A private equity firm is guaranteed to receive 80% of the residual value of a leveraged buyout investment, with the rema

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A private equity firm is guaranteed to receive 80% of the
residual value of a leveraged buyout investment, with the remaining
20% owing to management. The initial investment is $500 million,
and the deal is financed with 70% debt and 30% equity. The
projected EBITDA multiple is 3.0. The equity component consists
of:
At exit in 5 years, EBITDA is expected to be $400 million, the
value of debt is $150 million and the value of preference shares is
$300 million.
Calculate
(i) The payoff multiple (cash-on-cash return) for
the private equity firm and for management, respectively
(ii) The IRR (compound annual rate of return) of the PE
firm