profit the company is likely to receive after selling all the 200,000 boards to SAEL. In addition, a decision tree for BUYU is drawn and BUYU’s preferred course of action is discussed. The other aspect looked at in the paper is the expected value of perfect information about whether SAEL will exercise its option.

Profit for Manufacturing Boards

Total fixed costs is $250, 000

Marginal cost is $2per board = 2 x 200,000 boards = $400,000

Variable cost = sum of marginal costs of all units produced = $400,000

Total cost = variable costs + fixed costs

= 400,000 + 250,000 = 650,000

Contribution = sales — variable costs

= (selling price x product units) — variable costs

= (5 x 200,000) — 400,000

= 1,000,000 — 400,000 = 600,000

Contribution per unit = total contribution / product units

= 600,000 / 200,000 = 3

Breakeven = fixed costs / contribution per unit

= 250,000 / 3 = 83,333

83,333 is the number of products the company has to sell before earning any profit. The profit margin = sales — breakeven = 200,000 — 83,333 = 116,667. The profit is calculated by multiplying the remaining sales unit by the selling price = 116,667 x 5 = $583,335.

Decision Tree

Amount of sales

Probability

Profit

200,000

0.4

583,335

100,000

0.4

291,667.5

Less than 100,000

0.2

145,833.75

BUYU has recently received an offer from SAEL Company to supply the company with 200,000 boards guaranteeing a $583,335 profit for the BUYU. BUYU is also considering selling the half of the boards to the company then the reset be sold later. If the company sells all the 200,000 boards at ago, the profit will be $583,335 minus the production cost as well as other variable costs (Cha & Tappert, 2009). The marginal cost will be about $400,000 for the 200,000 boards regardless of how much is produced and used. The fixed cost will be $250,000 if the company’s boards are 100,000; $500,000 if the boards are 200,000 in number and $125,000 if they are less than 100,000.

Use of Expected Profit

The expected profit of selling the 200,000 boards at ago is $583,335. If the company sells only 100,000 boards to SAEL, the expected profit would be $291,667.5. Thus, the expected profit when BUYU sells less than 100,000 boards to SAEL would be $145,833.75. Thus, the expected profit when the company sells all the boards would be 583,335. It appears that the owner’s best option; profit maximizing option would be to manufacture and sell all the boards to SAEL Company (Garrison, Eric, & Peter, 2009).

Expected Profit with Perfect Information

The business is considering spending money to obtain a “reliable” forecast; how much is this forecast worth to the owner? To answer this question, let’s examine the decision tree (Hubbard, 2007). If SAEL does not buy the remaining boards as expected, what is the best action? To maximize profit, the firm should sell the first batch of the timber to SAEL which results in a profit of $291,667.5. If the company sells less than half of all the boards to SAEL, the best action for them is to keep the remaining boards which results in a profit of $145,833.75. Using the probabilities of the different amounts of boards sold shown in the table above, we can calculate the expected profit with perfect information as follows: $583,335 x .4 + $291,667.5 x .4 + $145,833.75 x .2 = $379,167.75. Without perfect information, the best action for the firm is to sell half the timber which results in an expected profit of $291.667.5. With perfect information, the expected profit is $379,167.75. Thus, for the firm, the value of perfect information is $379,167.75 – $291,667.5 = $88,000 (assuming accurate forecast).

BUYU’s Risk Averseness

Risk-averse investors dislike risks, and therefore stay away from adding high-risk stocks or investments to their portfolio and in turn will often lose out on higher rates of return. BUYU Company is reluctant to accept a bargain with an uncertain payoff rather than another bargain with more certain, but possibly lower, expected payoff (Chaitanya, 2012). The company has a choice between two scenarios, one with a guaranteed payoff and one without. In the guaranteed scenario, the company receives $583.335. In the uncertain scenario, the company may receive profit after the sales of the remaining boards of receive nothing for failure to sell the boards. The company is risk-averse as it can accept a profit of $291,667.5 after selling the remaining boards rather than receiving nothing. The average payoff of the gamble, known as its expected value, is $88,000. The amount that the company would accept instead of any bet is known as certainty equivalent, and the difference between the expected value and the certainty equivalent is called the risk premium. For risk-averse individuals, the risk premium is positive, and for risk-loving individuals their risk premium is negative.

References

Cha, S.-H., & Tappert, C.C. (2009). A Genetic Algorithm for Constructing Compact Binary Decision Trees. Journal of Pattern Recognition Research, 1-13.

Chaitanya, S. (2012). www.psu.edu. Retrieved October 9, 2012, from Algorithms for Probabilistically-Constrained Models of Risk-Averse Stochastic Optimization with Black-Box Distributions: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.158.59

Garrison, R.H., Eric, N.W., & Peter, B.C. (2009). Managerial Accounting. McGraw-Hill.

Hubbard, D. (2007). How to Measure Anything: Finding the Value of Intangibles in Business. New York: John Wiley & Sons.