Question

A farmer is thinking about investing in a center pivot irrigation system to irrigate 120 acres of land in Dawson County. This land is used to produce cotton and is currently a dryland operation. Currently production is approximately % bale of cotton per acre. The current operating expenses are $100 per acre. With an irrigation system, operating expenses would increase by $125 per acre due to electricity, maintenance and additional labor (Total operating expense = $225). The irrigation system will be used during periods of low precipitation for the growing of cotton and for preparing the ground for breaking. It is estimated that the irrigation will increase yields and thus operating receipts by $200 per acre. The cost for drilling a well would be $9,180 (Table 1) and the cost for the center pivot irrigation system would be $33,000. The irrigation system would be 4 mile long and would irrigate 120 acres. This system would run off electricity and would be able to apply any amount of water over any given period. 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 $30,000 to the sale price. The farmer anticipates that his marginal tax rate over the next six years will be 15%. The IRS will allow the farmer to depreciate the investment ($33,000 + $9,180) using straight-line over 15 years. Assume that the terminal value of this investment is $30,000 at the end of five years. The farmer requires a 12% return to capital (pretax).

Answer 1

Layout the cash flows for the Investment

• Initial investment = $ (33000+9180) = 42180
• Incremental Net revenue per year = Incremental Revenue - Incremental cost = $ (200 -125) * 120acres = $ 9000
• Incremental annual depreciation = $ 42180/15 = $ 2812
• Annual operating cash flows after taxes = $ (9000 * 0.85 + 2812 * 0.15) =$ 8071.80
• After tax terminal cash flows:-
• Book value of irrigation system at the end of 5 years= 42180 - (2812 * 5) = $ 28120
• Gain on sale of asset = $ 30000 - $ 28120 = $ 1880
• After tax terminal cash flows = $ 30000 - (1880 * 0.15) = $ 29718

1.What is the after tax discount rate?

• Ans:- 12(1 - 0.15) = 10.2%

2. What is the present value of after tax returns?

• Ans:- PVF @ 10.5% of 5 years = 3.771498 * 7650= $28852

((200-125)*120=9000*(1-0.15)=$7650)

3. What is the present value of the tax savings from depreciation?

• Ans:- Depreciation=42180/15 = 2812,Tax savings = 2812 * 15% = $422
• PVF of tax savings from depreciation = 422 * 3.771498 = $1591

4. What is the present value of the after tax terminal value after 5 years?

• Ans:- PVF after tax terminal value after 5 years =$ (29718 * 0.6153) = $ 18285

5. What is Net present value?

• Ans:- Present value of cash inflows = Annual operating cash flows after tax * PVIF 10.2% 5 years + After tax terminal cash flows * PVIF 10.2% 5 years
• =$ (8071.8 * 3.771498 + 18285)= $ 48727
• NPV = $ 48727 - $ 42180 = $ 6547

​​​​​​​6.What is the Internal rate of return(IRR)?

• Ans:- 15%

​​​​​​​Since NPV of the Investment is positive and IRR is higher,So it should be Profitable Investment.