Confused as how paying down debt faster juices returns in investments

Know that PE firms like to pay down debt faster with any excess cash they have on hand to juice returns. Is this b/c as investors, they only have to worry about the equity stake and not take into consideration the costs incurred with paying down debt since that's on the company-level and not coming out of their pockets?

I've been thinking through a simple home ownership example and it doesn't quite check out as I'd also be liable for the money used to pay the debt which makes me think that as a homeowner you'd prefer to drag out paying your debt and employ the money that could be used to pay down your debt faster on other investments? Can someone let me know if this is correct or if you'd still prefer to also pay down debt faster even as a homeowner?

In year 0, I put down a 20% down payment on a 100k house and use debt to fund the rest of the purchase. I'd therefore have put in 20k of my own money and 80k of debt is used.

Lets assume no mandatory amortization of debt or interest and I sell the house at beginning of year 2 for 150k. Paying back the debt, I'd pocket 70k giving me a MOIC of 3.5x and 250% return - (70k-20k)/20k.

Then lets assume a scenario where there is mandatory amortization of debt and interest. If life of loan is 8 years and annual interest of 10%, that means the mandatory amortization rate would be 10k for year 1 and an interest incurred of 8k (assuming no tax shields for simplicty). If i were to sell the house at beginning of year 2 for 150k, I'd pocket 80k now giving me a MOIC of 4x but my actual return falls since I've now spent additional money of 18k on this investment correct? So my return would be (80k - 38k) / 38k ~ 110% return?

Following in this same scenario lets say I decide to service the debt faster by paying another 10k on top of the required amortization of 10k. I'd pocket 90k now after paying back the 60k of debt still owed giving me a MOIC of 4.5x but I've also incurred 28k of additional expenses in addition to the 20k of cash I put in upfront. So my % return is (90k-48k)/48k = 87.5%?

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It doesn't really work with a house/mortgage example as the house itself doesn't generate free cash flow with which to pay down debt amortisation and interest, so you (i.e. the sponsor) has to fund those cash flows which depresses MOIC.

In a corporate example the business should be able to service debt without the sponsor putting in more money - this lowers period end cash AND debt, but because the average debt balance for the period is lower with amortisation than without, then the interest expense is lower and so the net effect is a reduction in net debt (i.e. maximisation in exit equity) compared to the no amortisation example.

Because in a corporate example the sponsor doesn't have to put in any money to pay debt amort / interest (unlike your house example), MOIC is simply (Exit Equity/Entry Equity) so your MOIC will be raised by debt paydown in nearly all cases.

 

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