Stock A is expected to provide a dividend of $13.4 a share forever. Stock B is expected to pay a dividend of $6.7 next year. Thereafter, dividend growth is expected to be 4% a year forever. Stock C is expected to pay a dividend of $6.7 next year. Thereafter, dividend growth is expected to be 20% a year for 5 years (i. e., years 2 through 6) and zero thereafter. If the market capitalization rate for each stock is 10%, which stock is the most valuable?

Answer: Stock A is expected to provide a dividend of $13.4 a share forever which means it is a perpetuity. The market capitalization is 10% which means that 10% is the required rate of return. The formula to find the value of a perpetuity is Cash Flow/Rate

The cash flow is 13.4 and rate is 10% so 13.4/0.1 = $134

The present value of Stock A is $134

Stock B is expected to pay a dividend of $6.7 next year and then have a constant growth rate of 6% forever, so we can find what the present value of Stock B will be next year using the DDM method and then discount that value to this year.

1 year from now dividend = 6.7

Growth = 4%

R = 10%

Formula = D * (1+G) / R-G

= 6.7 * (1+0.04) / 0.1-0.04=116.113

Now we need to discount 116.113 back one year so 116.113/1.1 = 105.57

The present value of Stock B is 105.57

For stock C the next year dividend is 6.7 and then for 5 years the growth rate is 20% and then 0 forever so we need to find the value of stock C 6 years from now and then discount it back.

Dividend 1 year from now = 6.7

Dividend 6 years from now = 6.7 * (1.2) ^5=16.67

Value of stock 6 years from now

D = 16.67

G = 0

R = 10

16.67 * (1+0) / (0.1-0)

=166.7174

Now we need to discount back this value 6 years to find the present value of the stock

166.7174/1.10^6

=94.10

The highest present value at a market capitalization of 10% for each stock is of stock A which is $134