CHAPTER 4-6

# CHAPTER 4-6 - equation to find the total asset turnover....

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19. We have all the variables to calculate ROE using the DuPont identity except the equity multiplier. Remember that the equity multiplier is one plus the debt-equity ratio. If we find ROE, we can solve the DuPont identity for equity multiplier, then the debt-equity ratio. We can calculate ROE from the sustainable growth rate equation. For this equation we need the retention ratio, so: b = 1 – .30 b = .70 Using the sustainable growth rate equation and solving for ROE, we get: Sustainable growth rate = (ROE × b) / [1 – (ROE × b)] .115 = [ROE(.70)] / [1 – ROE(.70)] ROE = .1473 or 14.73% Now we can use the DuPont identity to find the equity multiplier as: ROE = PM(TAT)(EM) .1473 = (.062)(1 / .60)EM EM = (.1473)(.60) / .062 EM = 1.43 So, the D/E ratio is: D/E = EM – 1 D/E = 1.43 – 1 D/E = 0.43 20. We are given the profit margin. Remember that: ROA = PM(TAT) We can calculate the ROA from the internal growth rate formula, and then use the ROA in this
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Unformatted text preview: equation to find the total asset turnover. The retention ratio is: b = 1 .25 b = .75 Using the internal growth rate equation to find the ROA, we get: Internal growth rate = (ROA b) / [1 (ROA b)] .07 = [ROA(.75)] / [1 ROA(.75)] ROA = .0872 or 8.72% Plugging ROA and PM into the equation we began with and solving for TAT, we get: ROA = (PM)(TAT) .0872 = .05(PM) TAT = .0872 / .05 TAT = 1.74 times 21. We should begin by calculating the D/E ratio. We calculate the D/E ratio as follows: Total debt ratio = .65 = TD / TA Inverting both sides we get: 1 / .65 = TA / TD Next, we need to recognize that TA / TD = 1 + TE / TD Substituting this into the previous equation, we get: 1 / .65 = 1 + TE /TD Subtract 1 (one) from both sides and inverting again, we get: D/E = 1 / [(1 / .65) 1] D/E = 1.86 With the D/E ratio, we can calculate the EM and solve for ROE using the DuPont identity:...
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