Question

In: Finance

6) A cash flow involves an initial investment of $1, 000 and then generates $70 revenue...

6) A cash flow involves an initial investment of $1, 000 and then generates $70 revenue at the end of each year, starting one year after the initial $1, 000 investment. Find the payback period and discounted payback period (the latter at an effective annual rate of 4%.)

Expert Solution

Compute the payback period (PBP), using the equation as shown below:

PBP = Initial investment/ Annual cash flows

= $1,000/ $70

= 14.28 years

Hence, the PBP is 14.28 years.

Compute the discounted payback period, using MS-excel as shown below:

The result of the above-excel table is as follows:

The cash flows occur for an infinite period, but the investment will be recovered one day. The payback period determines on the basis of the present value of cash flows are considered as discounted payback period.

The present value of cumulative cash flows till 21st year is $982.0412 and the present value of cumulative cash flows till 22nd year is $1,011.5781. This means the investment will be recovered after 21 years but before 22 years.

Thus, the discounted payback period is:

Discounted payback period = 21 years + (Remaining investment/ Present value of cash flow at year 22)

= 21 years + {($1,000 - $982.0412)/ $29.5369}

= 21 years + 0.608 years

= 21.608 years

Hence, the discounted payback period is 21.608 years.

jeff jeffy answered 1 year ago

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