The Slim Waist announced today that they will begin paying annual dividends. The first dividend will be paid next year in the amount of $.35 a share. The following dividends will be $.40, $.55, and $.70 a share annually for the following three years, respectively. After that, dividends are projected to increase by 2.5% per year. How much are you willing to pay to buy one share of this stock if your desired rate of return is 12%?

Question

Quizplus · Accepted Answer

To find the present value of the stock based on the given dividends and growth rate, we use the dividend discount model for a multi-stage dividend growth. The dividends for the first four years are given, and from the fifth year onwards, the dividends grow at a constant rate of 2.5%. The present value (PV) of each dividend is calculated using the formula PV = D / (1 + r)^n, where D is the dividend, r is the desired rate of return (12% or 0.12), and n is the number of years until the dividend is received. For the dividends growing at a constant rate from year 5 onwards, we use the Gordon Growth Model formula for the present value of a perpetuity: PV = D / (r - g), where D is the dividend at the start of the perpetuity period (year 5), r is the desired rate of return, and g is the growth rate. This value is then discounted back to the present value.Calculations:Year 1: $0.35 / (1 + 0.12)^1 = $0.3125Year 2: $0.40 / (1 + 0.12)^2 = $0.3190Year 3: $0.55 / (1 + 0.12)^3 = $0.3937Year 4: $0.70 / (1 + 0.12)^4 = $0.4446For the dividend starting from year 5 and growing at 2.5%:D5 = $0.70 * (1 + 0.025) = $0.7175PV of perpetuity from year 5 onwards, discounted back to the end of year 4: PV = $0.7175 / (0.12 - 0.025) = $7.5921Discounting this back to present value: $7.5921 / (1 + 0.12)^4 = $4.8072Adding the present values of the dividends for the first four years and the discounted value of the perpetuity:Total PV = $0.3125 + $0.3190 + $0.3937 + $0.4446 + $4.8072 = $6.2770Therefore, you would be willing to pay $6.27 for a share of this stock to achieve your desired rate of return of 12%.

The Slim Waist Announced Today That They Will Begin Paying