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DFB, Inc., expects earnings at the end of this year of $4.19 per share, and it plans to pay a $2.43 dividend at that time. DFB will retain $1.76 per share of its earnings to reinvest in new projects with an expected return of 15% 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. a. What growth rate of earnings would you forecast for DFB? b. If DFB’s equity cost of capital is 12.2%, what price would you estimate for DFB stock today? c. Suppose DFB instead paid a dividend of $3.43 per share at the end of this year and retained only $0.76 per share in earnings. If DFB maintains this higher payout rate in the future, what stock price would you estimate now? Should DFB raise its dividend?

Question

DFB, Inc., expects earnings at the end of this year of 4.19pershare,anditplanstopaya4.19 per share, and it plans to pay a 2.43 dividend at that time. DFB will retain 1.76pershareofitsearningstoreinvestinnewprojectswithanexpectedreturnof15rate,retentionrate,andreturnonnewinvestmentsinthefutureandwillnotchangeitsnumberofoutstandingshares.a.WhatgrowthrateofearningswouldyouforecastforDFB?b.IfDFBsequitycostofcapitalis12.2c.SupposeDFBinsteadpaidadividendof1.76 per share of its earnings to reinvest in new projects with an expected return of 15% 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. a. What growth rate of earnings would you forecast for DFB? b. If DFB’s equity cost of capital is 12.2%, what price would you estimate for DFB stock today? c. Suppose DFB instead paid a dividend of 3.43 per share at the end of this year and retained only $0.76 per share in earnings. If DFB maintains this higher payout rate in the future, what stock price would you estimate now? Should DFB raise its dividend?

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Solution

a. The growth rate of earnings can be calculated by multiplying the retention rate by the return on new investments. In this case, the retention rate is 1.76/1.76/4.19 = 0.42 (or 42%) and the return on new investments is 15%. Therefore, the growth rate of earnings is 0.42 * 15% = 6.3%.

b. The price of DFB stock today can be estimated using the Gordon Growth Model, which is D1 / (r - g), where D1 is the expected dividend next year, r is the equity cost of capital, and g is the growth rate of earnings. In this case, D1 is 2.43,ris12.22.43, r is 12.2%, and g is 6.3%. Therefore, the price of DFB stock today is 2.43 / (12.2% - 6.3%) = $39.19.

c. If DFB instead paid a dividend of 3.43pershareattheendofthisyearandretainedonly3.43 per share at the end of this year and retained only 0.76 per share in earnings, the new retention rate would be 0.76/0.76/4.19 = 0.18 (or 18%) and the new growth rate of earnings would be 0.18 * 15% = 2.7%. Using the Gordon Growth Model again, the new price of DFB stock would be 3.43/(12.23.43 / (12.2% - 2.7%) = 35.79. Therefore, DFB should not raise its dividend because it would decrease the stock price.

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