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

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Answer 1

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)
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%
B	0	1	2	3	4	5	6
Investment	-24,500
Salvage							9,500
Cost		-7,000	-7,000	-7,000	-7,000	-7,000	-7,000
Depreciation		-2,450	-2,450	-2,450	-2,450	-2,450	-2,450
EBT		-9,450	-9,450	-9,450	-9,450	-9,450	-9,450
Tax (21%)		1984.5	1,985	1,985	1,985	1,985	1,985
Profits		-7,466	-7,466	-7,466	-7,466	-7,466	-7,466
Cash Flows	-24,500	-5,016	-5,016	-5,016	-5,016	-5,016	4,548
NPV	($41,127.01)
AE	($9,299.62)
Choose B as it has lower annuity equivalent cost than A.