Question

Cute Camel Woodcraft Company is a small firm, and several of its managers are worried about how soon the firm will be able to recover its initial investment from Project Sigma’s expected future cash flows. To answer this question, Cute Camel’s CFO has asked that you compute the project’s payback period using the following expected net cash flows and assuming that the cash flows are received evenly throughout each year.

Complete the following table and compute the project’s conventional payback period. For full credit, complete the entire table. (Note: Round the conventional payback period to two decimal places. If your answer is negative, be sure to use a minus sign in your answer.)

	Year 0	Year 1	Year 2	Year 3
Expected cash flow	-$5,000,000	$2,000,000	$4,250,000	$1,750,000
Cumulative cash flow
Conventional payback period:	years

The conventional payback period ignores the time value of money, and this concerns Cute Camel’s CFO. He has now asked you to compute Sigma’s discounted payback period, assuming the company has a 9% cost of capital. Complete the following table and perform any necessary calculations. Round the discounted cash flow values to the nearest whole dollar, and the discounted payback period to two decimal places. For full credit, complete the entire table. (Note: If your answer is negative, be sure to use a minus sign in your answer.)

	Year 0	Year 1	Year 2	Year 3
Cash flow	-$5,000,000	$2,000,000	$4,250,000	$1,750,000
Discounted cash flow
Cumulative discounted cash flow
Discounted payback period:	years

Which version of a project’s payback period should the CFO use when evaluating Project Sigma, given its theoretical superiority?

The discounted payback period

The regular payback period

One theoretical disadvantage of both payback methods—compared to the net present value method—is that they fail to consider the value of the cash flows beyond the point in time equal to the payback period.

How much value in this example does the discounted payback period method fail to recognize due to this theoretical deficiency?

$4,928,461

$1,763,323

$1,351,321

$3,186,183

Answer 1

Particulars	Year 0	Year 1	Year 2	Year 3
Expected cash flow	$(5,000,000)	$         2,000,000	$             4,250,000	$             1,750,000
Cumulative cash flow	$(5,000,000)	$       (3,000,000)	$             1,250,000	$             3,000,000
Conventional payback period			1.29
Particulars	Year 0	Year 1	Year 2	Year 3
Expected cash flow	$(5,000,000)	$         2,000,000	$             4,250,000	$             1,750,000
Discounted cash flow	$(5,000,000)	$         1,834,862	$             3,577,140	$             1,351,321
Working		=2000000/1.09	=4250000/1.09^2	=1750000/1.09^3
Discounted Cumulative cash flow	$(5,000,000)	$       (3,165,138)	$                412,002	$             1,763,323
Conventional payback period			1.12

Cumulative cash flow by year 3 is $1,763,323 which is ignored by discounted pay back period.

Answer is $1,763,323

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