Question

The asking price of an acre of farm land is currently $1,050 per acre. The current net cash flow is $65 per acre, the investor's nominal cost of capital is 8.5% and the planning horizon is 20 years. The inflation rate of current returns is 3% and land values are 2%.

A. Evaluate the profitability (NPV) of the investment assuming no taxes and no debt financing.

B. Evaluate the profitability (NPV) of the investment assuming a tax rate of 25%.

C. Evaluate the profitability (NPV) of the investment assuming a tax rate of 25% and debt financing. Assume a 30% down payment, 8% interest rate, equal payment method and a 25 year amortization period.

D. Using the data from problem B. Find the maximum bid price the investor can afford to pay in order to earn an 8.5% rate of return. Also, find the maximum price for the conditions of problem C.

Answer 1

Answer - A

Statement showing Net Cash Flows (considering inflation)

Year	Working / Notes	Net Cash Flow ($ per acre)
1	$65	65.00
2	$65 * 1.03	66.95
3	$66.95 * 1.03	68.96
4	$68.96 * 1.03	71.03
5	$71.03 * 1.03	73.16
6	$73.16 * 1.03	75.35
7	$75.35 * 1.03	77.61
8	$77.61 * 1.03	79.94
9	$79.94 * 1.03	82.34
10	$82.34 * 1.03	84.81
11	$84.81 * 1.03	87.35
12	$87.35 * 1.03	89.98
13	$89.98 * 1.03	92.67
14	$92.67 * 1.03	95.45
15	$95.45 * 1.03	98.32
16	$98.32 * 1.03	101.27
17	$101.27 * 1.03	104.31
18	$104.31 * 1.03	107.44
19	$107.44 * 1.03	110.66
20	$110.66 * 1.03	113.98

Statement showing Net Present Value

    Amount ($ per acre)

Year	Particulars	Notes / Working	Amount (A)	Discount Factor @ 8.5% (B)	Present Value (A * B)
0	Cost of Farm Land	per acre	-1050.00	1	-1050.00
1	Net Cash Flows	calculated above	65.00	0.9217	59.91
2	Net Cash Flows	calculated above	66.95	0.8495	56.87
3	Net Cash Flows	calculated above	68.96	0.7829	53.99
4	Net Cash Flows	calculated above	71.03	0.7216	51.25
5	Net Cash Flows	calculated above	73.16	0.6650	48.65
6	Net Cash Flows	calculated above	75.35	0.6129	46.19
7	Net Cash Flows	calculated above	77.61	0.5649	43.85
8	Net Cash Flows	calculated above	79.94	0.5207	41.62
9	Net Cash Flows	calculated above	82.34	0.4799	39.51
10	Net Cash Flows	calculated above	84.81	0.4423	37.51
11	Net Cash Flows	calculated above	87.35	0.4076	35.61
12	Net Cash Flows	calculated above	89.98	0.3757	33.80
13	Net Cash Flows	calculated above	92.67	0.3463	32.09
14	Net Cash Flows	calculated above	95.45	0.3191	30.46
15	Net Cash Flows	calculated above	98.32	0.2941	28.92
16	Net Cash Flows	calculated above	101.27	0.2711	27.45
17	Net Cash Flows	calculated above	104.31	0.2499	26.06
18	Net Cash Flows	calculated above	107.44	0.2303	24.74
19	Net Cash Flows	calculated above	110.66	0.2122	23.49
20	Net Cash Flows	calculated above	113.98	0.1956	22.30
	Net Present Value	-285.72

Answer - B

Statement showing Cash Flows (after considering tax)

    Amount ($ per acre)

Year	Net Cash Flow (A)	Depreciation (B) ($1,050 / 20)	Tax (C )       [(A-B) * 25%]	Cash Flow (A - C)
1	65.00	52.50	3.13	61.88
2	66.95	52.50	3.61	63.34
3	68.96	52.50	4.11	64.84
4	71.03	52.50	4.63	66.40
5	73.16	52.50	5.16	67.99
6	75.35	52.50	5.71	69.64
7	77.61	52.50	6.28	71.34
8	79.94	52.50	6.86	73.08
9	82.34	52.50	7.46	74.88
10	84.81	52.50	8.08	76.73
11	87.35	52.50	8.71	78.64
12	89.98	52.50	9.37	80.61
13	92.67	52.50	10.04	82.63
14	95.45	52.50	10.74	84.72
15	98.32	52.50	11.45	86.86
16	101.27	52.50	12.19	89.08
17	104.31	52.50	12.95	91.35
18	107.44	52.50	13.73	93.70
19	110.66	52.50	14.54	96.12
20	113.98	52.50	15.37	98.61

Statement showing Net Present Value

      Amount ($ per acre)

Year	Particulars	Notes / Working	Amount (A)	Discount Factor @ 8.5% (B)	Present Value     (A * B)
0	Cost of Farm Land	per acre	-1050.00	1	-1050.00
1	Cash Flows	calculated above	61.88	0.9217	57.03
2	Cash Flows	calculated above	63.34	0.8495	53.80
3	Cash Flows	calculated above	64.84	0.7829	50.77
4	Cash Flows	calculated above	66.40	0.7216	47.91
5	Cash Flows	calculated above	67.99	0.6650	45.22
6	Cash Flows	calculated above	69.64	0.6129	42.69
7	Cash Flows	calculated above	71.34	0.5649	40.30
8	Cash Flows	calculated above	73.08	0.5207	38.05
9	Cash Flows	calculated above	74.88	0.4799	35.93
10	Cash Flows	calculated above	76.73	0.4423	33.94
11	Cash Flows	calculated above	78.64	0.4076	32.06
12	Cash Flows	calculated above	80.61	0.3757	30.28
13	Cash Flows	calculated above	82.63	0.3463	28.61
14	Cash Flows	calculated above	84.72	0.3191	27.04
15	Cash Flows	calculated above	86.86	0.2941	25.55
16	Cash Flows	calculated above	89.08	0.2711	24.15
17	Cash Flows	calculated above	91.35	0.2499	22.83
18	Cash Flows	calculated above	93.70	0.2303	21.58
19	Cash Flows	calculated above	96.12	0.2122	20.40
20	Cash Flows	calculated above	98.61	0.1956	19.29
	Net Present Value	-352.59

Answer - C

We have to first draw a debt repayment schedule for ascertaining the interest amount per annum.

Debt amount = $1,050 * 70% = $735

Let us assume that there are annual equal payments of $29.40 ($735 / 25 years) plus interest at the rate of 8%, since question is not certain about the frequency of payments in equal payment method and a 25 year amortization period.

Debt amortization schedule

Year	Opening Loan Amount (A)	Interest (B)     [A * 8%]	Principal Amount (C )	Payment Amount (D)   [B + C]	Closing Loan Amount         (A + B - D )
1	735.00	58.80	29.40	88.20	705.60
2	705.60	56.45	29.40	85.85	676.20
3	676.20	54.10	29.40	83.50	646.80
4	646.80	51.74	29.40	81.14	617.40
5	617.40	49.39	29.40	78.79	588.00
6	588.00	47.04	29.40	76.44	558.60
7	558.60	44.69	29.40	74.09	529.20
8	529.20	42.34	29.40	71.74	499.80
9	499.80	39.98	29.40	69.38	470.40
10	470.40	37.63	29.40	67.03	441.00
11	441.00	35.28	29.40	64.68	411.60
12	411.60	32.93	29.40	62.33	382.20
13	382.20	30.58	29.40	59.98	352.80
14	352.80	28.22	29.40	57.62	323.40
15	323.40	25.87	29.40	55.27	294.00
16	294.00	23.52	29.40	52.92	264.60
17	264.60	21.17	29.40	50.57	235.20
18	235.20	18.82	29.40	48.22	205.80
19	205.80	16.46	29.40	45.86	176.40
20	176.40	14.11	29.40	43.51	147.00
21	147.00	11.76	29.40	41.16	117.60
22	117.60	9.41	29.40	38.81	88.20
23	88.20	7.06	29.40	36.46	58.80
24	58.80	4.70	29.40	34.10	29.40
25	29.40	2.35	29.40	31.75	0.00

Statement showing Cash Flows (after considering tax and debt financing)

    Amount ($ per acre)

Year	Net Cash Flow (A)	Interest (B)	Depreciation (C) ($1,050 / 20)	Tax (D)                [(A-B-C) * 25%]	Cash Flow (A - B - C)
1	65.00	58.80	52.50	-11.58	17.78
2	66.95	56.45	52.50	-10.50	21.00
3	68.96	54.10	52.50	-9.41	24.27
4	71.03	51.74	52.50	-8.30	27.59
5	73.16	49.39	52.50	-7.18	30.95
6	75.35	47.04	52.50	-6.05	34.36
7	77.61	44.69	52.50	-4.89	37.82
8	79.94	42.34	52.50	-3.72	41.33
9	82.34	39.98	52.50	-2.54	44.89
10	84.81	37.63	52.50	-1.33	48.51
11	87.35	35.28	52.50	-0.11	52.18
12	89.98	32.93	52.50	1.14	55.91
13	92.67	30.58	52.50	2.40	59.70
14	95.45	28.22	52.50	3.68	63.55
15	98.32	25.87	52.50	4.99	67.46
16	101.27	23.52	52.50	6.31	71.44
17	104.31	21.17	52.50	7.66	75.48
18	107.44	18.82	52.50	9.03	79.59
19	110.66	16.46	52.50	10.42	83.77
20	113.98	14.11	52.50	11.84	88.02

Statement showing Net Present Value

    Amount ($ per acre)

Year	Particulars	Notes / Working	Amount (A)	Discount Factor @ 8.5% (B)	Present Value     (A * B)
0	Down payment for Farm Land	$1,050 * 30%	-315.00	1	-315.00
1 to 20	Debt Principal payments	$29.40 per annum	-29.4	9.4633	-278.22
1	Cash Flows	calculated above	17.78	0.9217	16.38
2	Cash Flows	calculated above	21.00	0.8495	17.84
3	Cash Flows	calculated above	24.27	0.7829	19.00
4	Cash Flows	calculated above	27.59	0.7216	19.91
5	Cash Flows	calculated above	30.95	0.6650	20.58
6	Cash Flows	calculated above	34.36	0.6129	21.06
7	Cash Flows	calculated above	37.82	0.5649	21.36
8	Cash Flows	calculated above	41.33	0.5207	21.52
9	Cash Flows	calculated above	44.89	0.4799	21.54
10	Cash Flows	calculated above	48.51	0.4423	21.45
11	Cash Flows	calculated above	52.18	0.4076	21.27
12	Cash Flows	calculated above	55.91	0.3757	21.01
13	Cash Flows	calculated above	59.70	0.3463	20.67
14	Cash Flows	calculated above	63.55	0.3191	20.28
15	Cash Flows	calculated above	67.46	0.2941	19.84
16	Cash Flows	calculated above	71.44	0.2711	19.37
17	Cash Flows	calculated above	75.48	0.2499	18.86
18	Cash Flows	calculated above	79.59	0.2303	18.33
19	Cash Flows	calculated above	83.77	0.2122	17.78
20	Cash Flows	calculated above	88.02	0.1956	17.22
	Net Present Value				-197.94

Answer - D

Maximum bid price the investor can afford to pay in order to earn an 8.5% rate of return in Answer-B above is the sum of present value of all future cash flows of 20 years and that is $697.41 ($1,050 - $352.59) per acre.

Maximum bid price the investor can afford to pay in order to earn an 8.5% rate of return in Answer-C above is the sum of present value of all future cash flows of 20 years and that is $395.28 ($315 + $278.22 - $197.94) per acre.