THE IMPACT OF THE PRICE ELASTICITY

ON NET INCOME AND PROFIT MARGIN

  To determine how the price elasticity may affect the net income, the net income (NI) before the price cut is measured first as follows:

Equation 2

N1 = (1 – )[PQ(1 - V) – F – I]

  where is the corporate tax rate, V is the variable operating cost as a percentage of the original price, F is the fixed operating cost, and I is the fixed interest expense. Then, the new level of net income after the price reduction (NIN) is given by:

Equation 3

NIN = (1 )[P(1 x)Q(1 x) VPQ(1 x) F I]

= (1 )[PQ(1 x)(1 x V) F I]

  See Appendix A for the derivation of equation (3). This new net income after the price cut is not necessarily larger than the original amount of net income of equation (2).

For wealth-maximizing managers, Appendix B shows the condition, under which the net income increases after a price cut, as follows:

Equation 4



  where x is the fraction of the price reduction from the original price.2 If the above condition is met, the net income will increase after the price cut; otherwise it will be the same as or less than the original net income. Equation (4) offers three implications. First, as the demand of the product gets more elastic, it is more likely that the net income would increase after the price reduction. Second, the chance of higher net income decreases, when the company cuts the price more. Third, the probability of higher net income also decreases, if the variable operating cost as a percentage of the original price increases.

  Taking advantage of equation (3), the optimum level of price cut (x*), which maximizes the wealth of the stockholders, is derived as follows in Appendix C:

Equation 5

x*=

  If the price is cut more or less than (1 + V)/2, the net income will be below the maximum possible amount.Hence, the wealth-maximizing manager should cut the price to the level indicated by the above condition.

  After a price cut, the profit margin may increase or decrease depending upon the price elasticity and other factors. To show the profit margin increasing condition, the profit margin (m) is examined here, which is defined as:

Equation 6

  It is generally agreed among textbook writers that the higher this margin, the better. See Block and Hirt (1994, pp. 55-56), Gitman (1997, p. 136), and Van Horne and Wachowicz (1995, pp. 140). Also agreed is that a low profit margin is bad for the stockholders, because it indicates high costs from inefficient operations and heavy use of debt (Brigham; 1995, p. 79), or low sales, high costs, or both (Brigham and Gapenski, 1997, pp. 52-53; and Weston and Brigham, 1993, p.57). Keown, Scott, Martin, and Petty (1996, footnote 9 on p.100) take a more in-depth look to conclude that the profit margin is affected by the operating and financing activities of the company.

  However, a low profit margin is not necessarily bad for the stockholders. The reason is that, although the reduced price may decrease the profit margin, the net income may improve after a price cut due to the more than proportionately increased quantity. The following condition is derived by Appendix D, under which the profit margin increases after a price cut by x:

Equation 7

  The numerator on the left side of the above inequality is the total variable cost after the cut, and its denominator is the total fixed cost before and after the price reduction.

  The profit margin will increase after a price cut if this ratio is less than the benchmark value, which is -1+x.If this ratio is greater than that, the profit margin will decline even if the net income increases. The implication is that managers should go by the net income after the price cut because it is the true representative measure of the stockholders’ wealth. The profit margin should not be considered in the decision-making process of a price Reduction.