Including Capital Costs in Network Design Analysis
When making infrastructure planning decisions regarding adding new facilities, or adding capacity to existing facilities, you will want to take into account a variety of facility costs to ensure you make the right decisions. These costs include…
- variable cost, dependent on the volume through the facility
- operating fixed cost, to cover costs such as taxes, security, leases, etc.
- depreciation, based on the life of the equipment, and
- cost of the capital used to construct / purchase the facility
In an optimization model you can capture all of these costs separately, or perhaps you will want to consider the fixed costs as a “lump sum”.
Here are two ways that you could build the cost of capital into the decision-making process:
- Add a Capital Recovery Cost to the objective function, to reflect the cost of the capital required to build or expand a facility. One way to do this is the approach used in the Microsoft Excel PMT function, which asks for four inputs to the calculation of recovery cost for a time period:
- capital cost of the asset to be added, e.g. a plant, production line, distribution facility, waste water treatment facility, etc.
- useful life of the asset – the entry here for the number of time periods should be consistent with the frequency of time in your model
- salvage value at the end of the asset’s used useful life, if any
- capital cost charge (interest) rate to be charged in each time period – again, the entry here should be consistent with the frequency of time in your model. (This number could be annual, monthly, or based on another frequency, depending on how you have defined your model.)
The Capital Recovery Charge can be thought of as a loan repayment for the amount of capital required in purchase and install the facility. Excel has help files describing the details of the PMT function, so we will go into more detail here.
- Use Economic Profit as the objective of the model, or as a measure that you use to compare alternative solutions. Economic Profit is your standard accounting profit, less the opportunity cost of capital invested in the business. The opportunity cost is the return that the company would have been able earn if it had invested in the next best alternative project. For instance, if you consider a future alternative where
- the accounting profit for the time period (say, year) is 100, with the additional asset, but
- the asset has a capital cost of 1000, and
- the opportunity cost for capital is 15% per year (the company could have received a 15% return by investing the capital elsewhere) , then
- the Economic Profit for the year is 100 – .15*1000 = -50.
If you are minimizing cost rather than maximizing profit in your model, then you can calculate Impact on Economic Profit for a given alternative, adjusting the operating costs from the model for the effective tax rate, and subtracting the capital charge.
Including the cost of capital appropriately will allow you to present a more complete analysis.