You buy a $100 EBITDA business for a 10x multiple, funded with 5x Debt/EBITDA, and the company repays 50% of debt over 5 years with no extra cash. How much EBITDA growth is needed to realize a 20% IRR?

You buy a $100 EBITDA business for a 10x multiple, funded with 5x Debt/EBITDA, and the company repays 50% of debt over 5 years with no extra cash. How much EBITDA growth is needed to realize a 20% IRR?

• A. 25%
• B. 40%
• C. 50%
• D. 60%

Answer: (C)

This question tests how leverage affects the equity investor’s IRR and how to translate a target IRR into the needed EBITDA growth given a debt repayment plan and a fixed exit multiple. Start with the basics: purchase price is 1000 (10x on 100 EBITDA). Debt at purchase is 500 (5x EBITDA), so equity invested is 500. Over five years, debt is reduced by 50% to 250, with no extra cash being distributed to equity. At exit, Enterprise Value is 10 times the EBITDA at that time, and equity value equals EV minus remaining debt: Equity_end = 10 × EBITDA_end − 250. To realize a 20% IRR on a five-year horizon, the equity investor’s exit cash flow must satisfy: Equity_end = Equity_initial × (1 + IRR)^5 = 500 × (1.20)^5 ≈ 1244.16. Set 10 × EBITDA_end − 250 = 1244.16, which gives 10 × EBITDA_end ≈ 1494.16, so EBITDA_end ≈ 149.42. Growth from the initial 100 to about 149.42 is roughly 49.4%, i.e., about 50% EBITDA growth. Therefore, about 50% EBITDA growth is needed to hit a 20% IRR.

This question tests how leverage affects the equity investor’s IRR and how to translate a target IRR into the needed EBITDA growth given a debt repayment plan and a fixed exit multiple.

Start with the basics: purchase price is 1000 (10x on 100 EBITDA). Debt at purchase is 500 (5x EBITDA), so equity invested is 500.

Over five years, debt is reduced by 50% to 250, with no extra cash being distributed to equity. At exit, Enterprise Value is 10 times the EBITDA at that time, and equity value equals EV minus remaining debt: Equity_end = 10 × EBITDA_end − 250.

To realize a 20% IRR on a five-year horizon, the equity investor’s exit cash flow must satisfy:

Equity_end = Equity_initial × (1 + IRR)^5 = 500 × (1.20)^5 ≈ 1244.16.

Set 10 × EBITDA_end − 250 = 1244.16, which gives 10 × EBITDA_end ≈ 1494.16, so EBITDA_end ≈ 149.42.

Growth from the initial 100 to about 149.42 is roughly 49.4%, i.e., about 50% EBITDA growth.

Therefore, about 50% EBITDA growth is needed to hit a 20% IRR.