Question

In: Finance

DFB, Inc. expects earnings next year of $ 5.49 per​ share, and it plans to pay...

DFB, Inc. expects earnings next year of $ 5.49 per​ share, and it plans to pay a $ 3.55 dividend to shareholders​ (assume that is one year from​ now). DFB will retain $ 1.94 per share of its earnings to reinvest in new projects that have an expected return of 14.6 % per year. Suppose DFB will maintain the same dividend payout​ rate, retention​ rate, and return on new investments in the future and will not change its number of outstanding shares. Assume next dividend is due in one year.

a. What growth rate of earnings would you forecast for​ DFB?

b. If​ DFB's equity cost of capital is 11.4 % what price would you estimate for DFB​ stock?

c. Suppose instead that DFB paid a dividend of $ 4.55 per share at the end of this year and retained only $ 0.94 per share in earnings. That​ is, it chose to pay a higher dividend instead of reinvesting in as many new projects. If DFB maintains this higher payout rate in the​ future, what stock price would you estimate for the firm​ now? Should DFB raise its​ dividend?

Solutions

Expert Solution

Answer a.

Retention Ratio, b = Earnings Retained / Expected Earnings
Retention Ratio, b = $1.94 / $5.49
Retention Ratio, b = 0.3534

Return on Equity, ROE = 14.60%

Growth Rate, g = ROE * b
Growth Rate, g = 14.60% * 0.3534
Growth Rate, g = 5.2%

Answer b.

Cost of Capital, k = 11.40%
Expected Dividend, D1 = $3.55

Current Price, P0 = D1 / (k - g)
Current Price, P0 = $3.55 / (0.114 - 0.052)
Current Price, P0 = $3.55 / 0.062
Current Price, P0 = $57.26

Answer c.

Retention Ratio, b = Earnings Retained / Expected Earnings
Retention Ratio, b = $0.94 / $5.49
Retention Ratio, b = 0.1712

Return on Equity, ROE = 14.60%

Growth Rate, g = ROE * b
Growth Rate, g = 14.60% * 0.1712
Growth Rate, g = 2.5%

Cost of Capital, k = 11.40%
Expected Dividend, D1 = $4.55

Current Price, P0 = D1 / (k - g)
Current Price, P0 = $4.55 / (0.114 - 0.025)
Current Price, P0 = $4.55 / 0.089
Current Price, P0 = $51.12

No, DFB should not raise dividends because companies should always reinvest as much as possible.


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