Economics
How net present value, payback period and accumulated cash flow come about — and what the discount rate and debt do to them.
Three figures are at the center of the results page: Net Present Value, Payback Time and Accumulated Cash Flow. They are connected, but the net present value is not simply "annual savings × project term". Furo calculates a separate cash flow for every project year and discounts it. This page goes through the calculation item by item, so you can explain every figure to your customer.
Step 1: The annual savings
The Savings Breakdown per Year shows what the first year's savings consist of. Depending on the use case, Furo adds up self-consumption, peak shaving, procurement optimization in a dynamic electricity tariff, feed-in tariff or direct marketing and additional revenue — and deducts electricity costs for charging, the efficiency loss, the Optimization fee and the Debt Interest Cost.
Every bar is a difference: Furo calculates the same year once without and once with battery, with the same load profile, the same PV profile and the same prices. What changes in a cost item is the bar.
| Bar | How Furo calculates it |
|---|---|
| Peak Shaving | demand charge costs without battery minus demand charge costs with battery. Under atypical grid usage the bar is labelled "Atypical Peak Shaving" |
| Self-consumption | electricity costs without battery minus electricity costs with battery |
| Procurement Optimization | the part of the electricity cost savings that arises because the battery charges cheap grid power |
| Feed-in Revenue or Direct Marketing | feed-in revenue with battery minus feed-in revenue without battery |
Procurement optimization only exists with a dynamic, structured or custom tariff. There Furo splits the electricity cost savings between self-consumption and procurement optimization in the ratio of PV charging to grid charging. With a static tariff the entire savings count as self-consumption.
Step 2: From savings to cash flow
The savings do not stay constant over the term. Two effects change them:
- Battery ageing. Capacity and efficiency decrease with the full cycles. Furo accounts for this from the cell chemistry and the full cycles per year determined by the optimizer; you don't have to enter anything for it.
- Savings Adjustment. You'll find this field in step 3 under "Additional costs". Your percentage compounds across all items: at +2% the savings in year 10 are higher by a factor of 1.02^9. With it you model price increases, and with a negative value correspondingly falling revenue.
If you have entered debt, Furo deducts that year's interest from it. What is left is that year's cash flow.
Step 3: Accumulated Cash Flow
The chart adds up these annual cash flows. Year 0 is the full investment — even if you finance part of the project with a loan. Every following year adds that year's cash flow, which is why the bars are negative up to the zero crossing and positive after it. The Project Lifetime line marks the end of the period considered.
The principal repayment of your loan deliberately does not appear here as a separate item: the investment is already in year 0 in full. If the repayment were deducted on top, it would be counted twice. The cash flow therefore only contains the Debt Interest Cost.
Step 4: Net present value
Money that only arrives in a few years' time is worth less today than money today. That's why Furo discounts every annual cash flow back to its present value — the later the year, the more strongly. For a single year it looks like this:
Value today = that year's cash flow ÷ (1 + discount rate) to the power of the year number
The net present value is the sum of these present values, less the investment. An example with a €250,000 investment, €30,000 savings per year, a 15-year project term and a 2% discount rate:
| Year | Cash flow | divided by | Value today |
|---|---|---|---|
| 1 | €30,000 | 1.02 | €29,412 |
| 2 | €30,000 | 1.02 × 1.02 = 1.040 | €28,835 |
| 3 | €30,000 | 1.02^3 = 1.061 | €28,270 |
| … | … | … | … |
| 15 | €30,000 | 1.02^15 = 1.346 | €22,290 |
| Sum | €450,000 | €385,478 |
So the €30,000 from the final year is only worth €22,290 today — around 74 cents per euro. After deducting the investment, a net present value of €135,478 is left.
The obvious calculation "€30,000 × 15 years − €250,000" would by contrast arrive at €200,000 and thus be €64,522 too high. That difference is the discounting effect, and it is the most common reason for questions about the net present value.
What is discounted are the cash flows after interest — that is, what is left to you after servicing the loan.
Additional costs
Besides the battery and PV there are further costs that shift the economics. You record them in step 3 under Additional costs. Every field is optional and counts as 0 when empty.
One-off costs are added to the investment and therefore sit in year 0 of the accumulated cash flow:
| Field | What for |
|---|---|
| Plant certificate | Certification of the plant to VDE-AR-N 4110 or 4105 |
| Construction costs | Foundation, mounting, electrical installation, fire protection |
| EMS hardware | Control technology for storage operation |
| Margin | Your mark-up as the installer — as a fixed amount or as a percentage of the battery costs (switch the unit right in the field) |
| Other one-off costs | Everything else that comes up once |
| Discount | Rebate or subsidy, as an amount or as a percentage of the battery costs. Enter it positive — the value is deducted |
In the tooltip of the Investment tile on the results page you can see how the total is made up of the pure battery costs and these additional costs.
Recurring costs apply in every project year and lower the annual savings:
| Field | What for |
|---|---|
| Optimization fee | Operating costs of the optimization, in €/kWh of installed storage capacity per year. Typical range €3–10/kWh/year — pure peak shaving at the lower end, flexibility marketing at the upper end |
| Additional revenue or costs | A constant annual amount for everything else, such as flat-rate remuneration or maintenance. Costs you enter as a negative number |
The optimization fee appears as its own bar in the savings breakdown. It does not grow with the savings adjustment, because it is an agreed contract price and not revenue.
Discount rate and debt
Four further fields under "Project Specific Settings" in step 3 act on this calculation, and they do different things:
| Field | Effect |
|---|---|
| Discount Rate | your requirement on the equity employed. Acts only on the net present value, not on the annual savings. Default 2% |
| Debt Ratio | which share of the investment is assumed to be a loan. Above 0%, Furo calculates with a loan |
| Debt Interest Rate | interest rate of that loan |
| Loan Term | over how many years the loan runs |
The loan is calculated as an annuity: constant annual installments in which the interest share falls from year to year. After the end of the Loan Term no more interest accrues and the cash flow visibly rises there. The Debt Interest Cost bar in the savings breakdown shows the first year and therefore the highest interest burden.
A higher debt ratio lowers the annual savings, because interest accrues — the investment in year 0 is unaffected by it. If you want a pure equity view, set the debt ratio to 0%.
Payback period
The Payback Time is the point at which the accumulated savings reach the investment — not discounted, but after deducting the debt interest. Within the year Furo interpolates linearly, which is why you also see values such as 8.4 years. If the project does not pay for itself over the period considered, Furo does not report a payback period.
In the combined analysis, Payback Time - PV stands next to it. It sets the PV investment alone against the PV benefit, without interest and without ageing — which is why PV and storage pay back at different speeds. A separate payback for the storage alone does not exist in the combined analysis.
Two options, almost the same savings, a very different net present value
If two analyses save a similar amount per year but differ clearly in net present value, it is almost always down to one of these four points:
- different investment — at equal savings the price decides
- different project term — every additional year brings another discounted cash flow
- different savings adjustment — compounding acts strongly over the term
- debt — interest reduces every annual cash flow
Recalculating it yourself
In the CSV export and as placeholders in the PowerPoint report you get the intermediate steps: the accumulated cash flow per year, the savings per project year as well as the discount rate, debt ratio and debt interest cost. The internal rate of return (IRR) is in the PowerPoint report too.