Laserclock Corporation paid a dividend for 50 years until it experienced financial difficulty three years ago, at which time the dividend payment was suspended (that is, a dividend has not been paid during the past three years).The company is now much stronger financially, but Laserclock does not expect to pay a dividend for the next five years.Beginning six years from today, the company will pay a dividend equal to R2.10, which is 5 percent greater than the last dividend paid three years ago.After the dividend payments start again, Laserclock expects the dividend to continue to be paid and to grow at a constant rate of 5 percent.If the appropriate market rate for investments similar to Laserclock's shares is 15 percent, at what price should the shares currently be selling in the financial markets?

Question

Quizplus · Accepted Answer

To calculate the current stock price, we need to find the present value of all future dividends. We can divide this process into two parts, the current stock value and the present value of future dividends.
First, we need to find the current stock value, also known as the present value of all future dividends, discounted by the appropriate market rate. Since Laserclock does not expect to pay a dividend for the next five years, the current stock value is the present value of a growing perpetuity starting six years from today. We can use the formula P = D / (r - g) to find the current stock value, where D is the dividend, r is the market rate, and g is the constant growth rate. Plugging in the numbers, we get P = R2.10 / (0.15 - 0.05) = R21. This is the price the shares would be selling for if Laserclock were already paying the dividend.
Next, we need to find the present value of all future dividends, which starts six years from today. We can use the formula PV = D / (r - g) x (1 - (1 + g) ^ -n), where PV is the present value, n is the number of periods (in this case, infinity since the dividends are expected to continue indefinitely), and the other variables are the same as before. Plugging in the numbers, we get PV = R2.10 / (0.15 - 0.05) x (1 - (1 + 0.05) ^ -∞) = R10.44. This is the present value of all future dividends, discounted back to today at the appropriate rate.
Finally, we need to add the current stock value and the present value of future dividends to get the total stock price today. This is P + PV = R21 + R10.44 = R31.44. However, since Laserclock is not currently paying a dividend, we need to subtract the present value of the missing dividends for the next five years. The present value of these missing dividends is the present value of a growing annuity for five years, starting today. We can use the formula PV = C x (1 - (1 + g) ^ -n) / (r - g) x (1 + r) ^ -1, where C is the first dividend missed, which is the same as the last dividend paid three years ago, n is the number of periods (in this case, five years), and the other variables are the same as before. Plugging in the numbers, we get PV = R0 x (1 - (1 + 0.05) ^ -5) / (0.15 - 0.05) x (1 + 0.15) ^ -1 = R0. Therefore, we can subtract the present value of these missing dividends from the total stock price today to get P + PV - PV5 = R31.44 - R0 = R31.44. Therefore, the current stock price for Laserclock Corporation should be R10.44.

Laserclock Corporation Paid a Dividend for 50 Years Until It