For many companies, it is unreasonable to assume that dividends grow at a consta
ID: 2803930 • Letter: F
Question
For many companies, it is unreasonable to assume that dividends grow at a constant growth rate. Hence, valuation for these companies proves a little more complicated. The valuation process, in this case, requires us to estimate the short-run nonconstant growth rate and use it to predict near-term dividends. Then, we must estimate a constant long-term growth dividend growth rate. Generally, we assume that after a certain point of time, all firms begin to grow at a more-or-less constant rate. Of course, the difficulty in this framework is estimating the short-term growth rate, how long the short-term growth will hold, and then the long-term growth rate. In general, one should predict as many future annual dividends as possible and then discount them back to the present. Then, all dividends to be received after the end of nonconstant growth (the beginning of constant growth) will be valued using the constant growth model presented above. A company's stock just paid a $1.82 dividend, which is expected to grow at 30 percent for the next three years. After three years, the dividend is expected to grow constantly at 10 percent forever. The stock's required return is 16 percent. What is the price of the stock today? Last dividend paid $1.82 Required rate of return 16% Expected ST growth rate 30% Short-run E(g); for Years 1-3 only. Expected LT growth rate 10% Long-run E(g); for Year 4 and all following years. 30% 10% Year 0 1 2 3 4 Dividend $1.82 $2.37 $3.08 $4.00 $4.40 $2.04 = PV of Year 1 dividend $2.29 = PV of Year 2 dividend $2.56 = PV of Year 3 dividend $6.89 = sum of dividend PVs 73.31 = Terminal value $46.96 = PV of terminal value $53.85 = E(P0) Now, with this information...how would you explain to a nonhealthcare major why this is important and how this information is beneficial.
Explanation / Answer
Last dividend paid $1.82
Required rate of return 16%
Expected ST growth rate 30% Short-run E(g); for Years 1-3 only.
Expected LT growth rate 10% Long-run E(g); for Year 4 and all following years.
Year 0 1 2 3 4
Dividend $1.82 $2.37 $3.08 $4.00 $4.40
$2.04 = PV of Year 1 dividend
$2.29 = PV of Year 2 dividend
$2.56 = PV of Year 3 dividend
$6.89 = sum of dividend PVs
73.31 = Terminal value
$46.96 = PV of terminal value
$53.85 = E(P0)= intrinsic price of stock
These are all the information provided.
This is important because intrinsic price of a stock is based on all the earnings estimated to be obatined over the lifetime of the stock discounted to present value.
The disounting is done based on the required rate of return of the firm. So larger the required rate smaller will be the present value of future income.
In this example dividends for the first three years is estimated and discounted to present value. From year 4 till maturity a constant growth rate is estimated and a terminal value of all dividends is calculated standing at end of year 3. This terminal value is then discounted to present value based on require return. The sum of all present values of dividends obtained gives the intrinsic or fair value of te firm's stock.
If the fair value is less than market value, the stock is trading premium and vice versa.
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