Question

Mr. Agirich of Aggie Farms is thinking about investing in a center pivot irrigation system to irrigate 100 acres of land. The irrigation system costs $70,000. Mr. Agirich expects that the irrigation system will increase yield and thus operating receipts by $15,000 per year but it will cost $4,000 a year to pay for electricity, maintenance, and additional labor. Mr. Agirich plans on keeping the irrigation system for 4 years before replacing it with a new one and he thinks he can sell it for $50,000 at the end of 4 years. Assume that the Mr. Agirich expects that the inflation rate will be 4% and that operating receipts, operating expenses, and terminal value will increase at the rate of inflation (i.e., operating receipts, operating expenses and terminal value are stated as real dollars, thus, you must convert them to nominal dollars) . The bank has offered to lend Mr. Agirich $60,000. The loan will be fully amortized at a 10% interest rate over six years (annual payments). Mr. Agirich anticipates that his marginal tax rate over the next four years will be 20%. The IRS will allow Aggie Farms to depreciate the investment using straight‑line over 10 years. Mr. Agirich requires at least a 13% pre-tax, risk-free return on capital and a 2% risk premium on projects of comparable risk to the irrigation system.

A. Lay out the cash flows for the investment.

B. Calculate the net present value. [NPV=-$1,323.25]

C. Discuss whether or not the irrigation system is a profitable investment.

D. Evaluate the financial feasibility of this investment. Would there be a potential liquidity problem if the investment was profitable? Explain.

Answer 1

Incremental receipt in year 1 = 15,000 x (1 + 4%) = $ 15,600 (grows at the rate of 4% annually)

Incremental expenses in year 1 = 4,000 x (1 + 4%) = $ 4,160 (grows at the rate of 4% annually)

Salvage value in year 4 = 50,000 x (1 + 4%)⁴ = $  58,493

Discount rate = post tax discount rate = Pre tax discount rate x (1 - tax rate) = (13% + 2%) x (1 - 20%) = 12%

Part (A) and (B) Have been answered in the table below:

The rows highlighted in yellow contain answers to part (A) & (B). Figures in parenthesis, if any, mean negative values. All financials are in $. Adjacent cells in blue contain the formula in excel I have used to get the final output.

Part (C)

Annual mortgage payment = PMT(Rate, Period, PV, FV) = PMT (10%, 6, -60000,0) =  13,776.44

Interest portion from the mortgage can be calculated using the IPMT function in excel.

Please see the table below:

Year, n	Linkage	0	1	2	3	4
Annual Mortgage payment	A		13,776.44	13,776.44	13,776.44	13,776.44
Interest portion	B = IPMT(10%,n,6,-60000,0)		6,000.00	5,222.36	4,366.95	3,426.00
Principal repayment portion	C = A - B		7,776.44	8,554.09	9,409.50	10,350.45
EBIT	D (Calculated above)		4,440.00	4,897.60	5,373.50	5,868.44
[-] Interest	B (above)		6,000.00	5,222.36	4,366.95	3,426.00
EBT	E = D - B		(1,560.00)	(324.76)	1,006.56	2,442.45
[-] Taxes	F = E x 20%		(312.00)	(64.95)	201.31	488.49
Net income	G = E - F		(1,248.00)	(259.80)	805.25	1,953.96
OCF	H = G + Depreciation of 7000		5,752.00	6,740.20	7,805.25	8,953.96
[-] Principal repayment	C (above)		7,776.44	8,554.09	9,409.50	10,350.45
Cash flow for the year	I = H - C		(2,024.44)	(1,813.89)	(1,604.25)	(1,396.49)

Please see the row titled "Net Income". On a pure accrual basis,  the project is not profitable in year 1 & 2 but it is profitable over its entire lifespan. If we add net income over the entire life of the project, it's positive =  (1,248.00) + (259.80) + 805.25 + 1,953.96 = $ 1,251.40

Part D.

The project has negative NPV, hence it's not financially feasible.

Look at the row titled "Cash flow for the year". We are seeing negative cash flows year after year. So, there is indeed liquidity issue as well. So, there will be a potential liquidity problem in the project, specially in servicing the mortgage.