Question

The market consensus is that Analog Electronic Corporation has an ROE = 13%, a beta of 1.80, and plans to maintain indefinitely its traditional plowback ratio of 3/4. This year's earnings were $3.10 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 5% return a. Find the price at which Analog stock should sell (Do not round intermediate calculations. Round your answer to 2 decimal places.) Price b. Calculate the P/E ratio. (Do not round intermediate calculations, Round your answer to 2 decimal places.) PIE Ratio Loading Trailing c. Calculate the present value of growth opportunities. (Negative amount should be indicated by a minus sign. Do not found Intermediate calculations. Round your answer to 2 decimal places.) POO

Answer 1

Ans.

a.

Re = Rf + (Rm- Rf)* Beta

Risk free rate of return (Rf) = 5%

Market Return (Rm) = 14%

Required rate of return (Re): To be calculated

Beta = 1.8

Re = 5% + (14% - 5%) * 1.8 = 5% + 16.2% = 21.2%

Growth rate (g) = Retention Ratio * ROE

ROE = 13%

Retention Ratio = 3/4

g = 3/4 * 0.13 = 0.0975

D1 = E0 (1+g) * (1- b)

Where

E0 = $ 3.10

b = retention ratio

(1-b) = (1 - 3/4) = 1/4

D1 = $ 3.10 * ( 1 + 0.0975) * 1/4

D1 = $ 0.8505625

P0 = D1/(Re - g)

P0 = $0.8505625 /(0.212 - 0.0975 )

P0 = $0.8505625 /0.1145 = 7.4284 or 7.43

b)

E0 = $3.10
E1 = E0*(1+g)
E1 = $3.10*1.0975
E1 = $3.40

Leading P0/E1 = $7.43/$3.40
Leading P0/E1 = 2.19

Trailing P0/E0 = $7.43/$3.10
Trailing P0/E0 = 2.3967 or 2.40

c)

Present value of growth opportunities = P0 - E1 / Re

= 7.43 - (3.40/ 0.212)

= 7.43 - 16.0377 = - 8.6077

The present value of growth opportunities is negative, this is because the ROE (13%) is less than Re (21.2%).

d)

Now, if the plowback ratio, b = 1/4
Then, Growth rate = b*ROE
Growth rate = 1/4 * 13%
Growth rate = 3.25% or 0.0325

D1 = $3.1 * 1.0325 * 3/4
D1 = $2.40

V0 = $2.40/(0.212-0.0325)
V0 = $2.40/(0.212-0.0325) = $ 2.4 / 0.1795 = $ 13.37