31.

S= Previous year's sales A= Total assets E= Total equity g= Projected growth in sales PM= Profit margin b= Retention (plowback) ratio Assuming all debt is constant, show that EFN can be written as follows: EFN=PM(S)b+(APM(S)b)s [Hine, Asset needs will equal Ag. The addition to retained carnings will equal PM(S)b(1+8) ] 31. Growth Rates [ LO3] Based on the result in Problem 30, show that the internal and sustainable growth rates are as given in the chapter. (Hint: For the internal growth rate, set EFN equal to zero and solve for s.) 32. Sustainable Growth Rate [ LO3] In the chapter, we discussed the two versions of the sustainable growth rate formula. Derive the formula ROE b from the formula given in the chapter, where ROE is based on beginning of period equity. Also, derive the formula ROAb from the internal growth rate formula. S= Previous year's sales A= Total assets E= Total equity g= Projected growth in sales PM= Profit margin b= Retention (plowback) ratio Assuming all debt is constant, show that EFN can be written as follows: EFN=PM(S)b+(APM(S)b)s [Hine, Asset needs will equal Ag. The addition to retained carnings will equal PM(S)b(1+8) ] 31. Growth Rates [ LO3] Based on the result in Problem 30, show that the internal and sustainable growth rates are as given in the chapter. (Hint: For the internal growth rate, set EFN equal to zero and solve for s.) 32. Sustainable Growth Rate [ LO3] In the chapter, we discussed the two versions of the sustainable growth rate formula. Derive the formula ROE b from the formula given in the chapter, where ROE is based on beginning of period equity. Also, derive the formula ROAb from the internal growth rate formula