Question

6. The payback period The payback method helps firms establish and identify a maximum acceptable payback period that helps in their capital budgeting decisions. Consider the case of Green Caterpillar Garden Supplies Inc.: Green Caterpillar Garden Supplies 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 Alpha’s expected future cash flows. To answer this question, Green Caterpillar’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 -$4,500,000 $1,800,000 $3,825,000 $1,575,000 Cumulative cash flow $ $ $ $ Conventional payback period: years The conventional payback period ignores the time value of money, and this concerns Green Caterpillar’s CFO. He has now asked you to compute Alpha’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.)

The conventional payback period ignores the time value of money, and this concerns Green Caterpillar’s CFO. He has now asked you to compute Alpha’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	-$4,500,000	$1,800,000	$3,825,000	$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 Alpha, given its theoretical superiority?

The regular payback period

The discounted 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?

Answer 1

Project’s conventional payback period

	Year 0	Year 1	Year 2	Year 3
Expected cash flow	-$45,00,000	$18,00,000	$38,25,000	$15,75,000
Cumulative cash flow	-$45,00,000	-$27,00,000	$11,25,000	$27,00,000
Conventional payback period:	1.71 Years

Project’s conventional payback period = Years before full recover + (Unrecovered cash inflow at start of the year/cash flow during the year)

= 1.00 Year + ($27,00,000 / $38,25,000)

= 1.00 Year + 0.71 Years

= 1.71 Years

Project’s Discounted payback period

	Year 0	Year 1	Year 2	Year 3
Cash flow	-45,00,000	18,00,000	38,25,000	15,75,000
Discounted cash flow	-45,00,000	16,51,376	32,19,426	12,16,189
Cumulative discounted cash flow	-45,00,000	-28,48,624	3,70,802	15,86,991
Discounted payback period:	1.88 Years

Project’s Discounted payback period = Years before full recover + (Unrecovered cash inflow at start of the year/cash flow during the year)

= 1.00 Year + ($28,48,624 / $32,19,426)

= 1.00 Year + 0.88 Years

= 1.88 Years

DECISION

CFO must use the “Discounted Payback Period” while evaluating Project Alpha, since it takes the concept of Time Value of money while for discounting the annual cash inflows.

The amount cash flow that the discounted payback period method fails to recognize due to this theoretical deficiency

Therefore, the value that the discounted payback period method fails to recognize = Total Present value of cash inflows - Total cash outflow

= [$16,51,376 + $32,19,426 + $12,16,189] - $45,00,000

= $60,86,991 - $45,00,000

= $15,86,991

WORKINGS

Calculation of Discounted cash flow

Year	Cash Flows ($)	Present Value Factor at 9.00%	Discounted Cash Flow ($)
1	18,00,000	0.9174312	16,51,376
2	38,25,000	0.8416800	32,19,426
3	15,75,000	0.7721835	12,16,189

NOTE    

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.