Brach’s Candy Company (BCC) is considering producing a new type of candy product

Question

Brach’s Candy Company (BCC) is considering producing a new type of candy product called Aggie Sweets. BCC estimates that the annual demand for the new product will be one of the following values: 1. 30,000 with probability 0.3, 2. 50,000 with probability 0.4, 3. 80,000 with probability 0.3 Each box of candy will sell for $5 and incurs a variable production cost of $3. It cost $800,000 to build a plant to produce the candy. Assume that if $1 is received every year (forever), this is equivalent to receiving $10 at the present time. Considering the reward for each action and state of the world to be in terms of net present value, use each decision criterion (maximin, maximax, minimax regret, and expected value) to determine whether BCC should build the plant. Be sure to define the states, decision alternatives, and construct the payoff table.

Explanation / Answer

$1 received every year till perpetuity is equal to $10 (present value). Using the formula of perpetuity, $10 = 1/r

or r = 10%.

Now, profit when the annual demand is 30,000: 30,000*(price - variable costs) = 30,000*(5-3) = $60,000. If it continues forever, its present value will be 60,000/10% = $600,000. NPV = present value of profits - present value of investments = 600,000 - 800,000 = -$200,000

demand: 50,000: 50,000*(5-3) = $100,000. If it continues forever, its present value = 100,000/10% = $1,000,000. NPV = present value of profits - present value of investments = 1,000,000 - 800,000 = $200,000

demand: 80,000: 80,000*(5-3) = $160,000.  If it continues forever, its present value = 160,000/10% = $1,600,000. NPV = present value of profits - present value of investments = 1,600,000 - 800,000 = $800,000.

Payoff table:

Payoff table:

Suppose the deamnd is 30,000 and supply is also 30,000. Revenue = 30,000*5 = 150,000. Cost = 30,000*3 = 90,000. profit = 150,000-90,000 = 60,000. NPV = 60,000/10% - 800,000 = -200,000. Now suppose that demand is 30,000 but supply is 50,000. revenue = 30,000*5 = 150,000. cost = 50,000*3 = 150,000. profit = 0. NPV = 0/10% - 800,000 = -800,000. Now suppose that demand is 30,000 but supply is 80,000. cost = 80,000*3 = 240,000. revenue = 30,000*5 = 150,000. NPV = (150,000-240,000)/10% - 800,000 = - 1,700,000. The same method has been used to calculate the payoffs for other demand supply scenario:

Payoff table:

Maximin: The maximin rule involves selecting the alternative that maximises the minimum pay-off achievable. Minimum payoff for supply of 30,000 = -$200,000. Minimum for 50,000 = -$800,000 and minimum for 80,000 = -$1,700,000. Maximum of this is in case of supply of 30,000 candy box with pay off of -$200,000.

Maximax: The maximax rule involves selecting the alternative that maximises the maximum payoff available. Maximum payoffs for various supplies: 30,000 = -$200,000. 50,000 = $200,000 and 80,000 = 800,000. Maximum of this is when supply is 80,000 candry box and pay off is $800,000.

Minimax regret: The minimax regret strategy is the one that minimises the maximum regret. To solve this a table showing the size of the regret needs to be constructed. This means we need to find the biggest pay-off for each demand row, then subtract all other numbers in this row from the largest number. For example the biggest pay off for the demand row is -200,000 and this is subtracted from all other numbers

For supply of 30,000 maximum regret is $1,000,000. for supply of 50,000 maximum regret is $600,000 and for supply of 80,000 maximum regret is $1,500,000. Minimum of these regrets is $600,000 and thus the solution is a supply of 50,000 candy boxes.

expected value:

The NPV for each demand situation has already been calculated earlier. expected value = sum of (probability*npv)

expected value = -60,000+80,000+240,000 = $260,000

Demand 30,000 50,000 80,000 Probability 0.3 0.4 0.3 NPV -200,000 200,000 800,000

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