Question

Assume that Bolton Company will pay a $2.00 dividend per share next year, an increase from the current dividend of $1.50 per share that was just paid. After that, the dividend is expected to increase at a constant rate of 5%. If you require a 12% return on the stock, the value of the stock is Multiple Choice $31.78. $30.00. None of the options are correct. $28.57. $28.79.

Answer 1

None of the options are correct as the price today will be $26.786

Step-by-step explanation:

The price of a stock whose dividends are expected to grow at a constant rate forever can be calculated using the constant growth model of the dividend discount model approach (DDM). The DDM bases the value of a stock on the present value of the future expected dividends from the stock.

The formula for price under constant growth model is,

P0 = D1 / (r - g)

Where,

• D1 is the dividend expected for the next period
• r is the required rate of return or cost of equity
• g is the growth rate in dividends

However, as the constant growth rate in dividends is to be applied from Year 2 onwards, we will use the D2 to calculate the price at Year 1 and we will then discount this further for one year to calculate the price today.

P1 or Year1 price = 2 * (1+0.05) / (0.12 - 0.05)

P1 or Year 1 price = $30

The price of the stock today or P0 will be,

P0 = 30 / (1+0.12)

P0 = $26.786