Question

P7-6 Personal Finance Problem Common stock value: Zero growth Kelsey Drums, Inc., is a well-established supplier of fine percussion instruments to orchestras all over the United States. The company's class A common stock has paid a dividend of $5.00 per share per year for the last 15 years. Management expects to continue to pay at that amount for the foreseeable future. Sally Talbot purchased 100 shares of Kelsey class A common 10 years ago at a time when the required rate of return for the stock was 16%. She wants to sell her shares today. The current required rate of return for the stock is 12%. How much capital gain or loss will Sally have on her shares?

Answer 1

Price 10 years ago = Dividend / Old Required Return = $5 / 0.16 = $31.25

Price today = Dividend / Current Required Return = $5 / 0.12 = $41.67

Capital Gain = Price today - Price 10 years ago = $41.67 - $31.25 = $10.42

Answer 2

D₀=$ 5.00 per share 

r_so= 16%

r_s1= 12%

P₀=D₀/rso =$5/6%=$31.25

P₁= D₀ /r_s1 =$5/12%=$41.67

P1-P0= $41.67-$31.25= $10.42

Answer 3

SOLUTION :

Dividend paid for last 15 years is $5 per share each year.

Sally purchased 100 shares 10 years ago.

Let price 10 years ago be $P per share.

10 years ago, rate of return was = 16% = 0.16 

Rate of return possible when purchased = Dividend / P 

=> 0.16 = 5 / P 

=> P = 5/0.16

=> P = Price 10 years ago = 31.25 ($) per share.

Let price today be $P’ per share.

Today, rate of return is = 12% = 0.12

Rate of return possible  = Dividend / P 

=> 0.12 = 5 / P’ 

=> P’ = 5/0.12

=> P’ = Price today = 41.67 ($) per share.

Capital gain per share = P’ - P = 41.67 - 31.25 = 10.42 ($)

So,

Capital gain to Sally on her purchase of 100 shares 10 years ago

= 100 *10.42

= 1042 ($) (ANSWER)