A farmer is considering the purchase of a sprinkler system. He can choose to buy

Question

A farmer is considering the purchase of a sprinkler system. He can choose to buy system A or system B. Sprinkler A and B provide the same service so revenues can be ignored. The sprinkler system A costs $37,000, has a before-tax net return of -$5,900, has a life of 7 years, and a terminal value of $12,600. Sprinkler system B costs $24,500, has a before-tax net return of -$7,000, has a life of 6 years, and a terminal value of $9,500. Suppose that the pre-tax rate of return is 12%, the marginal tax rate is 21%, and the IRS allows him to depreciate the sprinkler systems (A and B) over 10 years using the straight-line method. The inflation rate is assumed to be 0.

(i) What is the NPV of sprinkler system A?
a. -$49,553.22 b. -$49,720.32
c. -$35,242.98 d. -$55,856.97
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(ii) What is the NPV of sprinkler system B?
a. -$51,422.89 b. -$39,407.00
c. -$47,627.99 d. -$41,127.01
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(iii) What is the annuity equivalent of sprinkler system A?
a. -$10,004.88 b. -$11,277.62
c. -$10,038.62 d. -$7,115.62
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(iv) What is the annuity equivalent of sprinkler system B?
a. -$8,910.69 b. -$11,627.72
c. -$9,299.62 d. -$10,769.62
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(v) Which sprinkler system should he choose?
a. A b. B

Explanation / Answer

For System A, NPV = -49,720.32, AE = -10,038.62

Here, Depreciation = 37,000 / 10 = 3,700

Cash Flows = Investment + Profits + Depreciation + After-tax Salvage Value

After-tax Discount Rate = 12% x (1 - 21%) = 9.48%

Choose B as it has lower annuity equivalent cost than A.

A 0 1 2 3 4 5 6 7 Investment -37,000 11100 Salvage 12,600 Cost -5,900 -5,900 -5,900 -5,900 -5,900 -5,900 -5,900 Depreciation -3,700 -3,700 -3,700 -3,700 -3,700 -3,700 -3,700 EBT -9,600 -9,600 -9,600 -9,600 -9,600 -9,600 -9,600 Tax (21%) 2016 2,016 2,016 2,016 2,016 2,016 2,016 Profits -7,584 -7,584 -7,584 -7,584 -7,584 -7,584 -7,584 Cash Flows -37,000 -3,884 -3,884 -3,884 -3,884 -3,884 -3,884 8,401 NPV -$49,720.32 AE -$10,038.62

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