Question: Calculating the maximum price for a stock? College Investments question?
You plan to buy a common stock and hold it for one year. You expect to receive both $1.50 from dividends and $26 from the sale of the stock at the end of the year. If you wanted to earn a 15 percent rate of return, what is the maximum price you would pay for the stock today?
a. $22.61
b. $23.91
c. $24.50
d. $27.50
This is my work and I think that I have done something wrong. Can someone help me???
Dividend Yield: 1.50/26=.0576= 5.76%
Percentage Return= Dividend Yield + Capital Gains
Percentage Return= 15%, Dividend Yield= 5.67%
15%=5.67%+Capital Gains
-5.67% -5.67%
Capital Gains=9.24%
Capital Gains=26-Price of (a-d)/26
Capital Gains (a)= 26-22.61/26= 13%
Capital Gains (b)= 26-23.91/26= 8.03%
Capital Gains (c)= 26-24.50/26= 5.7%
Capital Gains (d)= 26-27.50/26= -5.7%
None of these come out to be 9.24%, so what am I doing wrong?
Answer:
The denominator in your capital gains calculations is wrong. Your capital gains have the purchase price in the denominator not the sale price. Thus, for a) you want capital gains to be (26 - 22.61)/22.61, etc...
$23.91
What's all those percentages?
Your return is $26+$1.50=$27.50
This must equate to 15%+ original price, in other words it is 115%
So 100% is $27.50/115 x 100=$23.91 (b)
Purchase price = $A (say)
Sale Price = $26
Dividend earning = $ 1.5
Total Earning = $1.5 + $(26-A) = $(27.5-A)
Rate of return = (27.5-A)/A = 0.15
= 27.5/A-1=0.15
= 27.5/A = 1.15
= A = 27.5/1.15 = $23.91