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 Cute Camel Woodcraft Company: 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 Alpha'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 o Year 1 Year 3 Year 2 $3,825,000 -$4,500,000 $1,800,000 $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 Cute Camel's CFO. He has now asked you to compute Alpha's discounted payback period, assuming the company has a 8% 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.)

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	16,66,667	32,79,321	12,50,286
Cumulative discounted cash flow	-45,00,000	-28,33,333	4,45,988	16,96,273
Discounted payback period:	1.86 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 + ($28,33,333 / $32,79,321)

= 1.00 Year + 0.86 Years

= 1.86 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

= [$16,66,667 + $32,79,321 + $12,50,286] - $45,00,000

= $61,96,274 - $45,00,000

= $16,96,274

  

WORKINGS

Calculation of Discounted cash flow

Year	Cash Flows ($)	Present Value Factor at 8.00%	Discounted Cash Flow ($)
1	18,00,000	0.9259259	16,66,667
2	38,25,000	0.8573388	32,79,321
3	15,75,000	0.7938322	12,50,286

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.