An investment project costs $10,000 and has annual cash flows of $2,890 for six

Question

An investment project costs $10,000 and has annual cash flows of $2,890 for six years.

What is the discounted payback period if the discount rate is 0 percent? (Enter 0 if the project never pays back. Do not round intermediate calculations and round your answer to 2 decimal places. (e.g., 32.16))

What is the discounted payback period if the discount rate is 4 percent? (Enter 0 if the project never pays back. Do not round intermediate calculations and round your answer to 2 decimal places. (e.g., 32.16))

What is the discounted payback period if the discount rate is 21 percent? (Enter 0 if the project never pays back. Do not round intermediate calculations and round your answer to 2 decimal places. (e.g., 32.16))

An investment project costs $10,000 and has annual cash flows of $2,890 for six years.

Explanation / Answer

To begin with let us be clear about discounted payback, there is time value of money. If discount rate is ten percent , it means if 110$ are earned in next year then it is equivalent to 100$ earned this year. If the discount rate is 0 (zero) it means money earned in all the years are valued at their face value.

In the first part of the question Investment is $10,000 and annual cashflows for six years $2,890

Therfore assuming given cashflows as net inflows for the six years = 2890 x 6 = $17,340

Payback Period = Period in which we recovered total investment

The above table shows that Investment of $10,000 is recovered (payback) between three and four years, means more than three years but less than four years. Exact period can be interpolated by calculating no. of months to recover $1330 at the end of third year = 12 /2890 x1330 = 5.52 months

Therefore Payback period is Three years six months approximately

In the other parts of the question discount rate is not zero, therefore we are required to appropriate the values of inflows with the discount rates as follows:

From the above table The payback period is between thrird and fourth year that is more than three years and less than four years. This time because of discount factor of 4% the amount remaining at the end of third year is $1659.18 as compared to earlier one of $1330. Thus now number of months will increase to = 12 / 2569.2 x 1659.18 = 7.75

Now the discounted payback period is three years eight months approximately.

Similarlly in the third part the inflows have to be discounted with rate 21% which means $121 of next year are equated to $100 of this year.

The discounted inflows are calculated as 2890, 2388.43, 1973.91, 1631.33, 1348.21 and 1114.22

and corresponding net figures are -7110, -4721.57, -2747.66, -1116.33, 231.87, 1346.09

Hence now discounted payback period is more than four years and less than five years.

In fact after interpolation it works out to be four years ten months approximately.

year investment inflow net =inflow-outflow 1 10000 2890 -7110 2 2890 -4220 3 2890 -1330 4 2890 1560 5 2890 4450 6 2890 7340

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