Finance
Learning Objectives
You will understand the basic concepts of the time value of money
You will be able to calculate how financial instruments like loans and
credit cards work
Feedback on the reading
Review
Ideal circuit elements
Kirchoff's Laws
Equivalent resistors
Concepts
Ideal bank
Comparsion principle
Connection to energy efficiency
Many energy projects are made attractive to consumers by providing
financing so that people don't have to pay the entire cost at once.
Informal poll
Would you rather have
$1K now or $500 in a year?
$1K now or $1K in a year?
$1K now or $2K in a year?
$1K now or $5K in a year?
$1K now or $10K in a year?
Equivalence principle
Given a choice between money now and money later, most demand a larger
value if money is provided at a later date
Loans
With a loan we essentially rent money and pay a percentage of the
amount we still owe the lender
Discount rate based on equivalence principle
Banks have preferences that set their loan rates
People have preferences that dictate their discount rate
Discount Rate and Net Present Value
Learning Objectives
You will be able to use common financial methods (NPV, IRR, CRF) to compare energy
Capital Recovery Function (CRF)
Net Present Value (NPV)
Internal Rate of Return (IRR)
Guiding Questions
How do we compare two options with different costs over time?
Two cash flows
Discount Rate and Net Present Value
Activity
What is the present value of a $1000 payment 5 years from now with an
interest rate of 10%?
Strategy
Activity
What is the future value of $1000 payment today in 10 years at 7%
interest?
Strategy
Net Present Value (NPV)
Net Present Value
Provides a shorthand to calculate the present value of a stream of
payments.
Provides a method of comparison for two different cash flows
Cash flows can be compared for equivalence
Cash flow
We think of discrete events in time where cash is paid or recieved
Two options
Present Value
Two options
Internal Rate of Return (IRR)
Internal Rate of Return
Tells us at what interest rate a cash flow has a net present value of
zero
We will look at this on a spreadsheet
Capital Recovery Function
Capital Recovery Function
Tells you how much the loan payment is for a given balance, number of payments, and interest rate.
Capital Recovery Factor
Additional Metrics for Energy Projects
Cost of conserved energy
Cost of avoided carbon
Spreadsheet functions
NPV(rate, payments) net present value
IRR(payments, guess) internal rate of return
PMT(rate, number of payments, principal)
Learning Objectives
Use conserved cost of energy as an investment metric
Activity Objective
Be able to use NPV, IRR, and CCE on calculator and computer
Review
How did we determine the cost of a loan?
What were our methods?
Capital Recovery Factor (CRF)
Allows for the calculation of the annual or monthly payment to repay a
loan
Monthly payments
If payments are monthly, we divide the annual percentage rate (APR) by 12 and multiply the number of years ($n$) by 12.
Exercise
What is the annual payment for a $10K loan with an interest rate of 5%
paid over a period of 7 years?
Solution
Exercise
What is the CRF for a 10 year loan at 0% interest?
Solution
0.10 or 10%
Cost of conserved energy
Allows you to calculate the value of an investment as a per kWh cost
This allows easy comparison with the current or plausible future cost
of electricity
CCE (Meier 1984)
$$ CCE = \frac{\textrm{Investment}}{\textrm{Annual Energy Savings}} \cdot \frac{d}{1-(1+d)^{-n}}
$$ CCE = \frac{\textrm{Investment}}{\textrm{Annual Energy Savings}} \cdot \frac{i(1+i)^n}{(1+i)^n - 1}
Cost of avoided carbon
Allows you to calculate the value of an investment as the cost per
amount of carbon not emitted
Allows comparison with the current market price of carbon
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