Hetfield and Ulrich, Inc., has an odd dividend policy. The company has just paid a dividend of $7 per share and has announced that it will increase the dividend by $5 per share for each of the next 4 years, and then never pay another dividend. If you require a 14 percent return on the company's stock, you will pay $______ per share today.
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To calculate the present value of the stock, we need to find the present value of each future dividend and sum them up. The present value is determined using the formula:
PV = D1 / (1+r)^1 + D2 / (1+r)^2 + ... + Dn / (1+r)^n
Where:
PV = Present Value
D1, D2, ..., Dn = Dividends in each year 1, 2, ..., n
r = Required rate of return
In this case, we have 4 dividend payments: $7, $12, $17, and $22 (increasing by $5 per year). The required rate of return is 14 percent (0.14 in decimal form).
Plugging in the values and calculating:
PV = $7 / (1+0.14)^1 + $12 / (1+0.14)^2 + $17 / (1+0.14)^3 + $22 / (1+0.14)^4
Simplifying the equation:
PV = $7 / 1.14 + $12 / 1.2996 + $17 / 1.4801 + $22 / 1.6804
Doing the calculations:
PV = $6.14 + $9.24 + $11.49 + $13.09
Adding up the values:
PV = $39.96
Therefore, the present value of the stock is $39.96 per share today.