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303ex1-Notes

# 303ex1-Notes - ECON 303 Notes for Exam 1 1 Determining the...

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ECON 303 Notes for Exam 1 1. Determining the value of a firm (Ch. 1; p. 17-18) Managerial economics is the study of how to direct limited resources in ways that would most efficiently achieve managerial goals. The role of a manager is to direct resources toward achieving the goal of maximizing the firm’s profit. Total Profit (Π ) = Total Revenue (TR) - Total Cost (TC) This measure of profit is called economic profit. TR = PQ TC = Total explicit cost + Total implicit cost = Total opportunity cost Total Accounting Profit = TR - Total explicit cost It is possible for a firm to earn accounting profits but incur economic losses. Thus, the objective is to maximize economic profit. Maximization of economic profit leads to maximization of the value of the firm. The value of a firm is calculated as follows: T Value F = Π 0 + Π 1 /(1 + i) + Π 2 /(1 + i) 2 + … + Π T /(1 + i) T = Σ Π t /(1 + i) t t=0 where Π t is profit in time period t and i is the interest rate. Numerical examples: Consider a firm whose current profit, Π 0 = \$120 million. Suppose interest rate, i = 10%. A. If the firm continues for the next three years with this level of profit annually, the value of the firm is: Value F = PV Π0 = Π 0 + Π 0 /(1 + i) + Π 0 /(1 + i) 2 + Π 0 /(1 + i) 3 = 120 + 120/(1 + 0.1) + 120/(1 + 0.1) 2 + 120/(1 + 0.1) 3 = 120 + 120/(1.1) + 120/(1.1) 2 + 120/(1.1) 3 = 120 + 120/1.1 + 120/1.21 + 120/1.33 = 120 + 109.1 + 99.2 + 90.2 = \$418.5 million. B. Now suppose, the annual growth rate of the firm’s profit, g = 7%. If the firm continues for the next three years, the value of the firm is: Value F = PV Π0 = Π 0 + [Π 0 (1 + g)]/(1 + i) + [Π 0 (1 + g) 2 ]/(1 + i) 2 + 0 (1 + g) 3 ] /(1 + i) 3 = 120 + [120(1 + 0.07)]/(1 + 0.1) + [120(1 + 0.07) 2 ]/(1 + 0.1) 2 + [120(1 + 0.07) 3 ] /(1 + 0.1) 3 = 120 + [120(1.07)]/(1.1) + [120(1.07) 2 ]/(1.1) 2 + [120(1.07) 3 ]/(1.1) 3 Page 1 of 8

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ECON 303 Notes for Exam 1 = 120 + 128.40/1.1 + 137.39/1.21 + 147.01/1.33 = 120 + 116.7 + 113.5 + 110.4 = \$460.6 million. C. With annual profit and growth rate as given in part A, if the firm continues for ever, the value of the firm is: Value F = PV Π0 = Π 0 + [Π 0 (1 + g)]/(1 + i) + [Π 0 (1 + g) 2 ]/(1 + i) 2 + 0 (1 + g) 3 ] /(1 + i) 3 + … = Π 0 [(1 + i)/(i - g)] = 120[(1 + 0.1)/(0.1 - 0.07)] = 120(1.1/0.03) = 120(36.67) = \$4,400 million. D. With annual profit and growth rate as given in part A, if the firm pays its current profits of \$120 million as dividends and continues for ever, the value of the firm on the ex-dividend date (i.e., the day after the payment of dividend) is: Ex-Div Value F = PV Π0 - Π 0 = Π 0 [(1 + g)/(i - g)] = 120[(1 + 0.07)/(0.1 - 0.07)] = 120(1.07/0.03) = 120(35.67) = \$4,280 million. 2. Determining marginal benefit, marginal cost, the net benefit maximizing value of the decision variable, and maximum net benefits (Ch. 1; p. 19-24) A. Given total benefits and total costs when the decision variable is discrete: Level of Decision Variable (Q) Total Benefit (TB) Total Cost (TC) Net Benefit (NB) Marginal Benefit (MB) Marginal Cost (MC) 0 \$0 \$0 \$0 - - 1 16 2 14 16 2 2 30 6 24 14 4 3 40 11 29 10 5 4 48 20 28 8 9 5 54 30 24 6 10 6 58 45 13 4 15 7 61 61 0 3 16 8 63 80 -17 2 19 The rule for net benefit maximization is MB = MC. Note that when the Page 2 of 8
ECON 303 Notes for Exam 1 decision variable is discrete, MB is not usually exactly equal to MC and maximum net benefit occurs where MB is closest but greater than MC.

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303ex1-Notes - ECON 303 Notes for Exam 1 1 Determining the...

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