Question 7. [10 points total]

A private equity firm called Clark is considering a leveraged buyout (LBO) of a manufacturing company, MILSA, that prior to the LBO has zero net debt. MILSA generates EBITDA of $40 million, and Clark will need to pay a 6x EV/EBITDA multiple to buy it. Clark plans to finance the purchase with a $100 million loan issued to MILSA; the loan has a 10% annual interest rate and a balloon payment of $100 million due in five years, when Clark believes it will be able to exit its investment by selling MILSA to a larger competitor. The proceeds of the sale will first be used to make MILSAs debt balloon payment, and the remaining proceeds will go to Clark.

Clark expects to be able to grow MILSAs EBITDA at an annual rate of 5% during these five years. At what EV/EBITDA multiple M will Clark need to sell MILSA in order to generate an (annual) IRR of 20% from this investment?