Final answer:
The appropriate price to pay for a stock in Fake Company Lambda, which has a dividend of $1.85 growing at 2.5%, with a required return of 6.1%, is calculated using the Gordon Growth Model and comes out to be $51.39 per share.
Step-by-step explanation:
To determine an appropriate price to pay for a stock when a company announces a dividend and a growth rate, one would use the Gordon Growth Model, also known as the Dividend Discount Model. This model is used to calculate the present value of an infinite series of future dividends that are growing at a constant rate.
According to the question, Fake Company Lambda just paid a dividend to common shareholders of $1.85, and the dividends are expected to grow at a rate of 2.5% indefinitely. The required return on equity investments is 6.1%. Using the formula:
P = D / (k - g)
- P = price of the stock
- D = dividend per share
- k = required rate of return
- g = growth rate of the dividend
We plug in the values:
P = 1.85 / (0.061 - 0.025) = 1.85 / 0.036 = $51.39
An investor should be willing to pay $51.39 for a share of stock in Fake Company Lambda, based on these assumptions.