How to answer this technical I was asked at MM firm??
Had no idea how to answer and was stumped. My page was filled with numbers haha but I don't see how this is even possible without a calculator.
A PE firm buys a company for $500 with $300 debt and $200 equity. Tax rate is 50%. All LFCF goes to debt paydown. LFCFs are $90, $100, and $110. Exit EV is $500. An associate discovers SG&A was understated by the same fixed amount each year. After correction, MOIC drops from 2.5x to 2.2x. By how much was SG&A understated per year?
Anyone have any idea how to answer this without breaking out Excel??
.3 * 500 = 60
60/.5 = 120
120/3 = 40
months late but worth writing up.
the answer is 40 a year. losing 0.3x of moic on 200 of equity is 60 of exit value, that's 20 a year across the three years, and grossed up at the 50% tax rate it's 40 of sg&a.
the intuition is that moic is measured against your equity check, so the 0.3x applies to the 200. that's where people go wrong, anchoring it to the 500 purchase price instead. exit ev never changes here, so the only place the missing 60 can sit is debt you didn't pay down. debt gets paid down with after-tax cash, which is why you gross the 20 back up to reach a pre-tax line like sg&a. the 90/100/110 never enter it. they're there to confirm the 2.5x and to bait you into building the model.
Revised 2.2x MOIC on 200 entry equity represents a revised 440 exit equity value, which implies 60 debt remains at exit. 60 debt remaining at exit implies 60 less LFCF was generated cumulatively, and allocating uniformly as instructed, 20 less LFCF was generated in each year. This 20 represents a post-tax impact of understating SG&A, so we must remove to solve for 20/0.5 = 40 SG&A was understated each year.
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