In this workout, we've been told as a company is considering purchasing vans to support its operations and needs to decide whether to purchase petrol or hybrid vans. The company is planning to use the vans for six years and we've firstly been asked to calculate the NPV of buying hybrid vans versus petrol vans, excluding the cost of carbon to decide which option is preferable. But we are then gonna recalculate the NPV including the cost of carbon and we'll see if that changes our conclusion. We've been told to ignore taxes to assume that residual values of the vans after six years are the same and to use an 8% cost of capital. Let's start off by looking at the assumptions that we've been given. First of all, we can see that there's a significant price difference between the petrol vans and the hybrid vans. So the hybrid vans will cost 9,000 euros each more whereas as you would expect the petrol vans will have a higher annual fuel usage. We can calculate the annual fuel costs by taking our fuel price multiply it by the annual fuel usage and I can repeat that calculation for the hybrid vans. So the annual fuel cost for the petrol vans will be 3,740 euros and it'll be 2,125 euros for the hybrid vans. When we scroll down, we can see we've got some tables laid out that will help us to calculate the NPV of the hybrid vans versus the petrol vans. We'll start off with the initial outlay that's the additional CapEx for buying a hybrid van. So we just need to grab the difference in price and we can see that extra 9,000 outlay for the hybrid vans there. However, we know that the annual running costs will be cheaper for the hybrid vans because of the lower fuel usage and we can just grab the difference in the annual fuel costs. I'm gonna lock my cell references so that I can reuse my formulas and I just copy down that formula to give my annual savings. Because this is an NPV calculation, I now need to discount these numbers. So I'll take my annual cost difference divide it by 1 plus my cost of capital, which we've got right at the top. I'm gonna lock that cell reference and I raise that to the power of my year count. So that gives me my present value for my initial outlay and I can copy that formula down and reuse it in each forecast year.

The final thing to do then is just to sum the values above and that gives me my NPV. And we can see we have a very negative NPV here of 1,534. So clearly based on these calculations, the extra outlay for the hybrid vans is not gonna be clawed back through the annual cost savings. Now let's see if our conclusion changes when we incorporate the cost of carbon. Now, in order to do that we need to calculate the carbon cost for each option. And you can see here we've been told the carbon emissions and that's per liter of fuel usage. And we've also been given a carbon price of 105 euros per tonne. So first of all, we need to calculate the annual CO2 emissions and that'll be in kilograms. So we take our conversion of 2.3, multiply it by the fuel usage, and we now have the annual CO2 emissions in kilograms. The annual carbon cost we can then calculate by taking the CO2 emissions, we'll multiply that by our carbon price. We then need to divide by a thousand because we've been given the carbon price per tonne and we have CO2 emissions in kilograms. So we can see that our carbon cost for our petrol van will be 531.3 euros per year whereas it will be 301.9 euros per year for the hybrid vans. We can now add that annual carbon cost difference into our NPV calculations. So we'll start off by grabbing the additional CapEx that's still relevant to our calculations. However, when it comes to the annual savings we'll take the amounts we previously calculated but we are now gonna add in the carbon cost. I'm gonna lock my cell reference there. So we've got the carbon cost for the petrol vans versus the carbon cost for the hybrid vans and we can then copy that formula down. So we've got that difference in each forecast year. The next step as before is to calculate the present value of the cost differences. Take the cost difference, divide by 1 plus our cost of capital, lock that cell reference and then raise it to the power of our year account. And we can then reuse that formula throughout each forecast year. And when we sum those together we can see it is still negative which means we still don't claw back that additional outlay for the hybrid vans through the annual cost savings. Of course, this result is very sensitive to our carbon price assumption. For example, if we increase our carbon price to instead let's say 160 euros per ton then this does change the result of our calculation and would suggest that the hybrid vans would now be preferable. So it's important that we have confidence in our assumptions for our forecast carbon price.