Question

Crystal Glasses recently paid a dividend of​ $2.70 per​ share, is currently expected to grow at a constant rate of​ 5%, and has a required return of​ 11%. Crystal Glasses has been approached to buy a new company. Crystal estimates if it buys the​ company, its constant growth rate would increase to​ 6.5%, but the firm would also be​ riskier, therefore increasing the required return of the company to​ 12%. Should Crystal go ahead with the purchase of the new​ company?

Answer 1

Answer:

The purchase of the new company increases the price per share of Crystal from $47.25 to $52.28.As the price of the share will increase from purchase of the new company, Crystal should go ahead with the project.

Explanation:

To determine whether to purchase the company or not, we first need to calculate the current share price or fair value of share. We will use the constant growth model of DDM to estimate the current fair value as the dividends are expected to grow at a constant rate. It bases the value of a share on the present value of the expected future dividends.

The share price today can be calculated as,

P0 = D1 / r - g

Where,

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

P0 = 2.7 * (1+0.05)  /  (0.11 - 0.05)

P0 = $47.25

If the purchase of the new company increases the fair value of the share more than its current level, then Crystal Glasses should go ahead with the purchase. We estimate the price per share if the new company is purchased as,

P0 = 2.7 * (1+0.065)  /  (0.12 - 0.065)

P0 = $52.28

As  the price of the share will increase from purchase of the new company, Crystal should go ahead with the project.