Question

A corporation's stock pays a semi-annual dividend of 20 per share, payable on June 15 and December 15 each year. Assume that this dividend will remain level in the future. Using the dividend discount method and an annual effective interest rate of 12%, what is the value of one share of this stock as of April 15?

Answer 1

Effective semi-annual rate = (1 + 0.12)^(1/2) - 1 = 0.05830052443

Effective monthly rate = (1 + 0.12)^(1/12) - 1 = 0.009488792935

Stock price on Jan 15 = C/r

The present value of perpetual cash flow formula gives the pv one period (in our case 6 months) prior to the first cash flow.

First cash flow is on June 15. So, the PV = 20/ 0.05830052443 = 343.0500873798 is the price of the stock on Jan 15

So, we can move this PVto April 15 by compounding for 3 months using the monthly effective rate.

Stock price on April 15 = 343.0500873798 * (1 + 0.009488792935)^3

Stock price on April 15 = $352.9084359982

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