Question

Blue Hamster Manufacturing 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 from Project Sigma’s expected future cash flows. To answer this question, Blue Hamster’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. Round the payback period to the nearest two decimal places. Be sure to complete the entire table—even if the values exceed the point at which the cost of the project is recovered.

Year 0 $-4,500,000 ----- Year 1 $1,800,000 ---- Year 2 $3,825,000 ---- Year 3 $1,575,000

Expected cash flow:

Cumulative cash flow:

Conventional payback period: years The conventional payback period ignores the time value of money, and this concerns Blue Hamster’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 the nearest two decimal places. Again, be sure to complete the entire table—even if the values exceed the point at which the cost of the project is recovered.

Cash flow Year 0 $-4,500,000 ---- Year 1$1,800,000 --- Year 2 $3,825,000 --- Year 3 $1,575,000 ---

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

Answer 1

Cumulative cash flow is the sum of cash flows till date
Payback period is the time in which the initial investment is recovered
	Year 0	1	2	3
Expected Cash flow	-4,500,000	1,800,000	3,825,000	1,575,000
Cumulative cash flow	-4,500,000	-2,700,000	1,125,000	2,700,000
Conventional Payback period = 1 year + (2,700,000/3,825,000)
= 1.7059 years
	Year 0	1	2	3
Expected Cash flow	-4,500,000	1,800,000	3,825,000	1,575,000
Discount Factor @9%	1	0.917431	0.84168	0.77218348
Discounted Cash flow	-4,500,000	1,651,376	3,219,426	1,216,189
Cumulative cash flow	-4,500,000	-2,848,624	370,802	1,586,991
Discounted payback period = 1 + 2,848,624/3,219,426
= 1.8848 years
The discounted payback method