5. Example

Let's consider a (hypothetical) taxi company that is renewing its fleet of 25 cars. There are two alternatives, namely petrol cars and electric cars:

 

  • Petrol cars:
    • A petrol car costs $40'000 apiece for a total investment of $1 million today. 
    • Over the useful life of 5 years, the fleet is then expected to generate an annual net cash flow of $350'000.
    • Carbon dioxide emissions amount to 40 tons per car and year, for a total emission of 1'000 tons per year. There is no binding market price for carbon emissions. However, based on available research, you assume that the total social cost per ton of carbon could be as high as $80.
       
  • Electric cars:
    • An electric car costs $60'000 apiece for a total investment of $1.5 million today.
    • Over the useful life of 5 years, the fleet is then expected to generate an annual net cash flow of $400'000 (we assume electric cars have lower energy costs, which is why their NCF is higher).

  

Let's assume the relevant cost of capital is 7%.

  

With this information, we can value the two project alternatives. See also the accompanying Excel file.

 

Base Case Valuation

For the petrol option, the base case valuation compares the investment of $1 million today with the annual marginal NCFs of $350'000 per year over the next 5 years. The resulting base case valuation is $435'000 (in thousands):
 

\(NPV_{Base, Petrol}=-1'000 + \frac{350}{1.07}+\frac{350}{1.07^2}+...+\frac{350}{1.07^5}=435 \)

 

In contrast, the electric option has a NPV of $140'000:

 

\(NPV_{Base, Electric}=-1'500 + \frac{400}{1.07}+\frac{400}{1.07^2}+...+\frac{400}{1.07^5}=140 \)

 

Consequently, from a purely financial point of view, the petrol option is more attractive, as its base case NPV ($328'000) exceeds that of the electric option (140'000) by $295'000.

 

Adjusted Present Value

The computations above have ignored the carbon emissions of the petrol cars (1'000 tons per year), as the indicated price of $80 per ton is not a binding market price. 

  

In a second step, we can investigate how the project value would change if we incorporated the social costs of carbon emissions. The following table shows the annual carbon costs. Based on our assumptions, the total costs amount to $80'000 per year.

   

Year 1 Year 2 Year 3 Year 4 Year 5
Carbon emissions (tons) 1’000 1’000 1’000 1’000 1’000
Price per ton ($) 80 80 80 80 80
Total costs (thousands of $) 80 80 80 80 80

  

Assuming the same discount rate of 7% applies, we can compute the present value of the petrol fleet's carbon costs (in thousands):

  

\(PV_{Carbon, Petrol}=-\frac{80}{1.07}-\frac{80}{1.07^2}-...-\frac{80}{1.07^5}=-328 \)

  

According to our estimates, the present value of the carbon costs associated with the petrol fleet is −$328'000. 

 

With this information, we can now compute the Adjusted Present Value (APV) of the petrol fleet (in thousands):  

 

\(APV_{Petrol} = NPV_{Base,Petrol} + PV_{Carbon,Petrol} =435-328 = 107\)

 

After taking into account the carbon emissions, the NPV of the petrol fleet drops by $328'000 to $107'000. Since the electric fleet has no carbon emissions, its base case NPV from above ($140'000) remains unaffected. Consequently, after accounting for the carbon footprint of the project, the electric fleet would seem to be the financially more attractive option.