The Lighthouse Co. is in a downsizing mode. The company paid a $2.50 annual dividend last year. The company has announced plans to lower the dividend by $.50 a year. Once the dividend
Amount becomes zero, the company will cease all dividends permanently. You place a required rate
Of return of 16% on this particular stock given the company's situation. What is one share of this
Stock worth to you today?

Question

Quizplus · Accepted Answer

The correct answer is A because the present value of the dividends is $3.76. The present value of a perpetuity is calculated as the dividend divided by the required rate of return. In this case, the dividend is $2.50 and the required rate of return is 16%, so the present value of the perpetuity is $2.50 / 0.16 = $15.63. The present value of the declining dividend is calculated as the sum of the present values of each of the dividends. In this case, the dividends are $2.50, $2.00, $1.50, $1.00, and $0.50. The present value of each dividend is calculated as the dividend divided by the required rate of return raised to the power of the number of years until the dividend is paid. In this case, the present value of the first dividend is $2.50 / 0.16^1 = $15.63, the present value of the second dividend is $2.00 / 0.16^2 = $7.81, the present value of the third dividend is $1.50 / 0.16^3 = $3.91, the present value of the fourth dividend is $1.00 / 0.16^4 = $1.95, and the present value of the fifth dividend is $0.50 / 0.16^5 = $0.98. The present value of the declining dividend is the sum of the present values of each of the dividends, which is $15.63 + $7.81 + $3.91 + $1.95 + $0.98 = $30.28. The present value of the stock is the sum of the present value of the perpetuity and the present value of the declining dividend, which is $15.63 + $30.28 = $45.91. The price of one share of stock is the present value of the stock divided by the number of shares outstanding. In this case, the number of shares outstanding is not given, so the price of one share of stock cannot be determined. However, the present value of one share of stock is $45.91.