Question
In: Finance
A company is considering two alternative methods of producing a new product. The relevant data concerning...
| A company is considering two alternative methods of producing a new product. The relevant data concerning the alternatives appear below: | ||||||||
| Alternative | Alternative | |||||||
| I | II | |||||||
| Initial investment | $64,000 | $120,000 | ||||||
| Annual receipts | $50,000 | $60,000 | ||||||
| Annual disbursements | $20,000 | $12,000 | ||||||
| Annual depreciation | $16,000 | $20,000 | ||||||
| Expected life | 4 yrs | 6 yrs | ||||||
| Salvage value | 0 | 0 | ||||||
| At the end of the useful life of whatever equipment is chosen the product will be discontinued. The company's tax rate is 50 percent and the discount rate is 10 percent. | ||||||||
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a. Calculate the net present value of each alternative. |
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b. Calculate the benefit cost ratio for each alternative. |
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c. Calculate the internal rate of return for each alternative. |
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d. If the company is not under capital rationing which alternative should be chosen? Why? |
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| e. Again assuming no capital rationing, suppose the company plans to produce the product indefinitely rather than quit when the equipment wears out. Which alternative should the company select? Why? | ||||||||
| f. If the company is experiencing severe capital rationing, and plans to terminate production when the equipment wears out, would any of your answers above change? | ||||||||
Solutions
Expert Solution
a. Calculate the net present value of each alternative @ Discount rate of 10% is as follows
Calculation of Discount Rates
1-4 - Annuity Factor = 1/(1+r)^4 = 1/ (1.1) ^ 4 = 3.1699
1-6 - Annuity Factor = 1/(1+r)^6 = 1/ (1.1) ^ 6 = 4.3553
NPV for Project I
| Year/s | Cash Flow | Cash In / (Out) | Tax @ 50% | Cash Flow After Tax | Discount Rate @10% | Discounted Cash Flow |
| 0 | Initial | (64,000.00) | NA | (64,000.00) | 1.00 | (64,000.00) |
| 1-4 | Annual Receipts | 50,000.00 | 25,000.00 | 25,000.00 | 3.1699 | 79,247.50 |
| 1-4 | Annual disbursements | (20,000.00) | (10,000.00) | (10,000.00) | 3.1699 | (31,699.00) |
| 1-4 | Tax savings on Depreciation | 16,000.00 | 8,000.00 | 8,000.00 | 3.1699 | 25,359.20 |
| NPV | 8,907.70 |
NPV for Project II
| Year/s | Cash Flow | Cash In / (Out) | Tax @ 50% | Cash Flow After Tax | Discount Rate @10% | Discounted Cash Flow |
| 0 | Initial | (120,000.00) | NA | (120,000.00) | 1.00 | (120,000.00) |
| 1-6 | Annual Receipts | 60,000.00 | 30,000.00 | 30,000.00 | 4.3553 | 130,659.00 |
| 1-6 | Annual disbursements | (12,000.00) | (6,000.00) | (6,000.00) | 4.3553 | (26,131.80) |
| 1-6 | Tax savings on Depreciation | 20,000.00 | 10,000.00 | 10,000.00 | 4.3553 | 43,553.00 |
| NPV | 28,080.20 |
b. Calculate the benefit cost ratio for each alternative
for Project I
| Year | Cash Flow | Cash In / (Out) | Tax @ 50% | Cash Flow After Tax | Discount Rate @10% | Discounted Cash Flow |
| Cost | ||||||
| 0 | Initial | 64,000.00 | NA | 64,000.00 | 1.0000 | 64,000.00 |
| 1-4 | Annual disbursements | 20,000.00 | 10,000.00 | 10,000.00 | 3.1699 | 31,699.00 |
| Discounted Cost | 95,699.00 | |||||
| Benefit | ||||||
| 1-4 | Annual Receipts | 50,000.00 | 25,000.00 | 25,000.00 | 3.1699 | 79,248.00 |
| 1-4 | Tax savings on Depreciation | 16,000.00 | 8,000.00 | 8,000.00 | 3.1699 | 25,359.00 |
| Discounted Benefit | 104,607.00 | |||||
| The Benefit Cost is calculated by dividing the total discounted value of benefits by the total discounted value of cost | ||||||
| Therefore | 1.0931 | 104607 / 95699 | ||||
for project II
| Year | Cash Flow | Cash In / (Out) | Tax @ 50% | Cash Flow After Tax | Discount Rate @10% | Discounted Cash Flow |
| Cost | ||||||
| 0 | Initial | 120,000.00 | NA | 120,000.00 | 1.0000 | 120,000.00 |
| 1-6 | Annual disbursements | 12,000.00 | 6,000.00 | 6,000.00 | 4.3553 | 26,132.00 |
| Discounted Cost | 146,132.00 | |||||
| Benefit | ||||||
| 1-6 | Annual Receipts | 60,000.00 | 30,000.00 | 30,000.00 | 4.3553 | 130,659.00 |
| 1-6 | Tax savings on Depreciation | 20,000.00 | 10,000.00 | 10,000.00 | 4.3553 | 43,553.00 |
| Discounted Benefit | 174,212.00 | |||||
| The Benefit Cost is calculated by dividing the total discounted value of benefits by the total discounted value of cost | ||||||
| Therefore | 1.1922 | 174212 / 146132 | ||||
c. Calculate the internal rate of return for each alternative.
The internal rate of return on an investment or project is the the net present value of all cash flows (both positive and negative) from the investment equal to zero
The Discounted Cash Flow for Project I @ 10% = 8,907.7
The Discounted Cash Flow for Project I @ 16.28% = 0
Therefore the IRR = 16.28%
The Discounted Cash Flow for Project II @ 10% = 28,080
The Discounted Cash Flow for Project II @ 17.649% = 0
Therefore the IRR = 17.649%
d. If the company is not under capital rationing which alternative should be chosen
The Project II is the best alternative because it has the highest NPV, Benefit cost ratio and also IRR
jeff jeffy answered 2 years agoRelated Solutions
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