Question

I need help figuring out how to solve this.

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 realdollars, 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

Sale value at the end of the project = 50,000 x (1 + 4%)⁴ =  58,493

Annual depreciation = 1/10 = 10%

Accumulated depreciation over 4 years = 10% x 4 = 40%

Depreciated value = tax basis = 70,000 x (1 - 40%) = 42,000

Gain on sale =  58,493 - 42,000 =  16,493

Tax on gain on sale = 20% x  16,493 = 3,299

Hence, post tax salvage value = 58,493 - 3,299 =  55,194

Pre tax discount rate = 13% pre-tax, risk-free return on capital + a 2% risk premium = 13% + 2% = 15%

Post tax discount rate = Pre tax x (1 - tax rate) = 15% x (1 - 20%) = 12%

Please see the table below. The rows highlighted in yellow contain your answer. 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 (A) and (B) have been answered in the table itself by the first and second yellow colored row respectively.

U V W X 34 Linkage 0 1 2 (70,000) R 346 Year, n 347 Initial investment 348 Incremental receipt 349 Incremental expenses 350 Annual depreciation 351 Operating income 352 NOPAT 353 Operating cash flows 354 Post tax salvage value 355 356 Net cash flows 357 Discount rate 358 NPV B (15,000 growing @ 4% per year) C(4,000 growing @ 4% per year) D = A / 10 E = B + C + D F = Ex (1 - 20%) G=F-D 15,600 (4,160) (7,000) 4,440 3,552 10,552 16,224 (4,326) (7,000) 4,898 3,918 10,918 16,873 (4,499) (7,000) 5,374 4,299 11,299 17,548 (4,679) (7,000) 5,868 4,695 11,695 55,194 I = A +G+H 11,299 66,889 (70,000) 10,552 10,918 12.00% (1,323.25) '=NPV(T357,0356:X356)+T356 Excel NPV formula

Part (C)

Annual Interest expense in the first year = Loan x interest rate = 60,000 x 10% = 6,000. Subsequent interest payment has been calculated below using the IPMT function of excel.

W 361 Year, n 362 Operating income 363 Interest 364 4 4,440 4,898 5,374 5,868 (6,000) (5,222) (4,367) (3,426) '=IPMT(10%,U361,6,60000,0) '=IPMT(10%,V361,6,60000,0) "=IPMT(10%,W361,6,60000,0) "=IPMT(10%,X361,6,60000,0)

Operating income every year is less than the annual interest outgo, except in the last year and hence the project is not profitable.

Part (D)

NPV is negative, hence the project is financially infeasible.

Annual mortgage payment = PMT (Rate, Nper, PV, FV) = PMT (10%, 6, -60000, 0) = $  13,776

In none of the year, operating cash flows exceed this figure. So the project will not have enough cash to service the mortgage. Hence, there will be a potential liquidity problem if the investment was profitable