Question

You are interested in purchasing the common stock of Azure Corporation. The firm recently paid a dividend of $3.00 per share. It expects its earnings and hence its dividends—to grow at a rate of 6.1% for the foreseeable future. Currently, similar-risk stocks have required returns of 9.6%. a. Given the preceding data, calculate the present value of this security. Use the constant-growth dividend model (Equation 8.8) to find the stock value. b. One year later, your broker offers to sell you additional shares of Azure at $74. The most recent dividend paid was $3.18, and the expected growth rate for earnings remains at 6.1%. If you determine that the appropriate risk premium is 6.71% and you observe that the risk-free rate (Rp) is currently 5.32%, what is the firm's current required return? c. Applying Equation 8.8, determine the value of the stock using the new dividend and required return from part b. d. Given your calculation in part c, would you buy the additional shares from your broker at $74 per share? Explain. e. Given your calculation in part c, would you sell your old shares for $74? Explain.

Answer 1

(a)

Present value of security = Dividend for next period /(r-g) [ where r= required rate of return and g= growth rate]

Here, Dividend for next period = 1.061*$3 = $3.183 ; r= 9.6 %; g=6.1%

Hence Present value of security= 3.183/(0.096-0.061) = $90.9429 or $90.94

(b)

Required rate of return= risk free rate of return + risk premium=5.32%+6.71% = 12.03%

(c)

Dividend for next period = 1.061*$3.18 = $3.37398 or 3.374 ; r= 12.03 %; g=6.1%

Hence Present value of security= 3.374/(0.1203-0.061) = $56.8971 or 56.9

(d) No, the firm's stock value is lower than the current market price, hence its currently overvalued in the market. I would not buy the share at $74 per share.

(e) Yes, given the current situation, it makes sense to sell the share for $74 when the intrinsic value is lesser.