Question

The CEO of Asempa farms limited is considering whether to plant this year’s yam with a fertilizer or go organic (i.e. without fertilizer). In case of using a fertilizer, 10kg of either the Platinum or Standard type fertilizer would be needed at the start of the planting year. The Platinum type is GH¢1000 per kilogram and could lead to a high yield of 30 tons or a moderate yield of 20 tons of yam at the end of the year. The Standard type is GH¢800 per kilogram and could also lead to a high yield of 15 tons or a moderate yield of 10 tons of yam at the end of the year. The Standard has fewer chemicals and would lead to tastier yam that sells for a higher price than that of Platinum. There is a probability of 0.7 that high yield would be recorded at the end of the year.

Market price for yam is uncertain and depends on the type as well as the volume of yam on the market. Generally, a year of high yield results in higher volume whiles a year of moderate yield leads to moderate volume of yam on the market. Even then, there is 60-40 chance that yam from the Platinum fertilizer could sell for GH¢2000 or GH¢2400 per ton in times of high yield, and GH¢3000 or GH¢3500 per ton in times of moderate yield. The Standard fertilizer yam has a 40- 60 chance of selling for GH¢4000 or GH¢5000 per ton in times of high yield, and GH¢5500 or GH¢6000 in times of moderate yield.

Organic yam would take 2 years to harvest and would require the supply of manure that can be borrowed from a local shop at a total cost of GH¢8,500 at the end of year 2. This could lead to a high yield of 8 tons or a moderate yield of 6 tons at the end of year 2. Prices for organic yam are quite high and will sell for GH¢9,000 per ton in a high yield season and GH¢11,000 in moderate yield season. Assume interest rate of 10% per year and answer the following questions.

a. Draw a decision tree for the problem faced by the CEO indicating the probabilities of occurrence and monetary values of events.

b. Advice the CEO of Asempa farms on which decision to take if he wants to make his decision based on expected monetary value technique. Show your calculations.

c. Will your advice change if the total cost of manure at the end of year 2 is GH¢6000? Show your calculations.

d. What would be Asempa farms payoff if there happens to be a moderate yield, and price of yam is GH¢6000 per ton?

e. If the CEO of Asempa farms is risk averse, which decision do you think the CEO should opt for? Explain.

Answer 1

a) The Decision tree can be represented as

		15 tons (70%)	GH¢ 4000/ton    (40%)
	GH¢ 8000			GH¢ 5000/ton    (60%)
	Standard	10 tons (30%)	GH¢ 5500/ton    (40%)
Fertiliser				GH¢ 6000/ton    (60%)
	Platinum	30 tons (70%)	GH¢ 2000/ton    (60%)
	GH¢ 10000		GH¢ 2400/ton    (40%)
		20 tons (30%)	GH¢ 3000/ton    (60%)
				GH¢ 3500/ton    (40%)
Organic							GH¢ 8500	8 tons	GH¢ 9000/ton    (70%)
								6 tons	GH¢ 11000/ton    (30%)
	t=0			t=1			t=2

b)

Fertiliser Standard

Expected monetary value after one year

= 15 tons *70%* ( GH¢ 4000/ton * 40%+GH¢ 5000/ton * 60%) +   10 tons *30%* ( GH¢ 5500/ton * 40%+GH¢ 6000/ton * 60%)

=   GH¢ 48300 + GH¢ 17400

=GH¢ 65700

NPV = -8000 +65700/1.1 =  GH¢ 51727.27

Fertiliser Platinum

Expected monetary value after one year

= 30 tons *70%* ( GH¢ 2000/ton * 60%+GH¢ 2400/ton * 40%) +   20 tons *30%* ( GH¢ 3000/ton * 60%+GH¢ 3500/ton * 40%)

=   GH¢ 45360 + GH¢ 19200

=GH¢ 64560

NPV = -10000 +64560/1.1 =  GH¢ 48690.91

Organic (assuming high yield 70% of the time)

Expected monetary value = 8 tons *70%* GH¢ 9000/ton +6 tons *30%* GH¢ 11000/ton

=   GH¢ 50400 + GH¢ 19800

=GH¢ 70200

NPV = (-8500 +70200)/1.1^2 =  GH¢ 50991.74

So, the CEO of Asempa farms should go wth Standard Fertiliser

c) if the total cost of manure at the end of year 2 is GH¢6000

NPV of organic= (-6000 +70200)/1.1^2 =  GH¢ 53057.85

So, it is now better to go with Organic manure

d) Asempa farms payoff if there happens to be a moderate yield, and price of yam is GH¢6000 per ton

= 10 tons *   GH¢ 6000/ton =   GH¢ 60000 after one year

and NPV = -  GH¢ 8000+   GH¢ 60000/1.1 =   GH¢ 46545.45

e) If CEO is risk averse , he should go with Platinum fertiliser as the minimum payoff after one year (not two years as in case of organic) is GH¢ 60000