Question

Mr. Agirich of Aggie Farms is considering the purchase of 100 acres of prime ranch land that is adjacent the ranch he now owns. Mr. Agirich can operate the additional 100 acres with present labor, machinery and breeding livestock. The land is selling for $400 per acre. Mr. Agirich believes that the operating receipts per acre of land per year will $450 and operating expenses will be $420 in present dollars. Mr. Agirich expects that the inflation rate will be 3% and operating receipts and expenses per acre will increase at the rate of inflation. The farmer will sell the land in three years and he anticipates that land prices will increase at the rate of inflation (from a base price of $400). A bank will loan him $350 per acre of land and the loan will be fully amortized over 15 years at 10% (annual payments). The outstanding balance of the loan will be paid at the end of the third year (balloon payment). Assume that the marginal tax rate is 30% and that Mr. Agirich requires at least a 6% pre-tax, risk-free return on capital and a 4% risk premium on projects of comparable risk. (Do the analysis on a per acre basis.)

For Questions 19-27 please assume real net returns of $30.00 per acre and the real purchase price of land of $400 per acre are assumed to increase by 4% each year.

What is the after-tax nominal terminal value in three years?

What is the present value of the after-tax net returns?

What is the present value of after-tax terminal value?

What is the Net Present Value?

Answer 1

Cost of Debt: 10% | Marginal Tax rate: 30% | So, After-tax cost of debt will be: 7%

Risk-free rate: 6% | Market risk premium: 4% | Expected return will be= 6%+4% = 10%

Cost of land purchase = 400*100 = $40000 | Bank loan = 350*100 = $35000

So, Mr. Agirich would use $5000 to purchase this land which will be considered as equity.

WACC= (0.875)(0.07)+(0.125*0.1) = 0.06125+0.0125 = 0.07375 = 7.38%

EBIT= $30 which is increasing as 3%

EBIT(1-t)= 30*0.7 = $21/acre | Total EBIT = $2100

EBIT 1st year = $2100 | EBIT 2nd year = 2100*1.03 = $2163 | EBIT 3rd year = 2163*1.03 = $2228

Rate of Inflation	3%
Year		1	2	3
EBIT(1-t)		2100.0	2163.0	2227.9
Principle Payment		1101.6	1211.7	1332.9
Free cashflow		998.4	951.3	895.0
Terminal Value					21046.2
Present value		929.8	825.0	722.8	16998.2
Land purchase price	40000
Land selling price				43709.08
Free cash flow	-40000	929.8	825.0	36025	16998.2
IRR	10%
NPV	3224.73

1. What is the after-tax nominal terminal value in three years?

Ans. $21046.2

What is the present value of the after-tax net returns?

Ans, $54778

What is the present value of after-tax terminal value?

Ans. $16998.2

What is the Net Present Value?

Ans. $3224.73