Question

During the past year, Julia McGill planted a new vineyard on 150 acres of land that she leases for $30,090 a year. She has asked you, as her accountant, to assist her in determining the value of her vineyard operation. The vineyard will bear no grapes for the first 5 years (1–5). In the next 5 years (6–10), Julia estimates that the vines will bear grapes that can be sold for $61,290 each year. For the next 20 years (11–30), she expects the harvest will provide annual revenues of $112,320. But during the last 10 years (31–40) of the vineyard’s life, she estimates that revenues will decline to $86,420 per year. During the first 5 years, the annual cost of pruning, fertilizing, and caring for the vineyard is estimated at $8,910; during the years of production, 6–40, these costs will rise to $12,090 per year. The relevant market rate of interest for the entire period is 5%. Assume that all receipts and payments are made at the end of each year. Click here to view factor tables Button has offered to buy Julia’s vineyard business by assuming the 40-year lease. On the basis of the current value of the business, what is the minimum price Julia should accept?

Answer 1

the minimum price julia can accept should be equal to the average annual present value of net cash inflow

working note :

Table showing present value discounting factors at 5% interest

year	discounting factor (1/(1+r)^n)
1	0.9524
2	0.9070
3	0.8638
4	0.8227
5	0.7835
6	0.7462
7	0.7107
8	0.6768
9	0.6446
10	0.6139
11	0.5847
12	0.5568
13	0.5303
14	0.5051
15	0.4810
16	0.4581
17	0.4363
18	0.4155
19	0.3957
20	0.3769
21	0.3589
22	0.3418
23	0.3256
24	0.3101
25	0.2953
26	0.2812
27	0.2678
28	0.2551
29	0.2429
30	0.2314
31	0.2204
32	0.2099
33	0.1999
34	0.1904
35	0.1813
36	0.1727
37	0.1644
38	0.1566
39	0.1491
40	0.1420

Calculation of present value of cash inflows:

years	annual income from sale of grapes	cumulative present value of income ($) (annual income * cumulative discount factor of period)
1-5	Nil	Nil
6-10	61,290	207,907.94 [61,290 * 3.3922 ( cumulative discount factor of 6 to 10 years) ]
11- 30	112,320	859,304.16 [112,320 * 7.6505 ( cumulative discount factor of 11 to 30 years) ]
31-40	86,420	154,406.61 [86,420 * 1.7867( cumulative discount factor of 31 to 40 years) ]
	Total present value of income for the period of 40 years	1,221,618.71

Calculation of present value of cash outflows:

years	annual cost pruning fertilizing caring of of grapes	cumulative present value of annual cost ($) (annual cost * cumulative discount factor of period)
1-5	8,910	38,574.95 [8,910 * 4.3294 ]
6-40	12,090	1,55,107.45 [12,090 * 12.8294]
	Total present value of operating expense for the period of 40 years	193,682.40

Statement showing net present value of cashinflow for the period of 40 years

particulars	amount $
Total present value of income for the period of 40 years	1,221,618.71
less : Total present value of operating expense for the period of 40 years	193,682.40
Net present value of cash inflow for the period of 40 years	1,027,936.31

Calculation of average annual inflow at present value :

formulae

Net present value of cash inflow for the period of 40 years / 40 years

= 1,027,936.31 / 40

= 25,698.41 $

By maintaing the vineyard julia can earn an annual income of 25,698.41 $. Therefore the minimum price that julia should accept is 25,698.41 $

So, the leasing of the vineyard in the past year for 30,090 $ is profitable for julia than maintaining it by herself.