How can you value a company from a debt standpoint?

You make a base case estimate of value, based on forecast earnings. Those forecasts are typically the borrower/lender's forecasts, but you may tweak them to your own expected case. You check that the earnings (less non-P&L items like capex) can sustain the debt - interest coverage shows they can pay interest payments, free cash flow shows they can meet interest and principal payments, leverage ratios show that the debt delevers so that you can get refinance out before the loan gets to maturity or that the leverage will be low enough at maturity to support repayment by internal cash flows or new loans.

Then you run downside sensitivities - what could go wrong. In each case, you check interest coverage, free cash flow and leverage results. If those indicate default, you then make an assessment of the value of the business and check that against the debt balance - is the value enough that you can either force the owner to sell the business as a going concern, or you take control and sell the business, or you just liquidate it - and in each case is the valued realised enough to repay your debt.

In your cases, value is going to be a product of your forecasts eg you'll say something like "Assuming this is an 8x EBITDA enterprise value business in normal conditions and 6x EBITDA in a distressed situation like a debt default, I'd apply that multiple to the EBITDA produced in the breaching downside scenario to determine the value".

Bear in mind that senior debt ranks ahead of subordinate, so can tolerate a lot lower value than subordinated debt can, as senior only care about senior getting repaid, while subordinated has to wait for senior to get paid first. That's why you often see subordinated getting squeezed down or converted to equity in a restructure, while senior suffers less pain.

There's more nuance than this from a professional perspective, but I think that response would be fine if you were talking to interviewers approaching this from a fixed income desk perspective

And if you're asked why you take this approach and only focus on downsides, not upsides - the answer is that, as debt, you are a "fixed income" investor - ie regardless of the outcome, as long as the business can service its debt obligations, your returns are fixed. You don't give a shit about upsides because equity walks away with ALL the equity upsides in those scenarios, which is the whole point of leverage from equity's perspective.

You are only concerned about risks to your fixed income ie scenarios where the company can't make those fixed payments which represent your fixed income.

(bonus points answer) HOWEVER, if you are a debt underwriting/syndication bank, then you do have a secondary focus on the company's/PE buyer's equity returns.

The fatter those returns, the more ability you have as a bank to demand more flex on the interest rate (ie ability to market the debt at, say, LIBOR + 4% margin with "flex" to increase the margin by 2% if necessary to fully syndicate the debt to dbet market buyers). Why? Because the borrower/PE fund's returns are so fat, they can afford to reduce them a little bit.

On the other hand, if the borrower/PE fund's returns are skinny, then they don't have enough fat in their returns to give you more flex, which means you (as debt underwriter) bear more risk of having to syndicate the debt at sub-par value, which means you are taking a loss that can eat through your fees and, if your fees aren't fat enough, cause a loss.

Note that you'll never know for sure what the PE firm's forecast returns are, because it's not in their interests to tell you (because you'd just ask for more fees/more flex!). PE firms will provide a model to the debt underwriting banks, but you have to suspect that that their forecasts have been massaged to present a reasonable credit risk and avoid the underwriting banks demanding a bigger slice of the pie. (If anyone from a PE house has a differing experience, I'd love to hear that).

If you get this point on your first read, give it a go. If you don't get it on first read, don't use it at all. You will only get yourself into trouble.