# How to account for time-value of money in a total cost of ownership calculation?

I am attempting to conduct a total cost of ownership (TCO) analysis for purchasing a vehicle, to compare the TCO between an electric vehicle and a conventional gasoline car. I would like this calculation to be as accurate as possible. Given my TCO timeframe is 10 years, I feel as though I must account for the time-value of money (ie \$1 in 2020 is not equal to \$1 in 2030). To me, accounting for this time-value means accounting for 1. inflation and 2. a discount rate. The concepts appear straightforward enough, but I am concerned I am confusing them/not applying them correctly. Say I assume inflation is 2% yearly, and my discount rate is 4%. If I am looking at \$100 in 2030, to get this back to 2020 \$, I must do the following: 100*(1-.02-.04)^10? Is this correct? The rates are additive (in the negative direction), not opposing and therefore cannot cancel each other out, correct? I ask this specifically because it would be quite convenient for me to say they cancel out (if they were both the same percentage) and not really need to take into account either. However, they do not cancel, right? They are both in the same direction?

• Asking - What is your motivation to solve this? Are you comparing the potential purchase of two cars? Or is this for a finance class? Oct 16 '20 at 11:56
• @JTP-ApologisetoMonica, my apologies. Should have included that. It is a comparison between two cars, with different fuel types. Electric vs gasoline. Oct 16 '20 at 11:57
• Got it. No need to apologize, the question just happened to catch my attention. My gut reaction is that the variability of gas, maintenance, insurance, etc, will pretty much render the precision of this question moot. But, the question remains legit, of course. Oct 16 '20 at 12:12
• I am not sure (thus no answer, but merely a comment), but I think they indeed cancel each other out: if I have \$100 now, an inflation of 2% and an interest rate of 2%, in 10 years I have \$122 which buy me the same as the \$100 now. Oct 16 '20 at 13:12
• @Fattie - that's what I was saying. You expanded on that a bit. That's what prompted me to wonder if the question was a class problem. In the real world, the effort seems misguided. Oct 17 '20 at 13:53