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.)

                                                                                                  

            A.        Lay out the cash flows for the investment.

            B.        Calculate the net present value. [NPV=$6.12]

            C.        Layout the financing cash flows associated with this investment.

            D.        Is there a potential liquidity problem?

E.         What maximum price should Mr. Agirich be willing to pay for an acre of land?

                        F.         Calculate the net present value if the 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. Remember that you still need to adjust for inflation. Everything else is the same as before. [NPV=42.04]

Answer 1

A.Pre-tax cash flows' NPV analysis on a per acre basis
Year	0	1	2	3	Cost of land	400
Cost of land	-400				sale value	437.09
Pre-tax tax Sale value of land(400*1.03^3)				437.09	gain on sale	37.09
Pre-tax net opg. Revenues(450-420)		30	30.9	31.83	Tax on gain(37.09*30%)	11.13
					After-tax sale value(437.09-11.13)	425.96
Total pre-tax annual cash flows	-400	30	30.9	468.92
PV F at( 6%+4%)=10% (1/1.1^n)	1	0.9091	0.8264	0.7513
PV at 8.2%	-400	27.27273	25.53719	352.3043
NPV	5.1142
A.Total pre-tax annual cash flows	-400	30	30.9	468.917
B.NPV analysis on a per acre basis
Year	0	1	2	3	Cost of land	400
Cost of land	-400				sale value	437.09
After-tax tax Sale value of land				425.96	gain on sale	37.09
After-tax net opg. Revenues(450-420)*(1-30%)		21	21.63	22.2789	Tax on gain(37.09*30%)	11.13
Tax savings on interest exp.		10.5	10.1694	9.80574	After-tax sale value(437.09-11.13)	425.96
Total after-tax annual cash flows	-400	31.5	31.7994	458.0446
PV F at (4.2%+4%)=8.2% (1/1.082^n)	1	0.924214	0.854172	0.789438
PV at 8.2%	-400	29.11275	27.16217	361.598
NPV	17.87292
NPV=	17.87
Annual payments ,per acre,on the bank loan will be
350=Pmt.*(1-1.1^-15)/0.1
Pmt.=350/((1-1.1^-15)/0.1)=
46.02
Amortisation of the Bank Loan
Year	Annuity	Tow. Int.	Tow. Princ.	Princ. Bal.	Int.tax shield(Col.3*30%)
0				350
1	46.02	35	11.02	338.98	10.50
2	46.02	33.90	12.122	326.86	10.17
3	46.02	32.69	13.33	313.52	9.81
		0	313.52	0.00
Total	138.06	101.5838	350.00
C.Financing cash flows
Year	0	1	2	3
Bank Loan	350
After-tax interest payments		-24.5	-23.73	-22.88
Principal repayment		-11.02	-12.12	-13.33
Bal.Repayment				-313.52
Total Financing cash flows	350	-35.52	-35.85	-349.73
D.    Is there a potential liquidity problem?
Total pre-tax annual cash flows	-400	30	30.9	468.92
Total after-tax annual cash flows	-400	31.5	31.80	458.04
Total Financing cash flows	350	-35.52	-35.85	-349.73
Yes. Cash generated from operations have fallen short to meet the financing cash outflows , in the 1st 2 yrs.
Repayment of the balance principal was made out of the sale proceeds of land in the 3rd year.
E. Maximum price he should be willing to pay=
400+17.87=417.87
F.NPV analysis on a per acre basis
Year	0	1	2	3	Cost of land	400
Cost of land	-400				sale value	454.57
After-tax tax Sale value of land				438.2	gain on sale	54.57
After-tax net opg. Revenues(450-420)*(1-30%)		21	22.4952	24.09686	Tax on gain(37.09*30%)	16.37
Tax savings on interest exp.		10.5	10.1694	9.80574	After-tax sale value(437.09-11.13)	438.20
Total after-tax annual cash flows	-400	31.5	32.6646	472.1026
PV F at (4.2%+4%)=8.2% (1/1.082^n)	1	0.924214	0.854172	0.789438
PV at 8.2%	-400	29.11275	27.9012	372.6959
NPV	29.70984
NPV=	29.71