# Net Present Cost (NPC)

Net present value (NPV) is an economic tool used to equate the total cost of a project over a specified time period to the total cost today, taking into account the time value of money. The present value (PV) of each annual cash flow is discounted back to its PV using a suitable interest or discount rate. The NPV is determined by summing the PV for each year, staring at year 0 i.e. the investment, to the final year (N). NPV is a good indicator of how much value an investment or project brings to an investor, and is widely used in economic engineering to assess feasibility. However, there are many kinds of systems or projects, such as the SOFC tri-generation system, where there are no sales or incomes. In this case it is common to use net present cost (NPC). Equation 8.1 is used to calculate NPC (Pilatowsky et al. 2011).

AA_{TC} is the adjusted annual total costs (?), i_{r} is the interest rate, *n* is the year number and *I _{cc}* is the initial capital cost (?). Selection of a suitable interest/ discount rate is based upon risk, opportunity cost or an alternative investment.

In engineering based analysis 7 % is a widely used value. If inflation is being considered, the adjusted annual total cost (AA_{TC}) is calculated using Eq. 8.2.

A_{TC} is the non-adjusted annual total costs (?), *i _{f}* is the inflation rate and

*n*is the year number. The scrap value (SV) of the system at the end of the projectâ€™s life should be considered, and subtracted from the final expenditure. In NPC analysis the annual total expenditure or costs (AA

_{TC}) are given as positive figures (unlike NPV), and thus the NPC at the end of a system lifetime will be positive. When two or more systems are being evaluated over the same time period, the system with the lowest NPC should be selected.

# Equivalent Uniform Annual Cost (EUAC)

The equivalent uniform annual cost (EUAC) is the annual cost of the project or system equivalent to the discounted total cost or NPC. EUAC is calculated by multiplying the NPC by the capital recovery factor (CRF), as shown in Eq. 8.3.

# Simple Pay-Back Period (SPBP)

The simple pay-back period (SPBP) is used to determine the time required to recoup the funds expended in an investment, or to reach the break-even point. Generally, in engineering projects investors consider a SPBP of 5 years as acceptable. The SPBP does not account for the time value of money; however it is a useful tool for the quick assessment of whether a project or system is a viable option.

*I _{cc}* is the is the initial capital cost of the system (?). Annual savings are calculated by subtracting the annual total cost (A

_{TC}) of the base case system from the annual total cost of the proposed system.

Next, Sect. 8.2.2 presents the economic assessment results.