Question

please i need answer asap thank u

You own 100 acres of timberland,with young timber worth 20,000 if logged today this represent 500 cords of wood at $40 per cord. after logging the land can be sold today for 10,000($100 per acre). the opportunity cost of capital is 10%. you have made the following estimates: a) the price of a cord of wood will increase by 5% per year? b) the price of land will increase by 3% per year. c) the yearly growth rate of the cords of wood on your land are :

years 1-2: 15%:

year 3-4 :10%:

year 5-8 : 5%

years thereafter 2% please find the present value of the optimal decision.

Answer 1

Present worth of the decision will be calculated by use of concept of two stage valuation:

PV =

the calculation of annual cash flow till 8 years as

Year	0	1	2	3	4	5	6	7	8
Cord	500	575	661.25	727.375	800.1125	840.118125	882.1240313	926.2302328	972.5417445
Cost per cord	40	42	44.1	46.305	48.62025	51.0512625	53.60382563	56.28401691	59.09821775
Cost of timber	20000	24150	29161.125	33681.09938	38901.66978	42889.09093	47285.22275	52131.95808	57475.48379
cost of land	10000	10300	10609	10927.27	11255.0881	11592.74074	11940.52297	12298.73865	12667.70081
Opportunity Cost	10%
Total cash flow		34450	39770.125	44608.36938	50156.75788	54481.83167	59225.74572	64430.69674	70143.1846
PV		34450/1.1^1	39770.125/1.1^2	44608.3694/1.1^3	50156.758/1.1^4	54481.8316/1.1^5	59225.7457/1.1^6	64430.6967/1.1^7	70143.184/1.1^8
		$31,318.18	$32,867.87	$33,514.93	$34,257.74	$33,828.93	$33,431.39	$33,063.14	$32,722.31
Terminal value of land		12667.71*(1+0.03) /(0.10-0.03)(1+0.10)^8
		$3,99,557.03
Terminal value of Timber		57475.484*(1+0.07) /(0.10-0.07)(1+0.10)^8
		$43,94,269.02
Total PV		$50,58,830.55	Sum of all PV and terminal value

Net growth in timber = 2%+5%= 7% after 8th year.