An investment project has annual cash inflows of $4,500, $3,800, $5,000, and $4,

Question

An investment project has annual cash inflows of $4,500, $3,800, $5,000, and $4,200, and a discount rate of 15 percent. What is the discounted payback period for these cash flows if the initial cost is $5,600? (Do not round intermediate calculations and round your final 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 $7,700? (Do not round intermediate calculations and round your final 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 $10,700? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) Discounted payback period years

Explanation / Answer

Solution :

a. when we use discounted payback. we need to find the value of all cash flows today. The value today of the project cash flows for the first four year is:

Value today of year 1 cash flow =$4500/1.15 = $3913.04

Value today of year 2 cash flow = $3800/(1.15x1.15) = $2873.35

Value today of year 3 cash flow = $5000/(1.15x1.15x1.15) = $3287.58

Value today of year 4 cash flow = $4200/(1.15x1.15x1.15) = $2401.36

a. For an initial cost of $5600 the discounted payback is

Discounted payback = 1 + ($5600 - 3913.04)/$2873.35 = 1.59 years

b. For an initial cost of $7700 the discounted payback is :

Discounted payback = 2 + ($7700 - 3913.04 - 2873.35)/$3287.58 = 2.28 years

c. For initial cost of $10700 the discounted pay back is

Discounted payback = 3 + ($10700 - 3913.04 - 2873.35 - 3287.58)/$2401.36 = 3.26 years

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