Question

A farmer is thinking about investing in a center pivot irrigation system to irrigate 80 acres of land in Fresno. The current operating expenses are $80 per acre. It is estimated that the irrigation will increase yields and thus operating receipts by $100 per acre. The cost for drilling a well would be $10,000 and the cost for the center pivot irrigation system would be $22,000. The irrigation system would be ¼ mile long and would irrigate 80 acres. Suppose that the farmer wants to evaluate this investment over a five-year period of time. The farmer believes that if he sold the farm in five years, the irrigation system would add $20,000 to the sale price. The farmer anticipates that his marginal tax rate over the next six years will be 20%. The IRS will allow the farmer to depreciate the investment using straight line over 15 years. Assume that the terminal value of this investment is $20,000 at the end of five years. The farmer requires a 12% return to capital (pretax).

1. Calculate the after-tax terminal value

a. $22,960 b. $16,000 c. $4,000 d. $20,267

2. Which discount rate should be used for calculating the NPV of this investment?

a. 9.6% b. 11% c. 11.6% d. 15%

3. What is the break-even price of operating receipt?

a. $19,917.46 b. $ 12,128 c. $16,849.35 d. $12,593.84

Answer 1

1)	Original cost = 22000+10000 =	32000
	Depreciation year = 32000/15 =	2133
	Accumulated depreciation for 5 year = 2133*5 =	10667
	Book value = 32000-10667 =	21333
	Loss on sale = 21333-20000 =	1333
	Tax shield on loss at 20% = 1333*20% =	267
	After tax terminal value = 20000+267 =	20267
	Option [d] $20,267
2)	Discount rate to be used = 12%*(1-20%) =	9.60%
3)	Break even receipts should yield 0 NPV.
	Therefore, 0 = -32000+20267/1.096^5+C*80%*PVIFA(9.6,5)+2133*20%*PVIFA(9.6,5)
	where C is the total contribution after tax
	Solving for R
	32000-20267/1.096^5-2133*0.2*3.82984 = C*0.8*3.82984
	C = (32000-20267/1.06^5-2133*0.2*3.82984)/(0.8*3.82984) =	$          4,968.06
	Before tax contribution = 4968/80% =	$          6,210.08
	Total cost = 80*80 =	$          6,400.00
	Break even receipts	$       12,610.08
	Answer: Option [d] $12,593.84
	Note:
	Marginal difference of about $17 between solution and working
	would be due to difference in rounding off.