Question

In: Finance

An investment project has annual cash inflows of $3,700, $4,600, $5,800, and $5,000, for the next...

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

Solutions

Expert Solution

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).


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