Question

An investment project has annual cash inflows of $3,700, $4,600, $5,800, and $5,000, and a discount rate of 13 percent.

a.	What is the discounted payback period for these cash flows if the initial cost is $6,400? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b.	What is the discounted payback period for these cash flows if the initial cost is $8,500? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
c.	What is the discounted payback period for these cash flows if the initial cost is $11,500? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

(a)-Discounted payback period for these cash flows if the initial cost is $6,400

Year	Cash Flows ($)	Present Value Factor at 13%	Discounted Cash Flow ($)	Cumulative net discounted Cash flow ($)
0	-6,400	1.000000	-6,400.00	-6,400.00
1	3,700	0.884956	3,274.34	-3,125.66
2	4,600	0.783147	3,602.47	476.81
3	5,800	0.693050	4,019.69	4,496.50
4	5,000	0.613319	3,066.59	7,563.10

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

= 1.00 Year + ($3,125.66 / $3,602.47)

= 1.00 Year + 0.87 Years

= 1.87 Years

(b)-Discounted payback period for these cash flows if the initial cost is $8,500

Year	Cash Flows ($)	Present Value Factor at 13%	Discounted Cash Flow ($)	Cumulative net discounted Cash flow ($)
0	-8,500	1.000000	-8,500.00	-8,500.00
1	3,700	0.884956	3,274.34	-5,225.66
2	4,600	0.783147	3,602.47	-1,623.19
3	5,800	0.693050	4,019.69	2,396.50
4	5,000	0.613319	3,066.59	5,463.10

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

= 2.00 Year + ($1,623.19 / $4,019.69)

= 2.00 Year + 0.40 Years

= 2.40 Years

(c)-Discounted payback period for these cash flows if the initial cost is $11,500

Year	Cash Flows ($)	Present Value Factor at 13%	Discounted Cash Flow ($)	Cumulative net discounted Cash flow ($)
0	-11,500	1.000000	-11,500.00	-11,500.00
1	3,700	0.884956	3,274.34	-8,225.66
2	4,600	0.783147	3,602.47	-4,623.19
3	5,800	0.693050	4,019.69	-603.50
4	5,000	0.613319	3,066.59	2,463.10

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

= 3.00 Year + ($603.50 / $3,066.59)

= 3.00 Year + 0.20 Years

= 3.20 Years

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.