Simple bay back period
Investment / savings
ROR
rate of return
Rate of return
1 / PBP
annual return on investment
Strength of PBP and ROR
- results are independent on (assumptions of) time value of money
- works well for short term
Problems of PBP and ROR
- often companies want a PBP of <2 years, which is a ROR of 50%. This happens rarely, and is therefore not rational decision making
- they do not take lifetime into consideration
effect of lifetime (and PBP)
- if lifetime is shorter then PBP, the investment is a loss
- if lifemtime is 1 year longer then PBP, you only have 1 year of revenue
NPV
net present value
net present value
- I + (B-C)/a
annuity rate
r/ (1-(1+r)^-L)
discrount rate
r
expected rate of return from an alternative investment
(investment being - interest from a bank - stock market appreciation - expected profit from one’s own company)
A high discount rate
- reflects believe that a large profit can be made from another project
- works against projects with high initial investment
Private perspective (r)
a high discount rate > 10%
Negative NPV private perspective
may point the need for government intervention to regulate or subsidise
Postive NPV private perspective
does not mean that user will invest. Barriers are PBP, acces to capital, lack of information.
Social perspective (r)
modest discount rate 2-6%
Social perspective NPV
- results may be used for setting policy priorities
- taxes are not taken into account in cost calcuations
Irr = … for … is …
IRR = 0 for NPV = r
ΔNPV indicates
that one project is better then the other
marginal costs
costs of next unit of CO2
Specific costs
Costs of technology per unit of CO2
formula for specific (or marginal) costs
(a * ΔI + ΔC-ΔB)/ ΔCO2
cost of electricity
(a + I + O&M + fuel cost) / electricity production
real discount rate
r real = (r actual - r inflation)/(1 + r inflation)
Real $ values should always be expressed as
$ for specific year
