Final answer:
The student is seeking the discount rate for a stock priced at $20 with a $3 dividend, where 30% of earnings are reinvested at a 10% return rate. Using the Gordon Growth Model formula and rearranging it to solve for the discount rate, we apply algebra to find the rate that equates the current stock price with the present value of future dividends.
Step-by-step explanation:
The student's question pertains to finding the discount rate for a stock given certain conditions. This calculation is relevant to fields like finance and business.
The discount rate is the rate of return that could make the present value of future dividends equal to the current stock price. To find this rate, we often use the Gordon Growth Model (also known as the Dividend Discount Model) which assumes that dividends will grow at a constant rate indefinitely. The equation is:
P = D / (r - g)
where P is the current stock price, D is the dividend per share, r is the required rate of return (or discount rate), and g is the growth rate of dividends. Here, the stock sells for $20 and the next dividend will be $3 per share. The company reinvests 30% of earnings, and the rate of return on reinvested funds is 10%, implying a growth rate of 3% (0.3 * 10%). We can use these numbers to rearrange the formula and solve for the discount rate 'r':
20 = 3 / (r - 0.03)
The discount rate can therefore be calculated step by step as follows:
- Multiply both sides of the equation by (r - 0.03) to get rid of the denominator.
- Move everything to one side of the equation to set it equal to zero.
- Solve for r using algebraic methods or a financial calculator.
By solving the equation, we find that the discount rate is the rate at which the present value of future dividends is equal to the stock's current price.