Question

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

Answer 1

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).