Question

The market consensus is that Analog Electronic Corporation has an ROE = 11%, a beta of 1.50, and plans to maintain indefinitely its traditional plowback ratio of 1/5. This year’s earnings were $2.50 per share. The annual dividend was just paid. The consensus estimate of the coming year’s market return is 15%, and T-bills currently offer a 5% 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. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

c. Calculate the present value of growth opportunities. (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to 2 decimal places.)

d. Suppose your research convinces you Analog will announce momentarily that it will immediately change its plowback ratio to 4/5. Find the intrinsic value of the stock. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

(a) T-Bill Returns = Risk-Free Rate = 5 %, Market Return = 15 % = Rm, Beta = 1.5

Using CAPM, Analog's Required Rate of Return = Risk-Free Rate + Beta x (Rm - Risk-Free Rate) = 5 + 1.5 x (15 - 5) = 20 %

Plowback Ratio = 1/5 and ROE =11 %

Growth Rate = ROE x Plowback Ratio = 11 x 1/5 = 2.2 %

Current Earnings = $ 2.5 and Current Dividend = D0 = Earnings x (1-Plowback Ratio) = 2.5 x (1-1/5) = $ 2

Intrinsic Stock Price = P0 = [D0 x (1+Growth Rate) / (Required Return - Growth Rate)] = [2 x 1.022 / (0.2 - 0.022)] = $ 11.48

(b) Current PE Ratio = Current Price / Current Earnings = 11.48 / 2.5 ~ 4.59

(c) Present Value of Growth Opportunities as the name suggests is an estimate of the contribution of future growth opportunities in a stock's current price. It is the difference between the stock's intrinsic price and the stock's price in case of no growth.

A no-growth scenario implies a plowback ratio of 0 (entire earnings are paid out as dividends) and dividends (earnings) remaining perpetually constant at the current level.

Therefore, all future dividends (=earnings) = $ 2.5

Required Return = 20 %

No-Growth Stock Price = 2.5 / 0.2 = $ 12.5

PVGO = Intrinsic Stock Price - No-Growth Stock Price = 11.48 - 12.5 ~ - $ 1.02

NOTE: PVGO of negative indicates that the current level of plow back, ROE and Growth is actually destroying value and in fact firm value would have been higher in the absence of this negative growth inducing plow back. This is essentially happening because the firm's return generated on its equity (retained earnings in the form of plowed back earnings = ROE = 11 %) is lower than its cost of equity (required return = 20 %).

(d) New Plow Back Ratio = 4/5

New Growth Rate = ROE x New Plow Back = 11 x 4/5 = 8.8 %

New Current Dividend = (1-4/5) x 2.5 = $ 0.5

New Intrinsic Stock Price = [0.5 x 1.088 / (0.2 - 0.088)] = $ 4.86