What is the per gallon price of gasoline in real terms at which you just break even?

Question

You are running a cab business and your current cab fleet is expected to produce $250,000 per year (fixed in nominal terms) in revenues (after labor costs) for the next two years (1 and 2). Your cab fleet has a book value of $50,000 today, $30,000 one year from now, and $20,000 two years from now. All book values are recorded in real terms. If you try to sell your cab fleet you can only fetch its book value (in real terms) on the open market. Your cab fleet gets you 20 miles per gallon and it gets driven 400,000 miles per year. The maintenance costs you $150,000 per year (fixed in nominal terms). The tax rate is 34%, the nominal discount rate is 10%, and the rate of inflation is 2% (you should use a shortcut r = R +i to find the real rate). At the end of the second year you plan to get out of the cab business and get an MBA. What is the per gallon price of gasoline in real terms at which you just break even?

Answer 1

I like to begin with writing out these variables carefully to make it easier to understand.

Variables:

Nominal Revenue in Years 0 - 3: $250,000

Book Value in Real Terms Years 0 - 3: $50,000; $30,000; $20,000

Miles per Gallon: 20

Annual Miles Driven: 400,000 Miles

Total Variable Cost in Gallons of Gas: 20,000 gallons

Fixed Nominal Maintenance Cost: $150,000

Tax Rate: 34%

Nominal Discount Rate: 10%

Rate of Inflation: 2%

Real Discount Rate: 12%

With these variables in mind, we are going to apply a Net Present Value Calculation in Microsoft Excel (which is difficult to show on text) that begins with Years 0 through 2 applying an income statement approach.

It's difficult to explain what's happening without showing in Microsoft Excel though here's my best attempt to explain what is happening:

This is organized as follows:

Revenues for Years 0 through 2 is $250,000

subtract Maintenance cost of $150,000 each year

subtract oil variable cost

equal to earnings before taxation

this cell multiplied by (1 - taxation rate) is your earnings after taxation

We next calculate the NPV of these earnings 0 through 2 by dividing by 1.12 ^ 0-2 (dependent on year)

We calculate the sum of the NPV for each of the years

Next we need to fill in the blanks of the oil variable cost

The oil variable cost is solve for X growing by the rate of inflation each year. This figure multiplied by 20,000 gallons per year is the total gas cost.

Finally, we are going to use the Solver Function in excel as follows:

Adjust cell (Sum of NPV - bookvalue of $20,000 / 1.12^2) to equal $50,000 (the present book value) by changing variable X, the cost of a gallon of gasoline.

The answer is a gas of gasoline to breakeven is $4.17 in Year 0, growing 2% thereafter.