Question
In: Finance
An investment project costs $18,700 and has annual cash flows of $4,000 for six years. Required...
An investment project costs $18,700 and has annual cash flows of $4,000 for six years. Required : (a) What is the discounted payback period if the discount rate is zero percent? (b) What is the discounted payback period if the discount rate is 6 percent? (c) What is the discounted payback period if the discount rate is 22 percent?
Solutions
Expert Solution
Answer :
a) 4.68 Years
b) 5.66 Years
c) Never
Notes:
a) Discounted Payback Period =
( Last Year with a Negative Cumulative Cash Flow ) + [( Absolute Value of negative Cumulative Cash Flow in that year)/ Total Present Cash Flow in the following year)]
At Zero Percent :
Discounted Payback Period =
= 4+(2700/4000)
= 4.68 Years
Working:
| Cash Flow | Discounting Factor ( 0%) | Present Value (Cash Flow * Discounting Factor) | Cumulative Cash Flow (Present Value of Current Year+ Cumulative Cash Flow of Previous Year) | |
| 0 | -18,700 | 1 | -18,700.00 | -18,700.00 |
| 1 | 4,000 | 1.0000 | 4,000.00 | -14,700.00 |
| 2 | 4,000 | 1.0000 | 4,000.00 | -10,700.00 |
| 3 | 4,000 | 1.0000 | 4,000.00 | -6,700.00 |
| 4 | 4,000 | 1.0000 | 4,000.00 | -2,700.00 |
| 5 | 4,000 | 1.0000 | 4,000.00 | 1,300.00 |
| 6 | 4,000 | 1.0000 | 4,000.00 | 5,300.00 |
b) At 6% ,
Discounted Payback Period =
( Last Year with a Negative Cumulative Cash Flow ) + [( Absolute Value of negative Cumulative Cash Flow in that year)/ Total Present Cash Flow in the following year)]
= 5+(1850.54/2819.84)
= 5.66 years
Working :
| Cash Flow | Discounting Factor ( 6%) | Present Value (Cash Flow * Discounting Factor) | Cumulative Cash Flow (Present Value of Current Year+ Cumulative Cash Flow of Previous Year) | |
| 0 | -18,700 | 1 | -18,700.00 | -18,700.00 |
| 1 | 4,000 | 0.9434 | 3,773.58 | -14,926.42 |
| 2 | 4,000 | 0.8900 | 3,559.99 | -11,366.43 |
| 3 | 4,000 | 0.8396 | 3,358.48 | -8,007.95 |
| 4 | 4,000 | 0.7921 | 3,168.37 | -4,839.58 |
| 5 | 4,000 | 0.7473 | 2,989.03 | -1,850.54 |
| 6 | 4,000 | 0.7050 | 2,819.84 | 969.30 |
c) At 22% ,
Discounted Payback Period =
( Last Year with a Negative Cumulative Cash Flow ) + [( Absolute Value of negative Cumulative Cash Flow in that year)/ Total Present Cash Flow in the following year)]
= Never
Working :
| Cash Flow | Discounting Factor ( 6%) | Present Value (Cash Flow * Discounting Factor) | Cumulative Cash Flow (Present Value of Current Year+ Cumulative Cash Flow of Previous Year) | |
| 0 | -18,700 | 1 | -18,700.00 | -18,700.00 |
| 1 | 4,000 | 0.8197 | 3,278.69 | -15,421.31 |
| 2 | 4,000 | 0.6719 | 2,687.45 | -12,733.86 |
| 3 | 4,000 | 0.5507 | 2,202.83 | -10,531.03 |
| 4 | 4,000 | 0.4514 | 1,805.60 | -8,725.44 |
| 5 | 4,000 | 0.3700 | 1,480.00 | -7,245.44 |
| 6 | 4,000 | 0.3033 | 1,213.11 | -6,032.33 |
jeff jeffy answered 3 years agoRelated Solutions
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