Homework SourseConsider the mixed streams of cash flows shown in the follow
Consider the mixed streams of cash flows shown in the following? table
1)Find the present value of each stream using a 16?%discount rate.
2)?Compare the calculated present values and discuss them in light of the undiscounted cash flows totaling ?$175,000 in each case
1 $52,500 $17,500
2 $43,750 $26,250
3 $35,000 $35,000
4 $26,250 $43,750
5 $17,500 $52,500
Totals $175,000 $175,000
Solution
Cash flow 1:
Year
Cash flows = CF
Discount factor = Df = 1/(1+16%)^Year
Present Value = CF x Df
1
52,500
0.862069
45,258.62
2
43,750
0.743163
32,513.38
3
35,000
0.640658
22,423.02
4
26,250
0.552291
14,497.64
5
17,500
0.476113
8,331.98
Total of Present Value =
123,024.64
Cash flow 2:
Year
Cash flows = CF
Discount factor = Df = 1/(1+16%)^Year
Present Value = CF x Df
1
17,500
0.862069
15,086.21
2
26,250
0.743163
19,508.03
3
35,000
0.640658
22,423.02
4
43,750
0.552291
24,162.74
5
52,500
0.476113
24,995.93
Total of Present Value =
106,175.92
Present value of Cash flow 1 i.e. 123,024.64 is more than the present value of Cash flow 2 i.e. 106,175.92
The cash flows in totality are same but Present Values differ. The difference occurs because the cash flow 1 has major cash flows which falls in early years compared to the Cash flow 2. The discounting factor reduces the intensity of the cash flow as cash flow goes far in future. Hence, we are observing different present values for the cash flows having same total amount of cash flows.
| Year | Cash flows = CF | Discount factor = Df = 1/(1+16%)^Year | Present Value = CF x Df |
| 1 | 52,500 | 0.862069 | 45,258.62 |
| 2 | 43,750 | 0.743163 | 32,513.38 |
| 3 | 35,000 | 0.640658 | 22,423.02 |
| 4 | 26,250 | 0.552291 | 14,497.64 |
| 5 | 17,500 | 0.476113 | 8,331.98 |
| Total of Present Value = | 123,024.64 |
