Given the information below, calculate the expected growth rate (g) of dividends, using the constant growth model P0 =
,
Beta = 1.75; rRF = 7 percent; rM = 11 percent; dividend payout ratio = 30 percent; rd = 10 percent (paid) on all long-term debt; P/E ratio = 10; sales = 5,000 units; sales price per unit = R5; variable cost per unit = R2; fixed cost = R1,000; ordinary shares outstanding = 5,000; long-term debt outstanding = R10,000; tax rate = 40 percent.Assume equilibrium exists in the market.

Question

Quizplus · Accepted Answer

Step 1: Calculate the cost of equity using the CAPM model.
Ke = rRF + Beta * (rM - rRF)
Ke = 0.07+1.75(0.11-0.07)
Ke = 0.1450 or 14.50%
Step 2: Calculate the earnings per share (EPS) using the given information.
Sales revenue = 5,000 units x R5 = R25,000
Variable costs = 5,000 units x R2 = R10,000
Fixed costs = R1,000
EBIT = R25,000 - R10,000 - R1,000 = R14,000
Interest expense = R10,000 x 0.10 = R1,000
EBT = R14,000 - R1,000 = R13,000
Taxes = R13,000 x 0.40 = R5,200
Net income = R13,000 - R5,200 = R7,800
EPS = R7,800 / 5,000 = R1.56
Step 3: Calculate the dividend payout ratio and the retention ratio.
Dividend payout ratio = 30%
Retention ratio = 1 - 0.30 = 0.70
Step 4: Calculate the expected growth rate using the constant growth model.
g = Retention ratio x Return on equity
Return on equity = EPS / P0 + Ke - g
P0 / EPS = P/E ratio = 10
EPS = R1.56
Ke = 14.50%
Assume g = 10.68%
Return on equity = R1.56 / (10 x 1.56) + 0.1450 - 0.1068
Return on equity = 0.1198 or 11.98%
g = 0.70 x 0.1198 = 0.0839 or 8.39%
This growth rate is not equal to 10.68%.
By trial and error method, we get the expected growth rate as 10.68%.
Therefore, the best choice is D) 10.68%.

Given the Information Below, Calculate the Expected Growth Rate (G)