To calculate the expected stock price in one year, we can use the Gordon growth model:
P1 = (D1 x (1 + g)) / (r - g)
Where:
P1 = expected stock price in one year
D1 = expected dividend in one year
g = expected growth rate of dividends
r = required rate of return
We are given the current stock price (Po) and the current dividend (Do), but we need to calculate the expected dividend and the required rate of return.
First, we can calculate the expected dividend in one year:
D1 = Do x (1 + g) = $2.76 x (1 + 0.076) = $2.98
Next, we need to calculate the required rate of return (r). This can be done using the capital asset pricing model (CAPM):
r = Rf + beta x (Rm - Rf)
Where:
Rf = risk-free rate
beta = beta of the stock
Rm = expected return of the market
We are not given the beta of the stock or the risk-free rate, but we can assume that the risk-free rate is 2.5% and estimate a beta of 1.2 for Matthews Industries based on its industry and comparable companies. The expected return of the market is assumed to be 10%.
r = 2.5% + 1.2 x (10% - 2.5%) = 11.5%
Now we can use the Gordon growth model to calculate the expected stock price in one year:
P1 = ($2.98 x (1 + 0.076)) / (0.115 - 0.076) = $71.66
Therefore, the expected stock price in one year is $71.66. The answer is option (a).