|Fig. 1. Light emitting diode (LED) lamp (Philips|
MyVision 9W, equivalent to 40 watts, picture by
The light emitting diode (LED) lamps are better now, and for households the LED lamp is an alternative to the compact fluorescent lamp (CFL). They are both energy class A lamps.
LED lamps are more expensive, but they last longer, and they consume less electricity. A cash flow analysis shows it is economically worthwhile to replace a CFL by an LED lamp. The payback period is 15 years under certain assumptions. A simple analysis, that disregards interest and inflation, indicates a saving of 6.33 EUR after 25 years. A more elaborate analysis includes interest rate, inflation rate, and discount rate, resulting in higher savings.
Table of contents
The compact fluorescent lamp (CFL) is an energy saving lamp of energy class A. So is the light emitting diode (LED) lamp, but it has some advantages over the CFL: It switches on immediately, and it does not contain mercury. Furthermore, it lasts longer, and it is a little cheaper to use. Some models also have some disadvantages, however: The colour of the light can be rather blue and unpleasant, and sometimes the light flickers.
The following looks at the economy of replacing one CFL with one LED lamp. Or more specifically, the difference between the cash flows of an LED lamp and a CFL. The goal is to obtain a diagram of the investment account, a project balance, in order to appraise such an investment.
We choose an LED lamp equivalent to a 40 watt incandescent lamp. It is the same size as the lamps in the previous example concerning the incandescent lamp and the CFL (Introductory Example: Energy Saving Lamp).
The LED lamp consumes 9 watts (Fig. 1), where the CFL consumes 11 watts. That is not much difference in absolute numbers, but if electricity is expensive, then maybe there is money to be saved after all. The LED lamp is more expensive than the CFL, but it lasts longer than the CFL. Table 1 below contains the specific data, and also below there is a link to a datasheet for the LED lamp.
We assume the CFL lasts 10 years, before it breaks, but the LED lasts 25 years, so we choose a time horizon of 25 years. We assume also that the CFL is five years old at the beginning of the project period. Therefore it must be replaced after year 5 and again after year 15. After year 25 both lamps are scrapped with a scrap value of zero.
A time horizon of 25 years is rather long, especially for a household, and we must consider discounting.
Internal Rate of Return
We view the LED as an alternative, which hopefully saves money in the long run, and we shall apply the earlier quoted principle that only differences count. We therefore take the CFL as our reference and the LED as our investment scenario.
Consequently we form the two cash flow streams and subtract the reference stream from the CFL cash low stream. The resulting cash flow stream is the incremental stream (for assumptions and data see %SEAFigLEDpdf%). The resulting incremental cash flow stream shows that the internal rate of return (IRR) for the 25 year project period is 2.6%.
Earning a 2.6% interest (tax free) over 25 years is comparable to investing in secure bonds (after 50% tax).
Payback Period and Surplus
|Fig. 2. Simple project balance. The abrupt changes|
after year 5 and year 15 are due to the shorter
lifetime of the CFL.
Based on the incremental cash flow stream (not shown), Figure 2 shows the simple project balance (cumulative cash flows diagram). It is simple because it omits interest and inflation. The diagram shows that the payback period is 15 years.
The balance of the account steadily increases after the payback period. Finally, after 25 years, the surplus is 6.33 EUR (the initial investment was 20 EUR).
Project Balance with Interest
The previous analysis is a first approximation to the evolution of the project account. A more advanced — and possibly more accurate — model includes interest, inflation and time preference. For this we need:
- An estimate of the interest rate related to the project account,
- an estimate of the inflation rate, and
- an estimate of the discount rate affecting the present worth of the 25 years of cash flows.
These estimates are more or less subjective, and therefore the result will be uncertain corresponding to the uncertainty in the estimates. The result will be closer to reality, however. Using for instance real interest instead of actual interest will account for a loss of purchasing power in the future.
- Interest rate. Since we are looking at household lighting with LED lamps, we assume a household economy, that is, payments and receipts are related to a bank account. At the moment a typical rate is 0.13% per year for a standard savings account in the bank (in Denmark).
- Inflation rate. The current inflation rate is 2.5% (in Denmark), and it has been around that level for the last 15 years (Inflation), so we assume it stays on that level.
- Discount rate. In public projects the Danish government requires a fixed discount rate at 5% per year. But this is a private project, so we have freedom to choose it equal to the real interest rate, or higher.
|Fig. 3. Project balance with interest. This is the|
previous balance transformed into present worth. The
discount rate is chosen equal to the real interest rate.
|Fig. 4. Sensitivity. Project balance with heavy|
discounting (discount rate 5%).
As a result, the investment balance undergoes some changes, and Figure 3 is the result. The initial value is the same as previously, but the remainder is clearly affected. The payback period is still 15 years, but the surplus is now 14.69 EUR (was 6.33 EUR).
With a 2.5% inflation rate, and an interest rate of 0.13%, the real interest rate is actually negative (-2.31%). The surplus is thus higher than it was in the simple model, despite discounting. With a negative discount rate, a nearby euro is worth less than a distant euro.
In order to test the vulnerability of the result we change the discount rate.
With a discount rate of 5%, used in Danish public projects, the distant values become more suppressed and the surplus smaller, see Figure 4. The situation corresponds to a risk premium of 7.31% which again corresponds to a halving time of almost 10 years (the 72 rule under Discounting); the interpretation is that 1 euro today has the same preference as 2 euros in almost ten years time. This could be realistic for a house owner, because Danish families that live in a detached house move every 9 years on average, while people in row-houses, apartments and student dorms move more often (Danmarks Statistik 2003). The investment may be lost altogether if the family moves to another home, but of course, the time preference is individual.
If the discount rate were equal to the internal rate of return, then the surplus would be zero. This corresponds to a market interest rate of 5.17% (keeping the inflation rate fixed). That means the market rate has a margin from 0.13% to 5.17% where the net present worth of the project stays positive. The 5.17% is a socalled switching value beyond which the net present worth change from a surplus to a deficit.
Table 1: Assumptions regarding lamp types (Go Energi, Philips).
|Lifetime (h)||10 000||25 000|
|Usage (h/year)||1 000||1 000|
|Marginal electricity price (EUR/kWh)||0.23||0.23|
|Marginal electricity price (DKK/kWh)||1.75||1.75|