Charlie Dobbs is considering investing in Astrotech. His research has revealed the following: The market is returning 11%
Three month treasury bills are yielding 5%
Astrotech's beta is 1.2
Astrotech recently paid a dividend of $1.50
Analysts expect Astrotech to grow at 4% indefinitely
How much should Charlie be willing to pay for a share of Astrotech?
A)$19.02
B)$12.00
C)$10.26
D)$18.29

Question

Quizplus · Accepted Answer

To determine the price Charlie should be willing to pay for a share of Astrotech, we can use the Gordon Growth Model (also known as the Dividend Discount Model for a perpetually growing dividend). The formula is P = D / (k - g), where P is the price, D is the dividend, k is the required rate of return, and g is the growth rate.First, we need to calculate the required rate of return (k) using the Capital Asset Pricing Model (CAPM), which is k = risk-free rate + beta * (market return - risk-free rate). Plugging in the values: k = 5% + 1.2 * (11% - 5%) = 5% + 1.2 * 6% = 5% + 7.2% = 12.2%.Next, we use the Gordon Growth Model with D = $1.50, k = 12.2%, and g = 4%: P = $1.50 / (12.2% - 4%) = $1.50 / 0.082 = $18.29.Therefore, Charlie should be willing to pay $18.29 for a share of Astrotech.

Charlie Dobbs Is Considering Investing in Astrotech