# D/E shortcut

At some stage I came across a little shortcut for expanding the D/E ratio. You know, if D/E = 0.5 then E = 0.6667 of Debt. You can solve it using algebra, but I saw a shortcut that made it much quicker. Of course I have since forgotten it and didn’t write it down. Does anybody know what it is? Thanks

what do you exactly mean? D/E = Debt/Equity = 1/2 E = 2/3 * D? (wrong, since 1/2 != 2/3) Or D/(D+E) = 1/(1+E/D) = 1/(1+(D/E)^-1) = 1/(1+2) = 1/3? cheers

You might need to convert between D/E and A/E (the Equity Multiplier), or between D/E and D/A (Total Debt Ratio). So, just set up a little balance sheet. If D/E = 0.5 and you want D/A 1) set E to 1 2) ==> D = 0.5 3) ==> A = 1.5 4) so, D/A = 0.5/1,5 If you want A/E. use the same steps 1–3, but now A/E ==1.5/1 ==1.5 You can convert between any of the three ratios the same way. Just take the ratio given, set the denominator to one, the numerator to the whatever the ratio is, and complete the "balance sheet (i.e. make A = L+E). Then calculate the new ratio. This way is not as algebraically elegant (in fact, it’s identical, but takes a few seconds longer), but it’s easier to remember on the exam (particularly under stress).

No, what I was thinking of was: Say D/E = 2 And you know that Total Assets = \$100 What is Total Equity? You can use the D/E Ratio to calculate the value of Debt - in this case Debt is 0.667 of Assets. The shortcut (which I finally figured out), is to set D + E =1 and from the ratio D = 2E and then simply solve for E, as below 2E + E =1 3E = 1 E = 0.33 Therefore Total Equity = \$33, Total Debt = \$77

67

whoops, yeah \$67