Question

The market consensus is that Analog Electronic Corporation has an ROE of 9% and a beta of 1.65. It plans to maintain indefinitely its traditional plowback ratio of 2/3. This year's earnings were $2.8 per share. The annual dividend was just paid. The consensus estimate of the coming year's market return is 14%, and T-bills currently offer a 6% return. a. Find the price at which Analog stock should sell. (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. Calculate the P/E ratio.

Answer 1

a.

P0 = $7.49494949492 rounded off to $7.49

b.

P/E ratio = 2.67676767676 times rounded off to 2.68 times

Step-by-step explanation:

a.

The constant growth model of dividend discount model (DDM) can be used to calculate the price of the stock today. DDM calculates the price of a stock based on the present value of the expected future dividends from the stock. The formula for price today under constant growth DDM is,

P0 = D0 * (1+g) / (r - g)

Where,

• D0 * (1+g) is the dividend expected in Year 1 or next year

• g is the constant growth rate in dividends

• r is the discount rate or required rate of return

We first need to calculate the values for D0, g and r.

D0 can be calculate by multiplying the earnings per share by (1 - Plowback Ratio)

D0 = 2.8 * (1 - 2/3)

D0 = $0.93333333333 rounded off to $0.93

To calculate the value of g, we need to multiply the ROE by the Plowback ratio.

g = 0.09 * 2/3

g = 0.06 or 6%

To calculate the value of r, we will use the CAPM equation.

r = risk free rate + Beta * (Market return - risk free rate)

r = 0.06 + 1.65 * (0.14 - 0.06)

r = 0.192 or 19.2%

P0 = 0.93333333333 * (1+0.06) / (0.192 - 0.06)

P0 = $7.49494949492 rounded off to $7.49

b.

The P/E ratio can be calculated by dividing the price per share by the earnings per share.

P/E = 7.49494949492 / 2.8

P/E ratio = 2.67676767676 times rounded off to 2.68