Finding the Expected Rate of Return for Varying Expected Dividends.
An analyst expects JNJ’s (Johnson & Johnson, from Example 2 4) current dividend of $0.70 to grow by 14.5 percent for six years and then grow by 8 percent into perpetuity. JNJ’s current price is $53.28. What is the expected return on an investment in JNJ’s stock?
In performing trial and error with the two stage model to estimate the expected rate of return, it is important to have a good initial guess. We can use the expected rate of return formula from the Gordon growth model and JNJ’s long term growth rate to find a first approximation: r = ($0.70 X 1.08)/$53.28 + 0.08 = 9.42%. Because we know that the growth rate in the first six years is more than 8 percent, the estimated rate of return must be above 9.42 percent. Using 9.42 percent and 10.0 percent, we calculate the implied price in Table 2 12:
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TABLE 2 12 Johnson & Johnson |
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|
Ti me |
Dt |
Present Value of Dt and V6 at r = 9.42% |
Present Value of Dt and V6 at r = 10.0% |
|
1 |
$0.8015 |
$0.7325 |
$0.7286 |
|
2 |
$0.9177 |
$0.7665 |
$0.7584 |
|
3 |
$1.0508 |
$0.8021 |
$0.7895 |
|
4 |
$1.2032 |
$0.8394 |
$0.8218 |
|
5 |
$1.3776 |
$0.8783 |
$0.8554 |
|
6 |
$1 S774 |
$0.9191 |
$0.8904 |
|
7 |
$1.7035 |
||
|
6 |
$69.90 |
$48.0805 |
|
|
Total |
$74.84 |
$52.9246 |
|
|
Market Price |
$53.28 |
$53.28 |
|
The present value of the terminal value is V6/(1 + r)6 = [Dtl(r g)]/(l + r)6. For r = 9.42 percent, the present value is [1.7035/(0.0942 0.08)]/(1.0942)6 = $69.90. The present value for other values of r is found similarly. Apparently, the expected rate of return is slightly less than 10 percent, assuming efficient prices.