Confusion in Today's Interview?

If it's an ECM group, you don't need M&A comps, DCF, or LBO analyses.

• M&A comps: typically more applicable for control situations. If strategic-to-strategic, then there are likely substantial synergies / cost saving assumptions being underwritten - which would not occur in a public equity exit (i.e. no synergies with individual shareholders). If it's a sale to a PE firm, then the M&A comp is driven by the LBO (affordability analysis)
• DCF: in practicality, is a pure theoretical / academic exercise - not really used in practice and typically only thrown into pitch books as a reference point
• LBO: affordability analysis to a private investor (typically a PE firm / family office) which is an "affordability analysis" - how much can you afford to pay today based on the business' cash flow profile, attainable leverage levels, M&A arbitrage, etc. to meet a designated MoM or IRR. Includes both control and liquidity premia, theoretically
• Public markets: public equity trading comps really the best, most accurate comparison - focus on similar industries, operating models and direct competitors. Provides a sense for what investors (e.g. institutional investors) are interested in and the type of growth and equity story they are underwriting for an investment - the investor base also provides insight into how the "target for an IPO" will be viewed, as certain firms like diversity / stability and others may be interested in growth stock stories with significant consolidation opportunity