In this workout, we're asked to calculate enterprise value and EV to EBIT for a company. We're asked then to sensitize our results by demonstrating the effect of increasing return on invested capital, long-term growth and the cost of capital. Now, the information that we are given on the company includes the current level of invested capital of 100, and that the company is currently generating a return on invested capital of 8%. Now, an analyst has already calculated that this gives NOPAT for the first forecast year of 8, and based on an effective tax rate of 20%, EBIT for the first forecast year of 10. We're also told that the company's long-term growth rate is 3% and the cost of capital is 6%. Now, in order to calculate enterprise value we are going to need to identify the firm's free cash flows generated each year. The present value of these will give us the enterprise value, but how can we calculate free cash flows from the information that we've been given here? Well, let's start off with what we know. We know that the growth rate of the company is 3%. Now, this means that invested capital at the end of the first forecast year must be 3% larger than the invested capital at the start of the year. So invested capital at the end of the first forecast year must be 100 multiplied by 1 plus the growth rate of 3%, giving invested capital of 103.

Now, if invested capital at the end of the first forecast year is 103 and invested capital at the start of the first forecast year is a hundred, then that must mean that 3 was reinvested in the business that year. Now, before we move on, let's just scroll down a little bit so we can see more clearly the next step. If the company generates NOPAT in the year, that's the profit for debt and equity investors of 8, but it then reinvests 3 of that 8 in the business, then the amount that's not reinvested in the business is 5, and that 5 is available for debt and equity investors. So that 5 is the free cash flow generated by the business. So if we now have free cash flow, we can calculate enterprise value for the company, and that's gonna be using the growth perpetuity formula. That's the free cash flow in the first forecast year divided by the cost of capital, less the long-term growth rate, and that gives an enterprise value of 166.7. If we then divide that enterprise value by the EBIT in the first forecast year, that gives us an EV to EBIT multiple of 16.7. Now, this is actually hugely significant, because we've used a mini DCF calculation to derive a multiple, this demonstrates that relative and fundamental valuation are not two distinct things. They're actually linked because profits and cash flows are linked. It also means that if a company has stable growth and we know the first forecast year's earnings, the cost of capital and the expected growth rate, we should be able to predict the EBIT multiple for that company. However, that's not all, as the question then asks us to sensitize our answer. Firstly, we're gonna increase the return on invested capital and we're gonna increase that to 10% and you can see that our EV increases to 233.3, and our multiple increases to 18.7. So increasing returns increases the company valuation. Essentially, if a company increases its returns it's generating more profits out of a smaller capital base so the company will generate more cash for investors. Investors want free cash flow as these are their returns. So returns are an important driver of value. Let's undo that change and now think about what happens if we increase the long-term growth rate, and we're gonna increase that to 5%. And you can see now that our EV has increased to 300 and our multiple has increased to 30 times, wow! So increasing growth increases the company valuation. Actually, this should be intuitive to us because a company which grows more quickly will generate more free cash flow each year and we know investors want free cash flow. So growth is another important driver of value. Let's undo that change and now think about the cost of capital. If we increase the cost of capital to 7%, we can see that our EV has fallen this time, it's fallen to 125, and our multiple has fallen to 12.5 times. So increasing the cost of capital decreases company valuation. Essentially, this is showing us that if a company's cost of capital increases it's perceived as riskier for investors. So they aren't prepared to pay as much for their investment. So cost of capital or risk is an important driver of value but it has an inverse relationship with value. Finally, what happens if we set the cost of capital to the return on invested capital? So we set the cost of capital to 8%. The EV now falls to 100 which is equal to the invested capital and the multiple has fallen to 10 times. Essentially, the firm is not generating any value. The returns that it's generating match exactly the returns required by investors. So growth has no impact on value. This is important because it tells us that firms can only generate value if they generate returns in excess of the company's cost of capital. If they can't achieve this they should return the capital to investors so that those investors can invest in businesses or projects that do exceed their cost of capital.