In this workout, an analyst wishes to include the cost of carbon in their company valuation using the DCF valuation method. And the company is transitioning to clean technologies but is currently an emitter of CO2 emissions. It's set to remain so for the next three years, before fully transitioning to carbon-free technologies in year 4. And the analyst has forecasted CO2 emissions for each year, as well as the number of emissions permits which are expected to be allocated without charge. So what we need to do is firstly forecast how many emissions permits the company will need to purchase in years 1 to 4, and then use these forecasts, the model extracts, and the assumptions provided to calculate enterprise value, including the cost of carbon. So let's look at what we've been given first of all. We've been provided with an assumption for the price of carbon, and that's $130 per tonne. We've also been given the long-term growth rate for the company, the cost of capital, and the effective tax rate. The next thing is we've been given the analyst forecasts for emissions, and you can see that by year 4, those emissions have fallen to 0, because that's the year where they've fully transitioned to carbon-free technology. And we've also been provided with the analyst forecasts for the emission permits allocated without charge. So to forecast the emissions permits which need to be purchased by the company, we simply need to take the difference between the emissions and those covered by the permits allocated without charge, which means that the company needs to purchase permits to cover 7 million tons of CO2 emissions in our first forecast year. We can roll forward that calculation to the end of year 4, and we can see that by year 4, the company no longer needs to buy any emissions permits. We can now take these forecasts for the emissions permits purchased to incorporate the cost of carbon into our valuation. You can see below that we've got operational forecasts for the company from the analyst model, and that gives us our forecast EBITs. We've also got the company's net reinvestment requirements from the model, and below that, we've got space to build our free cashflow calculations. As usual, we'll start by calculating NOPAT, but the difference here is we don't just need the tax on EBIT in our NOPAT calculation, we're also gonna need the cost of carbon. We're gonna treat the carbon cost as a tax-like item in our free cashflow calculation. So for our tax on EBIT, we need our effective tax rate of 25%, and I'll lock that cell reference and multiply that by the EBIT forecast. So that gives us tax on EBIT of 1,000. For the cost of carbon, I need my carbon price, which is 130, I'm gonna lock that cell reference. And I'm gonna multiply that by my forecast of the number of emissions permits that need to be purchased. That gives me a cost of carbon of 910 in my first forecast year. My NOPAT is in my EBIT forecast, less my tax on EBIT, less my cost of carbon. So my NOPAT forecast, my first forecast year is 2,090. We can now calculate the net reinvestment requirements. We simply sum our depreciation, our CapEx, and our other adjustments. And when I add together my NOPAT and my net reinvestment, that gives me my free cash flow forecast of 590 in my first forecast year. Before we do anything else, let's roll forward that calculation to the end of year 4. And you can see that in year 4, my cost of carbon has fallen to 0, because by that point, we are no longer needing to buy any emissions permits. We're now gonna continue in the usual way with our valuation, which is to calculate the terminal value. I'm gonna use my final year free cashflow forecast, multiply that by 1 plus my long-term growth rate, and then divide that by my cost of capital, less my long-term growth rate.

And that gives me a terminal value of 78,818.2. We can now calculate our enterprise value by summing together the present value of my free cash flows and my present value of my terminal value. The present value of free cash flows, I'm gonna calculate using the NPV formula in Excel just to save time. I need the discount rate, first of all, and then I need my free cash flow forecasts for 4 years, and that gives me a present value for my free cash flows of 7,163.5. The terminal value, I need to discount by 4 years. So I'll take my terminal value number and divide that by 1, plus my cost of capital, and raise that to the power of 4.

When I sum together the present value of the free cash flows and the present value of the terminal value, that gives me an enterprise value of 66,182.6.

The only thing to note is that this valuation is gonna be very sensitive to my carbon price. For example, if I go up and change my carbon price to, let's say, $150 per tonne, you can see that has a negative effect on my valuation. My enterprise value has fallen to 65,833.4. So again, that's a really important assumption in our evaluation.