Question

A firm wishes to maintain an internal growth rate of 8.5 percent and a dividend payout ratio of 43 percent. The current profit margin is 9 percent, and the firm uses no external financing sources. What must total asset turnover be?

Answer 1

Retention Ratio = 100 - dividend payout ratio

= 100-43

= 57%

profit margin = Net Income / Turnover = .09

Net Income = .09*Turnover

internal growth rate = (ROA*Retention Ratio) / (1-(ROA*Retention Ratio)) = .085

(ROA*.57) / (1-(ROA*.57)) = .085

ROA*.57 = .085* (1-(ROA*.57))

= .085 - .04845ROA

ROA*.57 + .04845 ROA = .085

0.61845 ROA = .085

ROA = .085/0.61845

= 0.13744037513

ROA = Net Income / Total Assets = 0.13744037513

.09*Turnover / Total Assets = 0.13744037513

Total Assets = .09*Turnover / 0.13744037513

Total Assets = 0.65482941177*Turnover

total asset turnover = Turnover/Total Assets

=  Turnover/0.65482941177*Turnover

= 1/0.65482941177

= 1.53