Economics Fundamentals
Economics Fundamentals
Finances dictate most energy decisions and we choose the technology that is the least cost according to some criteria. In this chapter we introduce a few criteria that are commonly used.
Learning Objectives
Calculate equivalent sums of money using discount rates
Able to use the net present value (NPV) to get present value of future investments
Able to use the internal rate of return (IRR) to quantify an energy investment
Able to use the capital recovery function (CRF) to estimate a loan payment
Recognize cost of conserved energy (CCE) and cost of conserved carbon
Concepts
Time Value of Money
Equivalence and Comparison Principle
Net Present Value (NPV)
Future Value
Discounting
Discount rate
Interest rate
Time Value of Money
Equivalence principle
Given a choice between money now and money later, most demand a larger
value at a later date
When someone is indifferent between sum 1 now and sum 2 at a fixed
later date, the sums are considered equivalent
This equivalence can be expressed using a discount rate
Discount rate vs. Interest rate
Discount rate usually refers to personal preferences
Interest rate is usually a real rate charged by a bank
Discount Rate and Net Present Value
Present Value Notation
Monthly vs. Yearly interest rates
Many types of loans advertise a yearly interest rate, but charge
interest monthly.
The yearly interest rate is the APR or annual percentage rate
To find the monthly rate divide this by twelve
$i$ is the annual percentage rate
$n$ is the number of periods in months
Cash flow diagrams
Concepts
Internal Rate of Return (IRR)
Capital Recovery Function (CRF)
Spreadsheet solution for CRF
Inflation
Internal Rate of Return
Finding the IRR is the equivalent of asking, here is a loan, what was the interest rate you got?
Tells us at what interest rate a cash flow has a net present value of
zero
We will look at this on a spreadsheet
This doesn't have a closed-form solution
Usually solved by a computer
Inflation
The cost of goods usually rises over time
This rate is monitored by the Consumer Price Index
As prices rise, the value of money decreases
$r_0$ is the effective rate of interest
$r$ is the nominal rate of interest
$f$ is the inflation rate
For small inflation rates,
Capital Recovery Function
Capital Recovery Factor
Suppose we make a loan. We want to know what the yearly payment is so that the present value of all payments is equal to the loan amount.
This formula allows us to calculate this payment.
Conserved Cost of Energy
The conserved cost of energy is cost of the equivalent purchase of energy to a conservation measure.
This allows us to compare this metric to the cost of energy.
The key to this is a clear definition of the two scenarios you are comparing. The cost is the difference in cost and the energy is the difference in energy between the two scenarios.
The 1984 paper by Alan Meier uses the capital recovery function to convert the overall investment cost to a periodic cost with the appropriate discount rate.
Cost of Avoided Carbon
Similar to this is the cost of avoided carbon. In this case the annual energy savings can be substituted with the annual carbon savings. We would compare this to the cost of carbon in the carbon markets to determine whether it is an appropriate investment.
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