I would like to summon all the mathematicians and wizards (and magicians) here to share mathematical tricks and shortcuts that can be used to quickly analyze questions that usually ask whether X will be higher, lower or unchanged. I am thinking of three tricks at the moment:

If you are told that D/E=0.25, then to quickly find the % debt and % equity, simply add 1 to this ratio and reciprocate, i.e. E= 1/1.25=80% and D=20% so D/E=20/80=0.25. Very helpful for calculating WACC quickly.

When a ratio A/B is less than one , deducting an amount X from both numerator and denominator will reduce the ratio even further. For example, 3/10 > 2/9. This can be applied for instance to Return/Equity, which is normally less than one.

When a ratio A/B is greater than one , similarly deducting an amount X from both numerator and denominator will increase the ratio. For example, 10/3 < 9/2. This idea can be useful for interest coverage, asset turnover etc.

so what about in cases when you are adding instead of deducting when A/B ratio is less than 1 and greater than 1 which factor will dominate numerator or denominator?

For what it’s worth, I do the same thing with the D/E ratio. 1+D/E then hit the 1/x button and boom, Equity %. 1 - the result = Debt % obviously. When I discovered this I literally had an “aha” moment because I used to fumble a bit when trying to work out D/V and E/V percentages from a D/E ratio.

I can logic my way through a lot of problems but I stumble on simple mathematic relationships sometimes. I blame the US public school system (or my old age).

Confused on the calculation again. When are we using the method where we add numerator and denominator and take proportion and when do we just use the % given? I thought we said if the D/E ratio is 50% that is 0.5/1 therefore 1/3 D and 2/3 Equity?

Topic Test asks for a WACC calc. The answer says:

note that capital used is based on beginning-of-year values, and the debt ratio is 50%.

Economic profit (EP) = Net operating profit after taxes – WACC

dont know the exact question… but if you notice they tell you debt ratio, not debt/equity. Hope im reading that correct its 4AM and exam nightmares have begun!!

correct! Yeah… dont worry you are not alone… i feel the same sometimes… but sometimes when you take a break and approach it again with a more calm and rational mind… i find you understand it… but the key is to not let these small misunderstandings break your confidence… you already know a lot of stuff… so focus on what you know. Hope that helps…

No, that’s not quite right. If any question says “D/E” anywhere, it’s referring to the debt to equity ratio. A D/E ratio of .50 represents a 1 over 2 ratio, or 33.33% debt and 66.67% equity. Remember D + E = A. 1 + 2 = 3. 1/3 = debt, 2/3 = equity.

If a question says “debt ratio”, it’s only referring to the percentage of debt in the capital structure. So a debt ratio of 40% would be 40% debt and 60% equity.