- Spend $954 to remove a wild horse from his home range
- Spend $568 per year to keep him in long-term holding
- Collect $16 per year from the rancher to whom his food is sold
So the question arises: By how much would the grazing fee have to increase to justify the endeavor from an economic viewpoint?
A crude approach to the problem would be to solve for x in the following expression, where 12 represents the forage that would have been consumed by the horse but is now available to livestock (AUMs per year), x is the grazing fee ($ per AUM) and 568 is the cost of long-term holding ($ per year).
12 × x = 568
The answer is x = $47.33 per AUM. The fee would have to increase from $1.35 to $47.33 to pay for long-term holding. But it doesn’t pay for the cost of capture and doesn’t reflect the time-value of money.
That’s why the BLM used present values in the EA.
Another way to answer the question is to model the situation in a Excel, using the built-in present value functions. Most of the cells in this example have text and numbers except B13, B15, B17 and B19, which have formulas.
If you put the data in different cells the formulas won’t work. The sign convention for cash flows is negative for expenditures, positive for revenues.
The present value function discounts a series of future payments (or receipts) back to the present, for a given interest rate and time period, which in this case were taken from the EA.
The model assumes that a captured horse is not adopted and is transferred immediately to long-term holding. The analysis in the EA is a bit more complex, using both short-term and long-term holding, a topic for future discussion.
The present value of the capture cost is $954, as it occurs at the start of the process.
The other transactions are assumed to occur at the end of the year and are assumed to be constant over the life of the project.
- Beginning of year 1: Spend $954 to capture a wild horse
- End of year 1: Spend $568 for holding, receive $16 in grazing fees
- End of year 2: Spend $568, receive $16
- End of year 3: Spend $568, receive $16
- End of year 25: Spend $568, receive $16
The present value of the proposal is the difference between the present value of the grazing revenues and the present value of the holding costs, minus the capture cost.
The formulas are as follows:
- B13: =12*B5
- B15: =PV(B9/100,B11,-B13)
- B17: =PV(B9/100,B11,B7)
- B19: =B15+B17-B3
The cell formats were changed to two decimals, getting rid of the accounting formats applied by Excel when entering financial functions. You can download a copy of the spreadsheet here.
The present value of the proposal, in cell B19, is negative, meaning the present value of the costs exceeds the present value of the revenues. It is a bad investment.
By how much would the grazing fee have to increase to make the present value of the proposal positive?
Try entering some larger values in cell B5, observing the effect in B19. You may have to enable editing when the file opens, depending on the security settings of your computer.
The amount that flips the present value from negative to positive would be the smallest fee that makes wild horse roundups economically viable. If the proposal involved a mix of short-term and long-term holding, as in the EA, the fee would be higher.
Of course, everything is off the table until areas identified for wild horses and burros are managed principally for wild horses and burros, as specified in the original statute.