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

GIVEN THAT :-

According to the question we have that the

the ceo of  Asempa farms limited is considering whether to plant this year’s yam with a fertilizer
or go organic

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

==> cost of platinum fertilizer =1000/kg

cost of standared type = 800/kg

organic : total manure cost = 1500

now taking the tree diagram as :-now finding the values of ABCDEFG

A= max (B,C) ( 58500,28500) = 58500

B=max(58500,57000)=58000

C= 0.6*65000+0.4*4500=57000 FOR 2 YEARS

= 28500FOR 1 YEAR

In the same finding all

D=57000

E=57000

F= 57500

G=60000

TO FIND :-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.

From all the above values we ahve obsrved that

B is greater than C in terms of monitary values CEO of asempa should choose platinum type fertilizer.

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

As the shift is the payoff per year. NO, the device will not change

for origems will be less than fertilizer

C= [0.6(80000-6500)]+0.4*[60000-6500]*1/2

solving the above calculation we get that

C=32750

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

For finding we have a formula

D= 0.4*G

substituting the value of G as 60000

therefore ,

D= 0.4*60000

D= 24000

the CEO of asempa forms to be moderte yield is 24000

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