16B) A rancher is considering the purchase of additional land to expand operatio

Question

16B)

A rancher is considering the purchase of additional land to expand operations. He can operate an additional 750 acres with present labor and machinery. The land is selling for $650 per acre. This rancher believes that the operating revenue per acre of land will be $550 and operating expenses will be $400 in present dollars. He expects the inflation rate will be 3%. The rancher will sell the land in 3 years and he anticipates that land prices will increase at the rate of inflation from the base of $650 per acre. A bank will loan him $500 per acre of land and the loan will be fully amortized over 15 years at 12% (annual payments). The outstanding balance of the loan will be paid at the end of the third year. Assume that the marginal tax rate is 13% and that he requires at least a 8% pre-tax, risk-free return on capital and a 2% risk premium on projects of comparable risk.

Calculate the nominal after-tax net returns at the end of year 2.

            a. $126.33                                                      b. $138.45

            c. $117.05                                                       d. None of the answers are correct

What is the present value of the nominal after tax net return after 3 years?

            a. $382.61                                                      b. $368.92

            c. $351.86                                                     d. None of the answers are correct

(iii) What is present value of the after-tax terminal value after 3 years?

            a. $532.07                                                      b. $572.29

            c. $546.91                                                     d. None of the answers are correct

What is the net present value?

            a. $248.77                                                     b. $251.69

            c. $264.08                                                       d. None of the answers are correct

Explanation / Answer

Year 1 Revenue: Revenue per acre * 750, Year 2 Revenue: Year 1 revenue *1.03, Year 3 revenue: Year 2 revenue * .1.03. Similarly, for opex @ 400/acre.

Debt: (500*750) 375000, annual repayments in years 1 & 2: 375000/15 = 25000. Debt repaid in Year 3: 325000

Interest in year 1: 0.12*375000, interest in year 2: 0.12*(375000-25000), interest in year 3: 0.12*(375000-50000)

Purchase price of land: 650*750. Proceeds from sale of land: 650*750*(1.03^3). Gain on sale of land: 650*750*((1.03^3)-1).

Tax: 0.13*(Revenue-Opex-Interest+Gain on Sale).

After tax return: Revenue-Opex-Interest+Gain on Sale-Tax.

Cash Flow: Revenue-Opex-Interest-Tax-Repayment-Capex+Proceeds from sale of land

Required pre-tax return: 8%. Thus, required post-tax return: 8*(1-0.13) = 6.64%

(i) After tax net returns in Year 2: 64271.25. (d)

(ii) PV (after tax return in Year 3): 109233.4/(1.0864^3) = 85189.54 (d)

(iii) As land is sold off after 3 years, there is no cash flow after 3 years, and thus, there is no terminal value. (d)

(iv) Using npv() function in excel with discount rate of 8.64% and the cash flows calculated earlier, we get NPV of (194461.48) (d).

Year 0 1 2 3 Capex -487500 Revenue 412500 424875 437621.25 Opex 300000 309000 318270 Interest 45000 42000 39000 Repayment 25000 25000 325000 Gain on sale 45204 Tax 8775 9603.75 16322.2 Proceeds from sale 532704 After tax return 58725 64271.25 109233.4 Cash flow -487500 33725 39271.25 271733.4

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