000
0.6290
629
48
Year before recovery is = 4.
Remaining years calculation = (629 – 48)/629
Year
Cash flows($)
Cumulative cash flows($)
0
-1,000
-1,000
1
1000
0
2
0
3
0
4
0
5
0