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One challenge in the creation of DCF models is the estimation of growth rates and tying them into the

model. How is growth in the operating income $($and eventually, free cash flow to the firm$)$ generated?

Overly simplified, firms can increase their revenue while maintaining their margins $($sell more of a unit

without incurring additional costs$),$ or firms can improve their margins while maintaining their revenue $($sell

the same number of units while making more profit on each$),$ or both.

Consider the following simplified income statement and balance sheet of a firm for $2022$:

Interest Expenses $$,40\mathrm{.}00$

Taxes $ $,65\mathrm{.}00$

Note that the tax rate is $t=25\%.$

The firm records capital expenditures of $$185\mathrm{.}00$ and no changes to non$-$cash working capital.

a$)$ What is the free cash flow to the firm and what is the firms EBITDA?

b$)$ What is firm's reinvestment rate, defined as

Reinvestment Rate $=\frac{\text{C}\text{a}\text{p}\text{E}\text{x}-D\text{\&}A+\text{C}\text{h}\text{a}\text{n}\text{g}\text{e}in\text{n}\text{o}\text{n}\text{c}\text{a}\text{s}\text{h}WC}{\text{E}\text{B}\text{I}\text{T}(1-t)}?$

c$)$ What is the firm's return on capital, defined as

ROC$=\frac{\text{E}\text{B}\text{I}\text{T}(1-t)}{BVof\text{e}\text{q}\text{u}\text{i}\text{t}\text{y}+BVof\text{d}\text{e}\text{b}\text{t}-\text{C}\text{a}\text{s}\text{h}}?$

Just like earnings and dividends could not grow faster than $b$ROE, free cash flow to the firm cannot

grow faster than Reinvestment Rate $$ ROC. These two numbers, roughly, represent increases in revenue

by growth and increases in margins, as discussed above.

d$)$ What is your expectation for the FCFF of the firm in $2023?$

Assume that the firm is able to maintain its reinvestment rate and that the appropriate discount rate is

$7\mathrm{.}63\%.$

a$)$ What is the firm's enterprise value $($EV$)$ and what is the firm's EV $/$ EBITDA multiple?

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