Question

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

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

Solutions

Expert Solution

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


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