1.
Metallica Bearings, Inc., is a young start-up company. No dividends will be paid on the stock
over the next 10 years because the firm needs to plow back its earnings to fuel growth. The
company will pay a $12 per share dividend in 11 years and will increase the dividend by 4
percent per year thereafter. If the required return on this stock is 12 percent, the current share
price is $.
(Do not include the dollar sign ($). Round your answer to 2 decimal places. (e.g.,
32.16))
Explanation:
Here we have a stock that pays no dividends for 10 years. Once the stock begins paying
dividends, it will have a constant growth rate of dividends. We can use the constant growth
model at that point. It is important to remember that general constant dividend growth formula
is:
P
t
= [D
t
× (1 +
g
)] / (
R
−
g
)
This means that since we will use the dividend in Year 11, we will be finding the stock price in
Year 10. The dividend growth model is similar to the PVA and the PV of a perpetuity: The
equation gives you the PV one period before the first payment. So, the price of the stock in Year
10 will be:
P
10
= D
11
/ (
R
−
g
) = $12 / (0.12 − 0.04) = $150
The price of the stock today is simply the PV of the stock price in the future. We simply
discount the future stock price at the required return. The price of the stock today will be:
P
0
= $150 / 1.12
10
= $48.3
2.
Consider four different stocks, all of which have a required return of 16 percent and a most
recent dividend of $4.50 per share. Stocks W, X, and Y are expected to maintain constant growth
rates in dividends for the foreseeable future of 9 percent, 0 percent, and -8 percent per year,
respectively. Stock Z is a growth stock that will increase its dividend by 24 percent for the next
2 years and then maintain a constant 10 percent growth rate thereafter. The dividend yield for
Stocks W, X, Y, and Z is percent, percent, percent, and percent, respectively. The expected
capital gains yield for the respective stocks is percent, percent, percent, and percent.
(Do not
include the percent signs (%). Negative amount should be indicated by a minus sign.
Round your answers to 2 decimal places. (e.g., 32.16))
Explanation:
We are asked to find the dividend yield and capital gains yield for each of the stocks. All of the
stocks have a 16 percent required return, which is the sum of the dividend yield and the capital
gains yield. To find the components of the total return, we need to find the stock price for each
stock. Using this stock price and the dividend, we can calculate the dividend yield. The capital