Answer to Question #238321 in Macroeconomics for Comfort

Question

GMC latest annual dividend of $1.25 a share was paid yesterday and maintained its
historic 7% annual rate of growth
You plan to purchase the stock today because you believe that the dividend growth rate will increase to 8% for the next three years and
the selling price of the stock will be $40 per share at the end of that time
I.) How much should you be willing to pay for the GMC stock if you require a 12% return?

II.) What is the maximum price you would be willing to pay for the GMC stock if you believe that the 8% growth rate can be maintained indefinitely and you require a 12% return.

III). If the 8% rate of growth is achieved. What will the price be at the end of year 3. Assume conditions (II)

Answer 1

(i) How much should you be willing to pay for the GMC stock if you require a 12% return?

 Projected dividends next 3 years:

 

Year 1 ($1.25 x 1.08) = $1.35

Year 2 ($1.35 x 1.08) = $1.46

Year 3 ($1.46 x 1.08) = $1.58

 

Required rate of return 12%

Growth rate of dividends 8%

​The present value of the stock is:

​1.35/1.12+1.46/(1.12)²+1.58/(1.12)³

1.35/1.12+1.46/1.2544+1.58/1.4049

1.21+1.16+1.12= of $3.49

(ii)What is the maximum price you would be willing to pay for the GMC stock if you believe that the 8% growth rate can be maintained indefinitely and you require a 12% return.

 Growth rate 8%

Required rate of return 12%

​

1.35/0.12-0.08=1.35/0.04

= of $33.75

(iii) If the 8% rate of growth is achieved. What will the price be at the end of year 3. Assume conditions (II)

1.58/0.12-0.08=1.58/0.04

 of $39.50