Problem 9-4 Calculating Discounted Payback [LO3] An investment project has annua

Question

Problem 9-4 Calculating Discounted Payback [LO3]

An investment project has annual cash inflows of $4,800, $3,500, $4,700, and $3,900, and a discount rate of 15 percent.

What is the discounted payback period for these cash flows if the initial cost is $5,300? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

What is the discounted payback period for these cash flows if the initial cost is $7,400? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

What is the discounted payback period for these cash flows if the initial cost is $10,400? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

An investment project has annual cash inflows of $4,800, $3,500, $4,700, and $3,900, and a discount rate of 15 percent.

Explanation / Answer

for 5300,

amount left after year 1 is 5300 - 4800 / 1.15 = 1126.09

present value of 3500 is 3500/1.15^2 = 2646.5

Hence discounted payback period is 1 + 1126.09 / 2646.5 = 1.43

for 7400

amount after 2 years is 7400 - 4800/1.15 - 3500 / 1.15^2 = 579.58

present value of 4700 is 4700 / 1.15^3 = 3090.33

discounted payback period is 2 + 579.58 / 3090.33 = 2.19

for 10400

amount after 3 years is 10400 - 4800/1.15 - 3500 / 1.15^2 - 4700 / 1.15^3 = 489.26

present value of 3900 = 3900 / 1.15^4 = 2229.84

discounted payback period is 3 + 489.26 / 2229.84 = 3.22

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