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Hi,

I'm happy to try and help!

This is a broad topic, so without any further info, some general points to consider (which you may already have!):

• Are you pitching to a corporate client — i.e., the party raising financing — or the party financing the deal, such as a private equity fund or investment bank underwriting a debt issuance? (I am assuming it is a corporate client).
• What sector does the client operate in? Some sectors like oil/gas and telecoms have high levels of gearing compared to other sectors like professional advisory and pharmaceutical industries. Unless the client has a good reason otherwise, you would not want deviate too aggressively from the industry norms.
• Has your client considered accessing internal forms of financing to fund the deal? If it has a high volume of retained earnings, rather than undergo a large one-off dividend or share buyback, it might consider reinvesting these retained earnings to keep the external sources of financing lower. This will depend on the financial performance of the company, as well as the industry. For instance, growth stocks like Amazon and Alphabet generally use a higher rates of internal financing because they do not issue dividends and have more cash on hand.
• As a general point, it is important to tailor advice to the client's own finances. An investment grade company can raise debt more cheaply than a company with less favourable credit ratings.
• In an interview, you are likely to score more points by considering wider macro-economic factors. I'm mainly thinking of interest rates and their impact on the cost of borrowing. Right now, the cost of credit worldwide is more expensive because interest rates are at their highest points since before the 2007-08 Global Financial Crisis. Therefore, financing a highly-levered buyout requires the predicted return on capital employed (from the client's perspective) to far exceed the minimum levels we saw two years ago. In other words, debt financing is more expensive now than in the past decade or so. There are therefore fewer deals out there that can justify the added interest costs. Therefore, your client might look into alternatives, like hybrid financing. I am thinking of issuing convertible debt securities. The investors get the option to convert the loan amount into equity in the future, which entitles the issuer to demand a lower interest rate. The issuer also avoids having to keep cash on hand to pay off the loan amount if it is reasonably confident that a sufficient number of noteholders will exercise their convertible options.
  • A corollary point that arises here is that pure equity financing in the form of an IPO is also less attractive because equity investors are more skittish due to wider market uncertainty. This has driven down valuations for companies looking to go public or raise further equity financing on the public market. But depending on the client's circumstances, a private placement might be a better option to raise equity finance.
• As you say, it is good to consider in broad terms the benefits of debt (interest payments are tax fee [whereas dividend payments are not], returns on shareholder equity are "juiced" with more gearing), compared to equity (requires less stringent financial management because there is no added interest payments to service, no need to bother with debt investors taking additional security or having to comply with loan covenants). 
• Is there any pending litigation or publicity issues that might influence financing decisions? Lenders are less likely to lend if a client is facing likely liability for a massive lawsuit, and bad publicity drives down the price of shares, which may make equity financing less viable (see Cineworld's financial troubles partly arising from a high-value judgment entered against it in Canada).

I am sure there are loads more points I have missed, so I'd welcome others adding on to this.

Also, it is important not to get too bogged down in the details. You'd have a hard time getting all these points across in an interview. So pick a few that are the most interesting to you.