THE NET PRESENT VALUE METHOD

THE PAY BACK TIME METHOD

Interest rates

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Nominal cost of capital

Saving
Reduced costs in terms of e.g. energy, power tariffs, water requirement, maintenance, etc. Normally expressed in Euro per year.

Click on the different interest rate methods to read more. Every interest rate method is shown in a separate box to the right of the buttons.

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THE ANNUITY METHOD

Real rate of interest

Nominal interest rateUsually, when people talk about interest rates (e.g. mortgage interest rates and savings rates), they are talking about the nominal interest rate. The nominal interest rate includes an estimate of annual inflation. If you base your calculation on the nominal interest rate, inflation needs to be taken into consideration when assessing the investment’s cost-effectiveness. Example: If you lend € 100 to the bank at a 4 % savings rate, you can withdraw € 104 one year later. But if inflation in the same year were 1 %, then the value of the € would have fallen and the actual yield would thus be around 3 %.

Technical useful life
The period of time the product will work as intended. Solar cells, for example, are expected to last 30 years or more and their efficiency/production of power up to that point will be expected to have diminished by a maximum of 20 %.

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THE INTERNAL RATE OF RETURN METHOD

Real rate of interestTo be able to ignore inflation, you can choose to look at future savings in today’s money by doing the calculation in real terms, with a real interest rate. Real interest rate ≈ Nominal interest rate – Inflation. Example: If you lend € 100 to the bank at a 4 % savings rate, you can withdraw € 104 one year later. Annual inflation at 1 % makes the real interest rate 4 % - 1 % = 3 %.

Real cost of capitalThe real cost of capital is the cost of capital adjusted for inflation, a real interest rate with the investor’s surcharge. It is the real cost of capital that is normally used when assessing cost-effectiveness. Real cost of capital ≈ real interest rate + the investor’s surcharge. Example: Nominal interest rate (bank interest rate) is 4 % and annual inflation is assumed to be 2 %. The investor’s surcharge is 3 %. The real cost of capital is thus 4 % - 2 % + 3 % = 5 %.

Nominal interest rate

Economic life
The period of time an investment can be considered to be cost-effective. Certain mechanical products require increasingly high maintenance expenditure and may, after a certain number of years, be considered to have only “scrap value” owing to excessive maintenance and repair costs.

Name of project:Information about the project:Investment: €Savings per year: €Period of calculation: yearReal cost of capital: %Cost-effectiveness requirement: %

This method works out how long it takes to recover the amount invested (reimbursement period). For an investment to be considered cost-effective, a company will often have a general view as to the maximum reimbursement period required for an investment decision to be made.
The advantage of this method is that it is easy to use and understand.

Period of calculation
The period of time chosen on which to base the cost-effectiveness assessment. If this is different from the economic life, the residual value at the end of the period of calculation needs to be taken into account, or if the period of calculation is longer than the economic life, a future reinvestment must be factored in.

Profitability calculations
You can use this page to read about and use different accepted calculation models to apply to your operations. Solar energy, thermal insulation, window replacement, etc. normally involve substantial initial costs followed by reduced operational and maintenance costs over a longer period. This can sometimes make it difficult to assess whether an investment is cost-effective.
There are several different financial methods for assessing whether an investment is cost-effective. Below we present four general methods of assessing cost-effectiveness that do not take into account which type of investment decision is to be made.

Investment
Investment includes the direct costs that are required such as materials and labour costs.

Useful life
This is a very important factor when assessing cost-effectiveness, and there are three different concepts that need to be kept separate: economic and technical useful life, and period of calculation. It is worth noting that the depreciation period is not related to the cost-effectiveness assessment and is an accounting concept.

Step 1Energy-saving measures are calculated to generate an annual saving of € 5 000/year over 10 years and require an investment of € 20 000. The investor’s requirement is for a 5-year pay-back time period.

Step 2The pay-back time will be four years: € 20 000/€ 5 000/year = 4 years

Step 3Since the reimbursement period of the investment is shorter than what the investor considers to be the longest acceptable reimbursement period, the investment is considered to be cost-effective.

The net present value method can also be used in comparisons of different options when there are no actual savings to be made. The present value of the total costs of the different options then shows which is the most cost-effective over a period of time.

Energy calculator

Step 1Energy-saving measures are calculated to generate an annual saving of € 5 000/year and require an investment of € 20 000. The period of calculation is 10 years and the investor’s real cost of capital is 8 %.

Steg 4The net present value is: € 33 500 – € 20 000 = € 13 500.
Since the net present value (present value surplus) is positive, the investment is considered to be profitable

The net present value method explained
The net present value method is based on calculating the present value of all costs and savings relating to the investment. The investment is considered to be cost-effective if the sum of the present value of annual net savings is greater than the investment, i.e. if the net present value (the difference between the present value and the investment) is positive.

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Step 3The total present value of annual savings is: € 5 000/year · 6.7101 = € 33 500 = € 33 500

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The pay-back time method explained
This method works out how long it will take to recover the amount invested. This period is referred to as the reimbursement period, or the pay back period. If the period calculated is shorter than the company’s reimbursement period requirement, the investment is assessed to be cost-effective.

Steg 4The net present value is: € 5 000/year – € 3 000/year = € 2 000/year.
Since the annual surplus is positive, the investment is considered to be profitable.

Step 2The conversion of annual savings to their present value uses the present value factor formula, which depends on the period of the calculation and the cost of capital. Real cost of capital at 8 % and a period of calculation of 10 years produces a present value factor of 6.7101.

The disadvantage is that it encourages short-term investments because it does not take technical lifetime and interest into account. For example, it assesses two similar investments attracting the same savings as always being equally cost-effective regardless of the technical lifetime and interest involved.
This example has 10 years as the economic life of the investment, but this is of no relevance for the pay back time method.

The pay back time method

This method is not suitable for use in the building and property sector. The method is often misleading for investments with a long reimbursement period such as solar cells, thermal insulation, window replacement, etc.

Result

Step 3The annual cost of the investment is: € 20 000/year · 0.1490 = € 3 000/year = € 3 000

The Pay back time method explained

This method operates on the basis of the same calculation as the present value and annuity methods. The difference is that the internal rate of return method determines that the present value of the annual savings should be equal to the investment, i.e. the net present value is zero, and calculates what interest rate fulfils that condition. This interest rate is called the internal rate of return.

The annuity method works on the same basis or formula as the net present value method, the difference being that instead of being shown as a present value, the investment is shown as an annual cost (annuity). The annual cost or annuity is calculated using an annuity factor which depends on the period of calculation and the cost of capital. The investment becomes cost-effective if the annual net saving is greater than the annual cost, or, in other words, if there is a positive annual surplus.

The annuity method explained
The annuity method works on the same principle as the net present value method. The difference is that instead of converting all annual savings to their present value, the investment is converted to an annual cost (or annuity). The annual cost is calculated using an annuity factor which depends on the period of calculation and the cost of capital. The investment is considered to be profitable if the annual net saving is greater than the annual cost, i.e. if the annual surplus is positive.

Explanations

The net present value method explained

Step 1Energy-saving measures are calculated to generate an annual saving of € 5 000/year and require an investment of € 20 000. The period of calculation is 10 years and required rate of return is 8 %.

This method converts all costs and savings to their present value. If the present value of all future savings is greater than the investment, it is considered to be cost-effective

Steg 2The investment is converted into an annual cost using the annuity factor, which depends on the period of calculation and the cost of capital. Real cost of capital at 8 % and a period of calculation of 10 years produces an annuity factor of 0.1490

Fundamental concept

The annuity method explained

The internal rate of return method explained
The internal rate of return method is closely related to the net present value and annuity methods. The difference is that the internal rate of return method determines that the present value of the annual savings should be equal to the investment, i.e. the net present value is zero, and calculates what interest rate fulfils that condition. This interest rate is called the internal rate of return.

Interest rates

Like the net present value method, the annuity method can also be used in comparisons of different investment options. The calculation produces an annual cost for each option as a basis for comparison between the options on offer.

Step 3Since the internal rate of return will be higher that the required rate of return, the investment is considered to be profitable.

The internal rate of return method explained

Click on the buttons below for more detailed explanations of the different concepts and the different types of interest rates

Fundamental concept

Corrected real cost of capitalHistorically, energy prices have not followed inflation. To calculate how energy prices might change otherwise than in line with inflation, the corrected real cost of capital can be used. The corrected real cost of capital is the real cost of capital plus/minus the change in energy prices compared with inflation. Corrected real cost of capital ≈ real cost of capital ± relative annual change in energy prices. Example: The real cost of capital is 5 % and the future relative change in energy prices apart from average inflation is 2 %. Corrected real cost of capital is thus 5 % - 2 % = 3 %.

The internal rate of return method produces a calculated internal rate of return that is equivalent to the annual return on the capital invested. Whether this return is acceptable can be seen immediately by comparing it with the investor’s required rate of return, the cost of capital.

Nominal cost of capitalA company’s financial requirement of its investments is often determined as the company’s cost of capital. That is the interest rate to be used in cost-effectiveness calculations. The cost of capital is a measure of the company’s depreciation requirement in relation to capital invested. What the cost of capital amounts to is established by the company’s management based on what actual interest rate applies to their investments, such as bank loans, and on the company’s general financial situation, long-term plans, investment options, the purpose of the investment, etc.
The cost of capital is thus the interest rate that is to be paid on investments with an “investor’s surcharge”, which the investor considers necessary for an investment to be financially defensible. If the nominal interest rate is used, inflation must be included in the investment analysis. Nominal cost of capital ≈ Nominal interest rate + the investor’s surcharge. Example: Nominal interest rate (bank interest rate) is 4 % and the investor’s surcharge is 3 %. Nominal cost of capital is thus 4 % + 3 % = 7 %.

All use of the information provided on the Energy Calculator, for example investments made following the results produced by the calculator, is at users’ own risk. The FSiÖMS project accepts no liability for any result that may follow from a user drawing on information presented on the Energy Calculator. The FSiÖMS project and its principals therefore accept no liability if the content presented either directly or indirectly leads to damages or loss, loss of profit or earnings for the user or any other person who accesses content on the Energy Calculator.

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Step 2The internal rate of return will be : 21 %

Real cost of capital

Corrected real cost of capital