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The risk-free rate of return is 8%, the expected rate of return on the market portfolio is 15%, and the stock of Xyrong Corporation has a beta coefficient of 1.2. Xyrong pays out 40% of its earnings in dividends, and the latest earnings announced were \(10 per share.

Dividends were just paid and are expected to be paid annually. You expect that Xyrong will earn an ROE of 20% per year on all reinvested earnings forever.

a. What is the intrinsic value of a share of Xyrong stock?

b. If the market price of a share is currently \)100, and you expect the market price to be equal to the intrinsic value one year from now, what is your expected one-year holding-period return on Xyrong stock?

Short Answer

Expert verified

a.$101.82

b. $18.52%

Step by step solution

01

Step by Step SolutionStep 1: Given information

rf= 8% or 0.08

E(rM) = 15% or 0.15

β= 1.2

ROE = 20% = 0.20

g = b x ROE = 0.6 x 0.20 = 0.12 = 12%

k = rf+β[E(rm) - rf[

= 0.08 + 1.2 x (0.15 – 0.08)

= 0.164 or 16.4%

02

Calculation of intrinsic value ‘a’

V0= D0(1 + g) / k – g

= $4 x (1 + 0.12)/ 0.164- 0.12

= $101.82

03

Calculation of expected one year holding period return ‘b’

P1= V1 = V0 x (1 + g)

$101.82 x (1 + 0.12) = $114.04

E(r) = D1 + P1 – P0/ P0

= $4.48 + $114.04 - $100 / $100

= 0.1852 or 18.52%

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