The common stock of Auto Deliveries sells for $28.16 a share. The stock is expected to pay $1.35 per share next year when the annual dividend is distributed. The firm has established a pattern of increasing its dividends by 3 percent annually and expects to continue doing so. What is the market rate of return on this stock

Market rate of return is 7.79%

Explanation:

The market rate of return on the stock can be computed using the market price of the stock , which is given below:

share market price =D1/(Expected market return-Dividend growth rate)

share market price is $28.16

D1 is the expected dividend next year which is given by $1.35

expected market return is the unknown

dividend growth rate is 3%

$28.16=$1.35/expected market return-3%

let y be the expected market return

$28.16=$1.35/y-3%

by cross multiplication the equation becomes

$28.16*(y-3%)=$1.35

y-3%=$1.35/$28.16

y=($1.35/$28.16)+3%

y=7.79%

7.794%

Explanation:

We can use the Gordon growth model to determine the price of the stock:

current stock price = next year's dividend / (market rate of return - growth rate)

$28.16 = $1.35 / (market rate - 3%)

market rate - 3% = $1.35 / $28.16 = 4.794%

market rate = 4.794 + 3% = 7.794%

*the market rate of return is equal to the required rate of return (RRR)