Question

An investment project has annual cash inflows of $5,000, $3,300, $4,500, and $3,700, for the next four years, respectively. The discount rate is 14 percent. a. What is the discounted payback period for these cash flows if the initial cost is $5,100? (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 $7,200? (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 $10,200? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) ſ years a. Discounted payback period b. Discounted payback period years c. Discounted payback period years

Answer 1

a

Project			Discount rate=	0.14
Year	Cash flow stream	Cumulative cash flow	Discounting factor	Discounted CF	Cumulative cash flow	Cumulative discounted CF
0	-5100	-5100	1	-5100	-5100	-5100
1	5000	-100	1.14	4385.965	-100	-714.035
2	3300	3200	1.2996	2539.243	3200	1825.208
3	4500	7700	1.481544	3037.372	7700	4862.58
4	3700	11400	1.68896	2190.697	11400	7053.277
Discounted payback period is the time by which discounted cashflow cover the intial investment outlay
this is happening between year 1 and 2
therefore by interpolation payback period = 1 + (0-(-714.04))/(1825.21-(-714.04))
1.28 Years
Where
Discounting factor =(1 + discount rate)^(corresponding year)
Discounted Cashflow=Cash flow stream/discounting factor
b
Project			Discount rate=	0.14
Year	Cash flow stream	Cumulative cash flow	Discounting factor	Discounted CF	Cumulative cash flow	Cumulative discounted CF
0	-7200	-7200	1	-7200	-7200	-7200
1	5000	-2200	1.14	4385.965	-2200	-2814.04
2	3300	1100	1.2996	2539.243	1100	-274.792
3	450000.00%	5600	1.481544	3037.372	5600	2762.58
4	3700	9300	1.68896	2190.697	9300	4953.277
Discounted payback period is the time by which discounted cashflow cover the intial investment outlay
this is happening between year 2 and 3
therefore by interpolation payback period = 2 + (0-(-274.79))/(2762.58-(-274.79))
2.09 Years
Where
Discounting factor =(1 + discount rate)^(corresponding year)
Discounted Cashflow=Cash flow stream/discounting factor
c
Project			Discount rate=	0.14
Year	Cash flow stream	Cumulative cash flow	Discounting factor	Discounted CF	Cumulative cash flow	Cumulative discounted CF
0	-10200	-10200	1	-10200	-10200	-10200
1	500000.00%	-5200	1.14	4385.965	-5200	-5814.04
2	3300	-1900	1.2996	2539.243	-1900	-3274.79
3	4500	2600	1.481544	3037.372	2600	-237.42
4	3700	6300	1.68896	2190.697	6300	1953.277
Discounted payback period is the time by which discounted cashflow cover the intial investment outlay
this is happening between year 3 and 4
therefore by interpolation payback period = 3 + (0-(-237.42))/(1953.28-(-237.42))
3.11 Years
Where
Discounting factor =(1 + discount rate)^(corresponding year)
Discounted Cashflow=Cash flow stream/discounting factor