Question

An investment project costs $17,400 and has annual cash flows of $4,400 for 6 years. If the discount rate is zero percent, the discounted payback period is __x__ years. If the discount rate is 4 percent, the discounted payback period is __y__ years. If the discount rate is 22 percent, the discounted payback period is __z__ years. (Enter 0 when there is no payback period. Round your answers to 2 decimal places. (e.g., 32.16))

What are the values for x, y and z?

Answer 1

(x)-Discount Payback Period if the discount rate is Zero Percent

Discount Payback Period = Initial Investment / Annual Cash Inflow

= $17,400 / $4,400

= 3.95 Years

(y)-Discount Payback Period if the discount rate is 4%

Year	Cash Flows ($)	Present Value Factor at 4%	Discounted Cash Flow ($)	Cumulative net discounted Cash flow ($)
0	-17,400	1.00000	-17,400.00	-17,400.00
1	4,400	0.96154	4,230.77	-13,169.23
2	4,400	0.92456	4,068.05	-9,101.18
3	4,400	0.88900	3,911.58	-5,189.60
4	4,400	0.85480	3,761.14	-1,428.46
5	4,400	0.82193	3,616.48	2,188.02
6	4,400	0.79031	3,477.38	5,665.40

Discounted Payback = Years before full recover + (Unrecovered cash inflow at start of the year/cash flow during the year)

= 4 Year + ($1,428.46 / $3,616.48)

= 4 Year + 0.39

= 4.39

Years

(z)-Discount Payback Period if the discount rate is 22%

Year	Cash Flows ($)	Present Value Factor at 22%	Discounted Cash Flow ($)	Cumulative net discounted Cash flow ($)
0	-17,400	1.00000	-17,400.00	-17,400.00
1	4,400	0.81967	3,606.56	-13,793.44
2	4,400	0.67186	2,956.19	-10,837.25
3	4,400	0.55071	2,423.11	-8,414.14
4	4,400	0.45140	1,986.16	-6,427.98
5	4,400	0.37000	1,628.00	-4,799.99
6	4,400	0.30328	1,334.42	-3,465.56
TOTAL			13,934.44

With the discount rate of 22%, The Project will not payback within 6 years. Therefore, The Discounted payback period is calculated as follows

= Initial Investment / Average Discounted cash flow

= $17,400 / ($13,934.44 / 6 Years)

= $17,400 / $2,322.41

= 7.49 Years

FINAL ANSWERS

Value of X = 3.95 Years

Value of Y = 4.39 Years

Value of X = 7.49 Years