Question

An investment project has annual cash inflows of $4,200, $5,300, $6,100, and $7,400, and a discount rate of 14%.

What is the discounted payback period for these cash flows if the initial cost is $7,000? (Do not round intermediate calculations. Round the final answer to 2 decimal places.)

Discounted payback period             years

What is the discounted payback period for these cash flows if the initial cost is $10,000? (Do not round intermediate calculations. Round the final answer to 2 decimal places.)

Discounted payback period             years

What is the discounted payback period for these cash flows if the initial cost is $13,000? (Do not round intermediate calculations. Round the final answer to 2 decimal places.)

Discounted payback period             years

Answer 1

The Discounted Payback Period (or DPP) is X + Y/Z Here • X = is the last time period where the cumulative discounted cash flow (CCF) was negative • Y = is the absolute value of the CCF at the end of that period X • Z = is the value of the DCF in the next period after X

Calculation of the Discounted payback period IF initial investment is $ 7000

Cumulative cash flows :-

Particulars	CF	PVF@14%	Discounted CF	Cumualtive DCF
Year 0	-7000	1	-7000	-7000
Year 1(x)	4200	0.877193	3684.210526	-3315.79(y)
Year 2	5300	0.769468	4078.177901(Z)	762.3884
Year 3	6100	0.674972	4117.326249	4879.715
Year 4	7400	0.59208	4381.394053	9261.109

Discounted payback period if initial investment is $ 7000 = 1years + 3315.79 /4078.177901 = 1 + 0.8130566 = 1.81 years

Calculation of the Discounted payback period IF initial investment is $ 10,000

Cumulative cash flows :-

Particulars	CF	PVF@14%	Discounted CF	Cumualtive DCF
Year 0	-10000	1	-10000	-10000
Year 1	4200	0.877193	3684.210526	-6315.79
Year 2(x)	5300	0.769468	4078.177901	-2237.61(y)
Year 3	6100	0.674972	4117.326249(z)	1879.715
Year 4	7400	0.59208	4381.394053	6261.109

Discounted payback period if initial investment is $ 10,000= 2years + 2237.61/4117.326249 = 2 + 0.5434623 = 2.54 years

Calculation of the Discounted payback period IF initial investment is $ 13,000

Cumulative cash flows :-

Particulars	CF	PVF@14%	Discounted CF	Cumualtive DCF
Year 0	-13,000	1	-13000	-13000
Year 1	4200	0.877193	3684.210526	-9315.79
Year 2	5300	0.769468	4078.177901	-5237.61
Year 3(X)	6100	0.674972	4117.326249	-1120.29(Y)
Year 4	7400	0.59208	4381.394053(Z)	3261.109

Discounted payback period if initial investment is $ 13,000= 3years + 1120.29/4381.394053 = 3+ 0.2546915 = 3.26years