Simple LBO question

Hi all,

following financial data for company A are given:
In Year 0:
Rev = 100 M$ growing by 10% CAGR
EBIT = 15% (constant margin throughout projection period)
D&A = 5 M$ (constant throughout projection period)
Inventory = 5 M$ (% of rev. constant)
A/R = 5 M$ (% of rev. constant)
A/P = 5 M$ (% of rev. constant)
CapEx = 6% of total rev (% of rev. constant)
Interest rate = 5% of total debt
Tax = 20%

Now company A will be bought for 5x EBITDA in Year 0 (i.e., 5 x 20 M$ = 100 M$) and sold for 8x EBITDA in Year 5.

For simplicity reasons, debt will be paydown after 5 years at once using all cash flow saved up to that point.

Question of the task: How much equity should be invested in Year 0 in order to get 2.5 MoM after sale of company A?

Now what I did: I assumed that the purchase of company A is done completely with debt (i.e., 100 M$ debt and interest expense of 5 M$ every year) and got to 42 M$ as total cash flow saved after 5 years.

With an EBITDA of 29 M$ in Year 5, company A would be sold for 232 M$. Now, using 42 M$ to pay down debt would leave us 58 M$ of debt.
Thus, 232 M$ Enterprise Value - 58 M$ net debt = 174 M$ equity value.

174 M$ Equity Value divided by 2.5 MoM equals ~70M$ equity value in Year 0.

So is this (70 M$ equity) the answer to the question of the task? Or what do I need to do in order to answer this?

I'm struggling to understand the connection between the calculated 70 M$ equity value in Year 0 and my initial assumption that the purchase price 100 M$ was completely financed with debt (i.e., equity should be 0 M$, shouldn't it?)?

Your help is much appreciated!

Best and thanks,
Andy