I struggled on a model test recently and wanted to see if anyone could assist my understanding of some basic valuation concepts. To create a simple question, the model assumed 100 Unlevered FCF growing at 2% for 20 years and the question was to determine the target purchase price of the business based on the following criteria:

• Target IRR of 15%

• Maximum debt to cap of 60%

• Cost of debt of 6%

• Financing fees of 2% of the debt issuance amount

I may be overcomplicating the question, but I am struggling to understand how to think about any potential regearing during to the 60% debt to cap over the life of the business as the value of the business grows? Would you do this each year?

Thanks for your help!

Region

I am assuming that this is a mental math LBO question and will answer it as such. You could do it on paper or by excel just as easily with more precision.

Usually its fine to just assume 60% debt to cap at entry and that we aren't refinancing. Then ideally you want to figure out how much debt you can pay off - gives you an indication of how much leverage you can convert to equity. Using the full 60% is going to lead to the highest possible initial equity check and still get our returns.

So you can slap on the growing annuity formula and see how much debt our cash flows pay off over time. Its 20 years so if you are doing this on paper you are probably fine to just use into perpetuity instead of time bound (as it is computationally more complex). Then just use 100 / (Interest Rate - Growth Rate) to see how much debt you can pay off. This will pay off more than our debt than we took out due to the extended hold period, but I usually net this out of the ending value as we would likely take this cash out of the business as a dividend every year anyways... so its like capturing that effect, more conservatively (think Net Debt... and TVM as to why its conservative). Our company generates 100 / (6% - 2%) = \$2500 (this is conservative because we pay down the debt early)

Then we can back in to what 15% IRR over 20 years is as a MOIC. If doing this on the fly then use the concepts of rule of 72, 114, 144. Since we have 15% over 20 years we get 72 * 2 = 144 * 2 = 288 * 2 = 576 -> 2 * 2 * 2 * 2 = 16. So we want to approximate using a MOIC of 16, maybe increment by a 1 / 3 to a half since we are about 1 / 3 shy of another 72.

Finally, we want to calculate what the company is worth at exit. Since we have stable growth we can just use a dividend discount model. Also we likely want to use WACC equivalent to what we are entering at which will be 60% * 6% + 40% * (say 10% to make it easy). 3.6% + 4%. WACC = 7.6%

We also need to account for growth of FCF. Again use rule of 72. 2% * 20 years = 40 or about half of 72% so we will assume that it grows about 1.5x. Thus at exit our equity value is 150 / (7.6% - 2%) = \$2700 - Debt + Cash = \$5200 - Debt

Now we just need to solve for purchase price and initial debt. Our biggest constraint is that we know we need to grow our equity 16x. Last part is tricky, but guess and check and you come down to something like \$800 for the entity -> WACC 12.5% (COE - 23%, small cap, highly levered sounds reasonable).

The number of shortcuts you take is going to affect your answer which is why speaking through your assumptions is critical. BUT the answer will likely be higher because of the debt and changing your cash accrual number may be worth it.  Anyways - thats how I'd approach a question like the above.