In: Finance
An investment project has annual cash inflows of $3,700, $4,600, $5,800, and $5,000, for the next four years, respectively. The discount rate is 13 percent.
What is the discounted payback period for these cash flows if the initial cost is $6,400? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
Discounted payback period ______ years
What is the discounted payback period for these cash flows if the initial cost is $8,500? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
Discounted payback period ______ years
What is the discounted payback period for these cash flows if the initial cost is $11,500? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
Discounted payback period ______ years
At $6400:
Year | Cash flows | Present value@13% | Cumulative Cash flows |
0 | (6400) | (6400) | (6400) |
1 | 3700 | 3274.34 | (3125.66) |
2 | 4600 | 3602.47 | 476.81 |
3 | 5800 | 4019.69 | 4496.5 |
4 | 5000 | 3066.59 | 7563.09 |
Hence discounted Payback period=Last period with a negative cumulative cash flow+(Absolute value of cumulative cash flows at that period/Cash flow after that period).
=1+(3125.66/3602.47)=1.87 years(Approx).
At $8500:
Year | Cash flows | Present value@13% | Cumulative Cash flows |
0 | (8500) | (8500) | (8500) |
1 | 3700 | 3274.34 | (5225.66) |
2 | 4600 | 3602.47 | (1623.19) |
3 | 5800 | 4019.69 | 2396.5 |
4 | 5000 | 3066.59 | 5463.09 |
Hence discounted Payback period=Last period with a negative cumulative cash flow+(Absolute value of cumulative cash flows at that period/Cash flow after that period).
=2+(1623.19/4019.69)=2.40 years(Approx).
At $11500:
Year | Cash flows | Present value@13% | Cumulative Cash flows |
0 | (11500) | (11500) | (11500) |
1 | 3700 | 3274.34 | (8225.66) |
2 | 4600 | 3602.47 | (4623.19) |
3 | 5800 | 4019.69 | (603.5) |
4 | 5000 | 3066.59 | 2463.09 |
Hence discounted Payback period=Last period with a negative cumulative cash flow+(Absolute value of cumulative cash flows at that period/Cash flow after that period).
=3+(603.5/3066.59)=3.20 years(Approx).