In this workout, we've been asked to use the analyst assumptions provided to calculate terminal value for the company using both the traditional growth perpetuity and the value driver formula. Now, the assumptions that we've been given include the long-term growth rates, the WACC. We also have the NPAT and free cash flow forecast of the analyst in a terminal year and the analyst expectation for long-term return on invested capital of the business. Let's start by calculating the terminal value of the business using the traditional growth perpetuity formula. So we'll take the analyst's free cash flow forecast in the terminal year. We'll multiply those by one plus the long-term growth rate of 5%, and then we'll divide that by the cost of capital, less the long-term growth rate.

So that gives us a terminal value for the business of 3,990. Now let's see what happens when we calculate the terminal value using the value driver formula. This time we're gonna start with the NOPAT of the business. We'll multiply that by one plus the long-term growth rate but this time, we're gonna multiply that by one minus long-term growth, divided by the return on invested capital of 10%. And then we divide all that by the cost of capital less the long-term growth rate. Now, this time we have a terminal value of 2,100. That's quite different. In fact, it's significantly lower than the terminal value calculated using the traditional growth perpetuity. So there must be some kind of inconsistency here between the analyst's forecast for free cash flow, NOPAT and return on invested capital. Let's start by looking at the net reinvestment in the terminal year. So that's going to be the difference between the NOPAT and the free cash flow.

Now, let's calculate the invested capital in the terminal year. And we can do this because we know what the return on invested capital is. That's 10%, and we know what the NOPAT is. So if we take our NOPAT of 200 and divided by the return on invested capital, that tells us the invested capital in the terminal year must be 2,000. Now, if we know the net reinvestment and the invested capital, we can then imply what the growth rate is in the terminal year. That's the net reinvestment of 10 divided by the invested capital of 2,000. So that tells us that the implied growth rate in the terminal year is 0.5%, but that is significantly different to the long-term growth rate that the analyst is forecasting of 5%. Why is that? Well, essentially what the analyst has done is that they've underestimated the amount of reinvestment that's required to achieve that 5% growth rate. In fact, the reinvestment that they are forecasting is only sufficient to achieve a growth rate of half a percent. If they want to achieve a long-term growth rate at 5%, the free cash flow forecasts are gonna have to come down significantly. Let's see, if we reduce that to 100, we can now see that the implied growth rate from that free cashflow forecast is 5%. And what we now have is the exact same result for the terminal value using a traditional growth perpetuity and using the value driver formula. So this shows us how powerful the value driver formula is at ensuring that our assumptions are appropriate, and in particular, that our growth rate assumption is underpinned by adequate levels of net reinvestment.