Question

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 $11 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 15%. She wants to sell her shares today. The current required rate of return for the stock is 10%. How much total capital gain or loss will Sally have on her​ shares?

The value of the stock when Sally purchased it was $ per share?

​

Answer 1

Answer: Capital gain (loss), dollars -Share value today - Share value when purchased Capital gain (loss), %-capital gain (loss), dollars / share value when purchased $110.00 $73.33 Share value today Share value when purchased Capital gain (loss), dollars per share $3.67 [$110.00 - $73.33] Number of shares held Total Capital gain (loss), dollars $3,666.67 [100 shares x $36.67] 100 Capital gain (loss), % 50% [$36.67 / $73.33] Workings: Stock price Annual dividends/ Required rate of return When Purchased $11 Today Annual dividends Required rate of return 15% Stock price That is, the value of the stock when Sally purchased it was $73.33 per share $11 10% $110.00 $73.33 [$11 / 15%-$73.33 $11 / 10%-$110.00]

Answer 2

SOLUTION :

Dividend paid for last 15 years is $11 per share each year.

Sally purchased 100 shares 10 years ago.

So,

Let price 10 years ago be $P per share.

10 years ago, rate of return was = 15% = 0.15 

Rate of return possible when purchased = Dividend / P 

=> 0.15 = 11 / P 

=> P = 11/0.15

=> P = Price 10 years ago = 73.33 ($) per share. 

Let price today be $P’ per share.

Today, rate of return is = 10% = 0.10

Rate of return possible today = Dividend / P 

=> 0.10 = 11 / P’ 

=> P’ = 11/0.10

=> P’ = Price today = 110 ($) per share.  

Capital gain per share = P’ - P = 110 - 73.33 = 36.67 ($)

So,

Price per share was $73.33 when Sally purchased 100 shares.

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

= 100*36.67

= 3667 ($) (ANSWER).