Answer to Question #118467 in Financial Math for syed

Question

Antique Replicas, Inc., has a beta of 1.40, the annual risk free rate of interest is currently 10 percent, and the required return on the market portfolio is 16 percent. The most recent dividend paid by the firm was $3.40. The firm estimates that its dividends will grow at 10 percent next year. The company expects slowing business in year 2 and 3, hence no growth in dividends in these two years. Then, the dividends will continue to increase at an annual compound rate of 5% per year for the indefinite life. Estimate the value of Antique Replicas, Inc., stock.

Answer 1

$PV1=\frac{3.4*1.1}{0.1+1.4*(0.16-0.1)+1}=3.16$

PV-present value; PV1-present value after one year; For the bond:

$PV=\frac{D}{(1+i)^n}$

D-dividens

$D=3.4*1.1$

i-discount rate

n-number of years

i for bond:

"i=i'+b*(i"-i')"

i'-annual risk free rate of interest

i"-the required return on the market portfolio

"PV=\\frac{D}{i'+b*(i"-i')+1}"

$PV2=\frac{3.16}{(0.1+1.4*(0.16-0.1)+1)^2}=2.25$

PV2-present value after 2 years

"P=\\frac{D}{i'+b*(i"-i')-ir}+PV1"

P-price of bond

ir- interest rate of dividens increase

$P=\frac{2.25}{0.1+1.4*(0.16-0.1)-0.05}+3.16=19.95$