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Company Z is currently financed solely by common stock and has 1000 outstanding shares with a (time 0) market price of 10 dollars per share. The company’s expected earnings is 1000 dollarseach year (earned at time 1, 2, 3,…) and the earnings are distributed as dividends. It now announces that it intends to issue $4000 of bonds and use the proceedings (4000 dollars) to buy back stocks. The bonds has an indefinite term, a face value of 100 dollars and coupon rate of 5% per year, the annual yield to maturity of the bonds is 5%.

(a)What is the price per share of stock after the announcement?

(b) How many shares are outstanding after the stock repurchase?

(c) Compare the stock holders’ expected earning per share before and after the stock repurchase?

(d) Calculate the price per share of company Z’s stock after stock repurchase using discounted cash flow model. That is, the price of a share of stock is the present value of all future dividends.

So I understand announcement doesn't change the price per share of the stock so it is still 10 dollars.

And Since 4000 dollars purchases 400 shares there are 600 shares left after the repurchase.

Before you earned 1000 dollars every year, but now you gotta pay 4000*0.05 as the coupon rate which means you get 800 dollars every year now. However there are only 600 shares as well. So 800/600 = 4/3 for the expected earning per share.

But I don't understand part D at all. I thought it would be expected earnings / rate of interest, and we know expected earnings is 4/3, and rate is 10%, so you do 4/3/0.1 which you get 13.3333. However the answer says its 10. Where did I go wrong?

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The problem is with discount rates. Earlier, you had a discount rate for the business (which was also equal to the cost of equity) of $10\%$.

Now as there is debt of $4000$ (which costs $5\%$) and equity of $6000$ (which costs $r\,\%$, say), you must have have $10\% = \dfrac{4000\times 5\%+6000\times r \,\%}{10000}$ giving a cost of equity of $13.33...\%$. The equity is now costlier as the additional debt makes its cash flows riskier. Discount the EPS with this new cost and you get your answer...

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