On July 1, Kevin purchases 6,000 shares of preferred stock for $25.13 per share.

Question

On July 1, Kevin purchases 6,000 shares of preferred stock for $25.13 per share. The stock is to pay a dividend for $0.29(1.02)^(k-1) at the end of each quarter of the k-th year Kevin holds the stock. That is to say, he first receives four successive end-of-the quarter payments at a rate of $0.29 per share and then four successive end-of-the quarter payments at a rate of $0.29(1.02) per share etc. Find the yield rate for this purchase assuming all dividends are paid and Kevin holds the stock forever.

Explanation / Answer

Returns for 1st year = 0.29*4 = $1.16

Returns for 2nd year = $0.29(1.02)*4= 1.1832

Returns for 3rd year = $0.29(1.02)^2*4= 1.1206864 etc.

Let yield = X

Hence

$25.13 = $1.16*(1/(1+X)+1.02/(1+X)^2+....) = 1.16/(1+X) * (1/(1-1.02/(1+X))

Hence X = yield = 6.616% = Answer

I am 10% sure of this

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