Question

Consider the following three stocks: Stock A is expected to provide a dividend of $14 a share forever. Stock B is expected to pay a dividend of $7 next year. Thereafter, dividend growth is expected to be 4% a year forever. Stock C is expected to pay a dividend of $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. a. If the market capitalization rate for each stock is 9%, which stock is the most valuable?

Answer 1

Price of Stock A = Dividend / Market capitalization rate

Price of Stock A = $14 / 9%

Price of Stock A = $155.56

Price of Stock B = Next Dividend / (Market capitalization rate - growth rate)

Price of Stock B = $7 / (9% - 4%)

Price of Stock B = $140

Dividend in year 1 = $7

Dividend in year 2 = Dividend in year 1 * (1 + growth rate)

Dividend in year 2 = $7 * (1 + 20%)

Dividend in year 2 = $8.4

Dividend in year 3 = Dividend in year 2 * (1 + growth rate)

Dividend in year 3 = $8.4 * (1 + 20%)

Dividend in year 3 = $10.08

Dividend in year 4 = Dividend in year 3 * (1 + growth rate)

Dividend in year 4 = $10.08 * (1 + 20%)

Dividend in year 4 = $12.096

Dividend in year 5 = Dividend in year 4 * (1 + growth rate)

Dividend in year 5 = $12.096 * (1 + 20%)

Dividend in year 5 = $14.5152

Dividend in year 6 = Dividend in year 5 * (1 + growth rate)

Dividend in year 6 = $14.5152 * (1 + 20%)

Dividend in year 6 = $17.41824

Dividend in year 7 = Dividend in year 1 * (1 + growth rate)

Dividend in year 7 = $17.41824 * (1 + 0%)

Dividend in year 7 = $17.41824

Price of Stock C in year 6 = Dividend in year 7 / (Market capitalization rate - growth rate)

Price of Stock C in year 6 = $17.41824 / (9% - 0%)

Price of Stock C in year 6 = $193.536

Price of Stock C = Dividend in year 1 / (1 + Market capitalization rate) + Dividend in year 2 / (1 + Market capitalization rate)² + Dividend in year 3 / (1 + Market capitalization rate)³ +Dividend in year 4 / (1 + Market capitalization rate)⁴ + Dividend in year 5 / (1 + Market capitalization rate)⁵ + Dividend in year 6 / (1 + Market capitalization rate)⁶ + Price of Stock C in year 6 / (1 + Market capitalization rate)⁶

Price of Stock C = ($7 / (1 + 9)) + ($8.4 /(1 + 9%)²) + ($10.08 /(1 + 9%)³) + ($12.096 /(1 + 9%)⁴) + ($14.5152 /(1 + 9%)⁵) + ($17.41824 /(1 + 9%)⁶) + ($193.536 /(1 + 9%)⁶)

Price of Stock C = $6.42 + $7.07 + $7.78 + $8.57 + $9.43 + $10.39 + $115.40

Price of Stock C = $165.06

StocK C seems to be the most valuable stock