Question

Cold Goose Metal Works Inc. is a small firm, and several of its managers are worried about how soon the firm will be able to recover its initial investment form Project Alpha’s expected future cash flows. To answer this question, Cold Goose’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 even.ly throughout each year.

Complete the following table and compute the project’s conventional payback period. For full credit, complete the entire table.

	year 0	year 1	year 2	year 3
expected cash flow	-6,000,000	$2,400,000	$5,100,000	$2,100,000
comulative cash flow	???	???	???	???
conventional payback period	???

The conventional payback period ignores the time value of money, and this concerns Cold Goose’s CFO. He has now asked you to compute Alpha’s discounted payback period, assuming the company has a %10 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 the nearest two decimal places. For full credit, compete the entire table.

	Year 0	year 1	year 2	year 3
cash flow	-6,000,000	$2,400,000	$5,100,000	$2,100,000
discounted cash flow	???	???	???	???
cumulative discounted cash flow	???	???	???	???
discounted payback period	???

Answer 1

Calculation of payback period
Year	Annual Cash flow	Cumulative cash flows
0	(6,000,000)	(6,000,000)
1	2,400,000	(3,600,000)
2	5,100,000	1,500,000
3	2,100,000	3,600,000
	So payback period will lie in 2nd year
	Payback period	=1+(3600000/5100000)
	Year	1.71
Calculation of Discountedpayback period
Year	Annual Cash flow	PV factor @ 10%	Present values	Cumulative Present values
0	(6,000,000)	1.000	(6,000,000)	(6,000,000)
1	2,400,000	0.909	2,181,818	(3,818,182)
2	5,100,000	0.826	4,214,876	396,694
3	2,100,000	0.751	1,577,761	1,974,455
	So payback period will lie in 2nd year
	Payback period	=1+(3818182/4214876)
	Year	1.91