Storico Co. just paid a dividend of $2.05 per share. The company will increase its dividend by 24 percent next year and then reduce its dividend growth rate by 6 percentage points per year until it reaches the industry average of 6 percent dividend growth, after which the company will keep a constant growth rate forever. If the required return on the company's stock is 10 percent, what will a share of stock sell for today

A share of stock sell for $74.21 today.

Explanation:

This can be calculated as follows:

Dividend per share in year 1 = Year 0 dividend * (1 + growth rate of year 1 dividend) = $2.05 * (1 + 24%) = $2.5420

PV of year 1 dividend per share = Year 1 dividend / (1 + rate of return)^1 = $2.5420 * / (1 + 10%)^1 = $2.31090909090909

Dividend per share in year 2 = Year 1 dividend * (1 + growth rate of year 1 dividend) = $2.5420 * (1 + (24% -6%)) = $2.5420 * (1 + 18%) =$3.00

PV of year 2 dividend per share = Year 2 dividend / (1 + rate of return)^2 = $3.00 / (1 + 10%)^2 = $2.47933884297521

Dividend per share in year 3 = Year 2 dividend * (1 + growth rate of year 2 dividend) = $3.00 * (1 + (18% -6%)) = $3.00 * (1 + 12%) =$3.36

PV of year 3 dividend per share = Year 3 dividend / (1 + rate of return)^3 = $3.36 / (1 + 10%)^3 = $2.5244177310293

Dividend per share in year 4 = Year 3 dividend * (1 + growth rate of year 3 dividend) = $3.36 * (1 + (12% -6%)) = $3.36 * (1 + 6%) =$3.5616

PV of year 4 dividend per share = Year 4 dividend / (1 + rate of return)^4 = $3.5616 / (1 + 10%)^4 = $2.43262072262824

Dividend per share in year 5 = Year 4 dividend * (1 + growth rate of year 4 dividend) = $3.5616 * (1 + 6%) = $3.775296

Price at year 4 = Year 5 dividend / (Rate of return – growth rate) = $3.775296 / (10% - 6%) = $94.3824

PV of price at year 4 = Price at year 4 / (1 + rate of return)^4 = $94.3824 / (1 + 10%)^4 = $64.4644491496482

Share price to day = PV of year 1 dividend per share + PV of year 2 dividend per share + PV of year 4 dividend per share + PV of year 4 dividend per share + PV of price at year 4 = $2.31090909090909 + $2.47933884297521 + $2.5244177310293 + $2.43262072262824 + $64.4644491496482 = $74.21

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