Part 1.

A stock is selling today for $40 per share. At the end of the year, it pays a dividend of $2 per share and sells for $44. What is the total rate of return on the stock?
What are the dividend yield and capital gains yield?

Part 2.
Suppose the year-end stock price after the dividend is paid is $36. What are the dividend yeild and capital gains yield in this case? Why is the dividend yield not affected?

Part 1:
(Total return= (dividend+appreciation)/(initial value) = (2 + 4)/40 = 15%
5% is dividen yield and the rest (10%) is capital gains yield.

Part 2.: Dividend yield = 2/40 = 5%, again, because the same dividend gets divided by the same initial stock value. Capital gains yield = -4/40
= -10%

because the stock price decreased. The dividend yield is not affected because the dividend is paid regardless of the stock price.

To calculate the total rate of return on the stock in Part 1, divide the sum of the dividend and appreciation by the initial value of the stock: (2 + 4) / 40 = 15%.

The dividend yield can be found by dividing the dividend by the initial value of the stock: 2 / 40 = 5%.

The capital gains yield is calculated by subtracting the initial value of the stock from the ending value and then dividing by the initial value: (44 - 40) / 40 = 10%.

Therefore, the dividend yield is 5% and the capital gains yield is 10% in Part 1.

In Part 2, the dividend yield remains the same because the dividend is still $2 per share. Dividend yield is calculated by dividing the dividend by the initial value of the stock.

So, the dividend yield is still 5% in Part 2.

The capital gains yield, on the other hand, changes in Part 2. To calculate the capital gains yield, subtract the initial value of the stock from the ending value and then divide by the initial value: (36 - 40) / 40 = -10%.

The reason the dividend yield is not affected is because it is based on the initial value of the stock and the dividend amount, both of which remain the same regardless of the ending value of the stock.

Part 1:

To calculate the total rate of return, we need to consider the dividend and the appreciation of the stock. The formula for total return is the sum of the dividend and the appreciation divided by the initial value of the stock.

Total return = (dividend + appreciation) / initial value

In this case, the dividend paid is $2 per share, and the appreciation is the difference between the selling price ($44) and the initial price ($40), which is $4.

Total return = (2 + 4) / 40 = 0.15 or 15%

To determine the dividend yield and capital gains yield, we need to look at the individual components of the total return. The dividend yield represents the dividend as a percentage of the initial stock value, while the capital gains yield represents the appreciation as a percentage of the initial stock value.

Dividend yield = dividend / initial value = 2 / 40 = 0.05 or 5%

Capital gains yield = appreciation / initial value = 4 / 40 = 0.10 or 10%

Therefore, the dividend yield is 5%, and the capital gains yield is 10% for this stock.

Part 2:
If the year-end stock price after the dividend is paid is $36, we can recalculate the dividend yield and capital gains yield using the same formulas.

Dividend yield = dividend / initial value = 2 / 40 = 0.05 or 5%

The dividend yield remains the same because it is based on the initial stock value and the unchanged dividend amount.

To calculate the capital gains yield, we need to consider the new appreciation, which is the difference between the selling price ($36) and the initial price ($40), resulting in a negative value of -$4.

Capital gains yield = appreciation / initial value = -4 / 40 = -0.10 or -10%

The capital gains yield becomes -10% because there is a decrease in the stock's selling price, resulting in a negative appreciation.

The dividend yield is not affected because it is determined by the initial stock value and the dividend amount, not by the change in stock price.