An investment project has annual cash inflows of $4,900, $3,400, $4,600, and $3,

Question

An investment project has annual cash inflows of $4,900, $3,400, $4,600, and $3,800, 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 $5,200? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

  

What is the discounted payback period for these cash flows if the initial cost is $7,300? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

  

What is the discounted payback period for these cash flows if the initial cost is $10,300? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

An investment project has annual cash inflows of $4,900, $3,400, $4,600, and $3,800, for the next four years, respectively. The discount rate is 13 percent.

Explanation / Answer

To calculate the payback period, we need to calculate the value of annual and cumulative discounted cash flows as follows:

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Part A)

The discounted payback period can be calculated with the use of following formula:

Discounted Payback Period = Years upto which Partial Recovery is Made + Balance Amount/Discounted Cash Flow of the Year in which Full Recovery is Made

It can be seen from the above table (cumulative discounted cash flow column) that the initial investment of $5,200 will get recovered between Year 1 and Year 2. The discounted payback eriod is calculated as follows:

Discounted Payback Period = 1 + (5,200 - 4,336.28)/2,662.70 = 1.32 Years

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Part B)

The discounted payback period can be calculated with the use of following formula:

Discounted Payback Period = Years upto which Partial Recovery is Made + Balance Amount/Discounted Cash Flow of the Year in which Full Recovery is Made

It can be seen from the above table (cumulative discounted cash flow column) that the initial investment of $7,300 will get recovered between Year 2 and Year 3. The discounted payback eriod is calculated as follows:

Discounted Payback Period = 2 + (7,300 - 6,998.98)/3,188.03 = 2.09 Years

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Part C)

The discounted payback period can be calculated with the use of following formula:

Discounted Payback Period = Years upto which Partial Recovery is Made + Balance Amount/Discounted Cash Flow of the Year in which Full Recovery is Made

It can be seen from the above table (cumulative discounted cash flow column) that the initial investment of $10,300 will get recovered between Year 3 and Year 4 . The discounted payback eriod is calculated as follows:

Discounted Payback Period = 3 + (10,300 - 10,187.01)/2,330.61 = 3.05 Years

Year Annual Cash Flow Discounted Cash Flow (Annual Cash Flow/(1+Discount Rate)^Years) Cumulative Discounted Cash Flow 1 4,900 4,336.28 (4,900/(1+13%)^1) 4,336.28 2 3,400 2,662.70 (3,400/(1+13%)^2) 6,998.98 3 4,600 3,188.03 (4,600/(1+13%)^3) 10,187.01 4 3,800 2,330.61 (3,800/(1+13%)^4) 12,517.62

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