D1 Consider the standard Gordon model of equity valuation Po = where Po is the time-zero...

 

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D1 Consider the standard Gordon model of equity valuation Po = where Po is the time-zero k-g price of an equity security, D is the dividend in the next period, k is the discount rate (the required return on equity) and g is the dividend growth rate. Let b be the reinvestment ratio, or the fraction of earnings retained in the corporation. Prove that reinvestment of earnings enhances firm value if ROE > k and decreases value if ROE < k where ROE is the firm's return-on-equity. Hint: use calculus. What can you say about the optimal dividend retention policy for the firm, b*? Again, consider the Gordon model from Question 1. Show that the return on the stock price from changes in the discount rate k or dividend growth g is proportional to the price-dividend ratio. The dividend yield today is around 2%. What does this imply for stock returns for a 1% increase in the discount rate? D1 Consider the standard Gordon model of equity valuation Po = where Po is the time-zero k-g price of an equity security, D is the dividend in the next period, k is the discount rate (the required return on equity) and g is the dividend growth rate. Let b be the reinvestment ratio, or the fraction of earnings retained in the corporation. Prove that reinvestment of earnings enhances firm value if ROE > k and decreases value if ROE < k where ROE is the firm's return-on-equity. Hint: use calculus. What can you say about the optimal dividend retention policy for the firm, b*? Again, consider the Gordon model from Question 1. Show that the return on the stock price from changes in the discount rate k or dividend growth g is proportional to the price-dividend ratio. The dividend yield today is around 2%. What does this imply for stock returns for a 1% increase in the discount rate?

Answer rating: 100% (QA)

Answer To prove that reinvestment of earnings enhances firm value if ROE k and decreases value if RO... View the full answer