Steve, a fresh graduate from an agric college plans to invest in one of two animal farming business with a Ghc 1 million loan sourced from Ecobank. Investing in Pig farming will have an estimated cost Ghc200,000 while the poultry business will cost Gh250,000. The year end demand (tons) of animal products from the two farms and their respective probabilities are shown in the Table below. A ton of animal product from the pig farm and poultry farm will be sold for Ghc15 and Ghc20 respectively Pig farming Poultry farming Demand (tons) Probability Demand (tons) Probability 25000 0.15 50000 0.1 45000 0.2 60000 0.2 40000 0.3 28000 0.3 20000 0.2 30000 0.2 19000 0.15 45000 0.2 If Steve is a risk averse lover, which of the two farming businesses will he choose? use 1 and 2 for poultry farming and pig farming respectively
Question
Steve, a fresh graduate from an agric college plans to invest in one of two animal farming business with a Ghc 1 million loan sourced from Ecobank. Investing in Pig farming will have an estimated cost Ghc200,000 while the poultry business will cost Gh250,000. The year end demand (tons) of animal products from the two farms and their respective probabilities are shown in the Table below. A ton of animal product from the pig farm and poultry farm will be sold for Ghc15 and Ghc20 respectively
Pig farming
Poultry farming
Demand (tons)
Probability
Demand (tons)
Probability
25000
0.15
50000
0.1
45000
0.2
60000
0.2
40000
0.3
28000
0.3
20000
0.2
30000
0.2
19000
0.15
45000
0.2
If Steve is a risk averse lover, which of the two farming businesses will he choose?
use 1 and 2 for poultry farming and pig farming respectively
Solution 1
To determine which business Steve should invest in, we need to calculate the expected value of each business. The expected value is calculated by multiplying each outcome by its probability and then summing these results.
For pig farming:
(25000 tons * Ghc15/ton * 0.15) + (45000 tons * Ghc15/ton * 0.2) + (40000 tons * Ghc15/ton * 0.3) + (20000 tons * Ghc15/ton * 0.2) + (19000 tons * Ghc15/ton * 0.15) = Ghc 1,687,500 + Ghc 1,350,000 + Ghc 1,800,000 + Ghc 600,000 + Ghc 427,500 = Ghc 5,865,000
For poultry farming:
(50000 tons * Ghc20/ton * 0.1) + (60000 tons * Ghc20/ton * 0.2) + (28000 tons * Ghc20/ton * 0.3) + (30000 tons * Ghc20/ton * 0.2) + (45000 tons * Ghc20/ton * 0.2) = Ghc 1,000,000 + Ghc 2,400,000 + Ghc 1,680,000 + Ghc 1,200,000 + Ghc 1,800,000 = Ghc 8,080,000
Subtracting the initial investment from the expected value gives us the expected profit:
For pig farming: Ghc 5,865,000 - Ghc 200,000 = Ghc 5,665,000 For poultry farming: Ghc 8,080,000 - Ghc 250,000 = Ghc 7,830,000
Since Steve is risk averse, he should choose the business with the higher expected profit. Therefore, Steve should choose poultry farming (option 1).
Solution 2
To determine which business Steve should invest in, we need to calculate the expected value of each business. The expected value is the sum of the product of each outcome and its probability.
For pig farming:
Expected demand = (25000 * 0.15) + (45000 * 0.2) + (40000 * 0.3) + (20000 * 0.2) + (19000 * 0.15) = 3750 + 9000 + 12000 + 4000 + 2850 = 33600 tons
Expected revenue = Expected demand * Price per ton = 33600 * Ghc15 = Ghc504,000
Expected profit = Expected revenue - Cost = Ghc504,000 - Ghc200,000 = Ghc304,000
For poultry farming:
Expected demand = (50000 * 0.1) + (60000 * 0.2) + (28000 * 0.3) + (30000 * 0.2) + (45000 * 0.2) = 5000 + 12000 + 8400 + 6000 + 9000 = 41400 tons
Expected revenue = Expected demand * Price per ton = 41400 * Ghc20 = Ghc828,000
Expected profit = Expected revenue - Cost = Ghc828,000 - Ghc250,000 = Ghc578,000
Given that Steve is risk averse, he should choose the business with the higher expected profit. Therefore, Steve should choose poultry farming (option 1) as it has a higher expected profit of Ghc578,000 compared to pig farming with an expected profit of Ghc304,000.
Solution 3
To determine which business Steve should invest in, we need to calculate the expected value of each business. The expected value is calculated by multiplying each outcome by its probability and then summing these results.
For pig farming:
Expected demand = (25000 * 0.15) + (45000 * 0.2) + (40000 * 0.3) + (20000 * 0.2) + (19000 * 0.15) = 3750 + 9000 + 12000 + 4000 + 2850 = 33600 tons
Expected revenue = Expected demand * Price per ton = 33600 * Ghc15 = Ghc504,000
For poultry farming:
Expected demand = (50000 * 0.1) + (60000 * 0.2) + (28000 * 0.3) + (30000 * 0.2) + (45000 * 0.2) = 5000 + 12000 + 8400 + 6000 + 9000 = 41400 tons
Expected revenue = Expected demand * Price per ton = 41400 * Ghc20 = Ghc828,000
Given that Steve is risk averse, he should choose the business with the higher expected revenue, which in this case is poultry farming (option 1).
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