Question

A farmer is thinking about investing in a center pivot irrigation system to irrigate 80 acres of land in Fresno. With an irrigation system, operating expenses would increase by $75 per acre due to electricity, maintenance and additional labor. It is estimated that the irrigation will increase yields and this operating receipts by $150 per acre. The cost of drilling a well would be $8,200 and the cost for the center pivot irrigation system would be $31,000. 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 $31,000 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 using straight line over 15 years. Assume that the terminal value of this investment is $31,000 at the end of five years. The farmer requires a 10% return to capital (pretax).

                           Calculate the initial cost

                           Calculate the after-tax net returns

                           Calculate the tax savings from depreciation

                           Calculate the after-tax terminal value

Suppose the discount rate is 8.5%. Using information from you answers above, what is the NPV for the investment?

Answer 1

Answer (a):

Initial cost = cost of drilling well + cost for the center pivot irrigation system = $8200 + $31000 = $39,200

Answer (b):

Annual after-tax net returns = (Increase in operating receipts - Increase in operating expense) * Number of acres * (1 - Tax rate)

= (150 - 75) * 80 * (1 - 15%)

= $5,100

Answer (c):

Annual tax savings from depreciation = Annual depreciation * Tax rate

= 39200 /15 * 15%

= $392.00

Answer (d):

After tax terminal value = 31000 * (1 - 15%) = $26,350

Answer (e):

Post tax discount rate = 10% * (1 - tax rate) = 10% * (1 - 15%) = 8.5%

NPV = (Annual after-tax net returns + Annual tax savings from depreciation) * PV of $ annuity for 5 years at 8.5% + Terminal value * PV of $1 for 5 years at 8.5% - Initial investment

= (5100 + 392) * (1 - 1 / (1 + 8.5%) ⁵) / 8.5% + 26350 * 1 / (1 + 8.5%) ⁵ - 39200

= - $35.05

NPV for the investment = -$35.05

If evaluated over 5 year period NPV is negative.