**2.1 Economic analysis and use of discounted cash flow**

The discounted cash flow concept can be presented in a simple equation. The total earning from the project in its life span is represented by, G. Overall return from the

project activities is R with the cost incurred C. The simple relation then looks like the following Eq.

$$\mathbf{G} = \mathbf{R} - \mathbf{C} \tag{1}$$

As the initial investment and the subsequent cash flows occurs in different time frames, so a time value effect is imparted to this simple equation. This time value is included in the relation using some correlation coefficients which equalize the time value of the money or the future payments of receipts are discounted. So, discounted cash flow (DCF) tries to figure out the value of an investment on the base year and highlights on how much money it will generate in the future.

Each of the future cash flows must be "deflated" first to go back to base year. So, future cash flows must be multiplied by the discount factor:

$$\frac{1}{(1+r)^{j}}\tag{2}$$

Where, *r* is the discount rate and *j* is the year index.

Thus, discounted cash flow is used to get Net Present Value (NPV) of an investment following the equation:

$$NPV = \sum\_{j=1}^{n} \frac{CF\_j}{(1+r)^j} - Io \tag{3}$$

Where.

Io - initial investment.

n = years of duration of the investment.

When the net present value (NPV) results to a positive figure, it means at the end of life of investment the discounted cash flows produced throgh out the entire life possess higher inflow than the cost of the initial investment, and other associated costs and therefore, the erection of a plant is justified from a financial point of view; vice versa when the NPV is negative.

Details of net present value and other indicators that uses discounted cashflow like internal rate of return (IRR), and discounted pay back period will be discussed in details in later sections.

#### **2.2 Tools used for economic performance analysis**

Economic performance is better understood with the value a product or service provides to the willing customers. A higher value means a higher price customer willingly pays for the product or service. Economic value that a customer is willing to pay for tradable goods, may be greater than the actual market price (thus creating an economic surplus) but it is not usually less [7]. Otherwise, customer would not buy the product replacing the available one. Economic performance must be justified with proper tools, so that the user of the product put their preferences over other available alternatives.

The following tools are commonly used for economic assessment of biomass-based energy projects:


#### **2.3 Life cycle cost analysis**

Life cycle cost (LCC) gives a basis for comparing bioenergy technologies to conventional energy technologies. This method accounts the total system cost during a specified time period (life of the project). It comprises the initial investment and operational cost during the useful life. LCC is the sum of total cost that includes not only initial investment but also costs directly related to repair, operation, maintenance, transportation to the site, and fuel used to run the system. All of these costs are discounted with a MARR to the present value (PV). An LCC analysis allows the designer to study the effect of using different components with different reliabilities and lifetimes. It is also helpful for comparing costs of different designs and/or determining whether a hybrid system would be cost – effective option.

The equation of life cycle cost analysis is [8].

$$L\mathbf{C}\mathbf{C} = \mathbf{C} + \mathbf{M}\_{wp} + E\_{wp} + R\_{wp} - \mathbf{S}\_{wp} \tag{4}$$

LCC = Life cycle cost.

C = initial cost of installation- the present value of the cost on capital resources. *MWP*= Aggregation of all yearly operation and maintenance costs- includes wage of the operators, site access, guarantees paid, and all other regular maintenance costs.

*EWP*= Aggregation of all yearly energy cost including fuel cost and its transportation to the plant site.

*Rwp*= Aggregation of all yearly replacement costs.

*Swp*= Salvage value.

#### **2.4 Net present value (NPV) analysis**

The net future earnings are discounted to the base year with the rate selected to justify minimum attractive rate of return (MARR). The investment is deducted from the present sum of benefits. This value is called NPV [9].

$$\text{NPV} = -\text{S} + \frac{\text{CF}\_1}{\left(\mathbf{1} + r\right)^1} + \frac{\text{CF}\_2}{\left(\mathbf{1} + r\right)^2} + \dots + \frac{\text{CF}\_T}{\left(\mathbf{1} + r\right)^T} = -\text{S} + \sum\_{j=1}^T \frac{\text{CF}\_j}{\left(\mathbf{1} + r\right)^j} \tag{5}$$
