Question

3.)

You buy a share of The Ludwig Corporation stock for $21.40. You expect it to pay dividends of $1.07, $1.1449, and $1.2250 in Years 1, 2, and 3, respectively, and you expect to sell it at a price of $26.22 at the end of 3 years.

a. Calculate the growth rate in dividends.

b. Calculate the expected dividend yield.

c. Assuming that the calculated growth rate is expected to continue, you can add the dividend yield to the expected growth rate to obtain the expected total rate of return. What is this stock’s expected total rate of return (assume the market is in equilibrium with the required return equal to the expected return)?

Answer 1

a. Calculation of growth rate in dividends.

While comparing year 1 and 2, dividend has been increased from $1.07 to $1.1449. growth rate is

= (1.1449 - 1.07) / 1.07 = 0.0749 / 1.07 = .07 = 7%

While comparing year 2 and 3, dividend has been increased from $1.1449 to $1.2250. growth rate is

= (1.2250-1.1449) / 1.1449 = .0801 / 1.1449 = .0699 = 7%

Hence the growth rate is 7%.

b. Calculation of expected dividend yield.

Expected dividend yield = Next year's expected dividend / current stock price *100

= (1.2250*1.07) / 26.22 *100

= 1.3108 / 26.22 *100

= 4.999% = 5%

c. Calculation of expected total rate of return

expected total rate of return. = dividend yield + expected growth rate

= 5% + 7%

=12%

-Alternativly Using Gordon Growth Mode

P3= D4 / (Ke-g)

Where

P3 - market price at the end of year 3

D4 - Expected dividend in year 4

Ke - rate of return

g - growth rate

26.22 = 1.3108 / (Ke-.07)

Ke-.07 = 1.3108 / 26.22 = 0.0499

ke = .0499 + .07

= .1199

ke =12%