Question

In: Finance

A farmer is thinking about investing in a center pivot irrigation system to irrigate 80 acres...

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

Solutions

Expert Solution

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.

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