Basically just need help at the step where you divide both sides by 0.12. Why is it (0.06 / 0.12) x (1+D/E)? When you divide by 0.12 at that step, shouldn't it be (0.06x(1+D/E)) / 0.12? I suck at algebra, is there a rearrangement happening here that I'm missing? Please help! Growth rate = 0.12 Dividend payout = 0.1 Total assets / sales = A/S = 1.5 Profit margin = p = 0.1 With a constant debt-equity ratio, payout ratio, and total assets to sales ratio, the growth rate of 12% is the sustainable growth rate. Therefore, we can use the sustainable growth rate formula Sg = [p(S/A)(1+D/E)R]/[1 (p(S/A)(1+D/E)R)] Looking at this formula, we need the variables p, S/A, D/E, and R. We have p = 0.1, and we need to derive S/A and R. S/A is the reciprocal of the total assets to sales ratio: S/A = 1/(A/S) = 1/1.5 The retention ratio, R, is calculated as 1 minus the dividend payout ratio: R = 1 dividend payout = 1 0.1 = 0.9 Plugging all the numbers we know into the formula, we have 0.12 = (0.1 x (1/1.5) x (1 + D/E) x 0.9) / [1 - (0.1 x (1/1.5) x (1 + D/E) x 0.9)] The numerator in this case can be multiplied out as 0.1 x (1/1.5) x (1 + D/E) x 0.9 = 0.06 x (1 + D/E) Plugging this back into the formula, we get 0.12 = 0.06 x (1 + D/E) / [1 (0.06 x (1 + D/E))] Multiplying both sides by [1 (0.06 x (1 + D/E))], we get 0.12 x [1 (0.06 x (1 + D/E))] = 0.06 x (1 + D/E) Dividing both sides by 0.12, we get [1 (0.06 x (1 + D/E))] = (0.06 / 0.12) x (1 + D/E) which gives us 1 (0.06 x (1 + D/E)) = 0.5 x (1 + D/E) Adding (0.06 x (1 + D/E)) to both sides, we get 1 = [0.5 x (1 + D/E)] + [0.06 x (1 + D/E)] Multiplying out the numbers on the right-hand-side, we get 1 = 0.5 + 0.5(D/E) + 0.06 + 0.06(D/E) This gives us 1 = (0.5 + 0.06) + (0.5(D/E) + 0.06(D/E)) Adding the sets of numbers on the right-hand-side together, we get 1 = 0.56 + 0.56(D/E) Subtracting 0.56 from both sides, we get 0.44 = 0.56(D/E) Dividing both sides by 0.56, we get D/E = 0.785714285 To check that we have gotten the correct D/E ratio, we plug it back into the sustainable growth rate formula to see if we can obtain the growth rate of 12%: Sustainable growth rate = (p(S/A)(1 + D/E) x R) / [1 - (p(S/A)(1 + D/E) x R) = (0.1 x (1/1.5) x (1 + 0.785714285) x 0.9) / [1 (0.1 x (1/1.5) x (1 + 0.785714285) x 0.9)] = 0.107142857 / (1 0.107142857) = 0.12 Now we know that the D/E = 0.785714285 is the correct answer. The correct answer is: 0.79