# QPAM: Investment Appraisal

To perform investment appraisal we need to analyse cost and revenues. First we need to find profitability indicators, then we need to assess the life cycle cost. Then we can perform a cost effectiveness analysis and last we need to also consider dynamics and sensitivities.

Profitability Indicators

On the cost side we have investment costs, O&M costs, taxes and running cost. On the revenue side the quantity of the output and the price of the output. The cash-flow is the sum of expenses and revenues over a period of time. It is, however, not representative of the investment as it does not include discount rates (not to be confused with social discount rate discussed later). The payback period is the time needed to recover the investment costs based on cash-flow.

Based on discount $real cashflow = \frac{nominal cashflow}{1+discount rate}$ the real value of nominal cash decreases over time. It therefore represent the opportunity cost of capital. It brings one to the question whether a “similar” investment could bring in more or less return.

Investment is based on equity and debt. The Weighted Average Capital Cost (WACC) combine the capital structure and the cost of debt and the cost of equity. $r = WACC_{pretax} = \frac{E}{V}\cdot k_E + \frac{D}{V} \cdot k_D$ where V is the investment volume. The Net Present Value (NVP) $NPV = -investment_0 + \sum_{t=1}^T \frac{cashflow_t}{(1+r)^t}$. The NVP is termed in a currency and alternatives are usually chosen based on the heighest NVP for the least investment.

The Internal Rate of Return (IRR) is the highest discount rate that can be used such that the NVP turns to 0. It allows to compare investments without having to take NVP. The IRR has disadvantages in complex scenarios where its meaning becomes unclear.

The Profitability Index (PI) is the NPV relative to invested capital.

Life Cycle Cost

The Life Cycle Costs (LCC) consider all cost and savings over the entire lifetime. Cost need to be discounted. $LCC = C_0 + \sum_{t=0}^T\frac{c_t}{(1+r)^t}$.

Levelised Cost of Electricity (LCOE) is the constant electricity price over the entire life of an asset to cover all operating expenses, debts and interests and returns to investors $LCOE = \frac{\sum_{t=0}^T (CAPEX + OPEX / (1 + r)^t)}{\sum_{t=0}^T (kWh_{initial,net} \cdot (1-Degrade)^t / (1+r)^t)}$ where CAPEX is the investment cost and OPEX the operation costs. It was first discussed for electricity, however, it is also applicable to any other good that needs to be bought over the lifetime of an asset. It is commonly used by policy makers, planners, researchers and investors. It can compare technologies (with different life times) as long as they produce the same outcome. A famous application are the Feed-in Tariffs (FIT) in Denmark and Germany.

Cost Effectiveness Analysis

Cost Effectiveness Analysis (CEA) has two starting point. One is to reach a certain target at minimal costs and the other is to achieve a maximal impact for a given cost.

First the LCC is performed. Based on the LCC the baseline cost and cost of different policy options can be assessed. The incremental cost of options is the difference to the baseline. Summed over different LCCs the abatement/relative costs  can be computed and options can finally be compared.

Computing the baseline is difficult and is often an issue of political contention.

Dynamics and Sensitivities

Dynamic developments in technology so far have shown that technology gets cheaper over time. Can the development be forecast to get a grasp on the discount rate?

Sensitivity analysis judges the different factors of a analysis and tries to order them according to the impact.