Simtek currently pays a $2.50 dividend (D0) per share. Next year’s dividend is expected to
be $3 per share. Aft er next year, dividends are expected to increase at a 9 percent annual
rate for three years and a 6 percent annual rate thereaft er.
a. What is the current value of a share of Simtek stock to an investor who requires a
15 percent return on his or her investment?
b. If the dividend in year 1 is expected to be $3 and the growth rate over the following
three years is expected to be only 7 percent and then 6 percent thereaft er, what will the
new stock price be?
To find the current value of a share of Simtek stock, we can use the dividend discount model (DDM) which takes into account the present value of future dividends. The DDM formula is as follows:
Current Stock Price = D1 / (r - g)
Where:
D1 = Next year's dividend
r = Required return on investment
g = Growth rate of dividends
Let's calculate the answers to both parts of the question:
a. To find the current value of a share of Simtek stock with a 15 percent required return, we'll use the given information:
D0 (current dividend) = $2.50
D1 (next year's dividend) = $3
Growth rate for the first three years = 9%
Growth rate after the first three years = 6%
Required return (r) = 15%
First, let's find the dividends for the first three years:
D2 = D1 * (1 + g) = $3 * (1 + 0.09) = $3.27
D3 = D2 * (1 + g) = $3.27 * (1 + 0.09) = $3.56
D4 = D3 * (1 + g) = $3.56 * (1 + 0.09) = $3.88
Now let's find the terminal value of the share price at the end of the third year:
Terminal Value = D4 / (r - g) = $3.88 / (0.15 - 0.06) = $3.88 / 0.09 = $43.11
Next, let's calculate the present value of the dividends:
PV(D1) = D1 / (1 + r) = $3 / (1 + 0.15) = $3 / 1.15 = $2.61
PV(D2) = D2 / (1 + r)^2 = $3.27 / (1 + 0.15)^2 = $3.27 / 1.3225 = $2.47
PV(D3) = D3 / (1 + r)^3 = $3.56 / (1 + 0.15)^3 = $3.56 / 1.520875 = $2.34
PV(Terminal Value) = Terminal Value / (1 + r)^3 = $43.11 / (1 + 0.15)^3 = $43.11 / 1.520875 = $28.37
Finally, let's sum up the present values to calculate the current stock price:
Current Stock Price = PV(D1) + PV(D2) + PV(D3) + PV(Terminal Value) = $2.61 + $2.47 + $2.34 + $28.37 = $35.79
Therefore, the current value of a share of Simtek stock to an investor who requires a 15 percent return on their investment is approximately $35.79.
b. If the dividend in year 1 is expected to be $3 and the growth rate over the following three years is expected to be 7 percent and then 6 percent thereafter, we need to recalculate the dividends and terminal value, while keeping the other variables the same.
Using the same process as in the previous calculation:
D2 = $3 * (1 + 0.07) = $3 * 1.07 = $3.21
D3 = $3.21 * (1 + 0.07) = $3.21 * 1.07 = $3.43
D4 = $3.43 * (1 + 0.07) = $3.43 * 1.07 = $3.67
Terminal Value = $3.67 / (0.15 - 0.06) = $3.67 / 0.09 = $40.78
Now, let's calculate the present values:
PV(D1) = $3 / (1 + 0.15) = $3 / 1.15 = $2.61
PV(D2) = $3.21 / (1 + 0.15)^2 = $3.21 / 1.3225 = $2.43
PV(D3) = $3.43 / (1 + 0.15)^3 = $3.43 / 1.520875 = $2.26
PV(Terminal Value) = $40.78 / (1 + 0.15)^3 = $40.78 / 1.520875 = $26.82
Current Stock Price = $2.61 + $2.43 + $2.26 + $26.82 = $34.12
Therefore, if the dividend in year 1 is expected to be $3 and the growth rate over the following three years is expected to be 7 percent and then 6 percent thereafter, the new stock price would be approximately $34.12.