Struggling with Debt to Equity Fraction

CFA Level II Equities
#1

One thing minor I continuously seem to find myself struggling with is how to functionally convert D/E.

For instance, I was just working through an equity problem requiring to un-lever then re-lever beta. I knew the formula for both and was ready to go.

They presented D/E in two ways:

Target company: 40% Debt-to-total-capital

Actual company: 75% Debt-to-equity

I tried ten different inputs and couldn’t get the answer right.

To un-lever you needed .40/.60, so .6666 (so it was Beta * (1/1.6666). To re-lever you didn’t need to do anything to it, so it was just .75 (so ulBeta * (1.75)

Other times I feel like I’ve seen it written as .40/1.40 or .75/1.75

I can’t seem to get down which fraction to use when.

#2

  1. Get rid of those decimals in the fractions (L2 is already terrifying enough!).

  2. Create “values” that might have led to those ratios:

D / C = D / (D+E)

So if D / C = 0.4 = 40 / 100 = 40 / (40+E)

=> Now you got values for D and E (and implicitly C) which you can use for your further calculations.

Similar for D / E

If D / E = 0.75 = 75 / 100

=> So D=75 and E=100

Obviously those are no correct values for absolute D and E but the ratio is unaffected.

I hope this helps!