This post is about investment appraisal and financial analysis.
These methods are explained in CSSTIAE topic 2020.56.
Investment Appraisal Concepts
Total cost of ownership (TCO) includes the purchase price of a particular asset, plus operating costs, over the asset’s life span.
Qn = In – Cn
Return of Investment (RoI), in Spanish retorno de la inversión.
ROI = Net Income / TCO
Take into account that ROI is a ratio or percentage, not a time or date (like pay-back or break even point).
Investment Appraisal Methods
Investment appraisal method categories:
- Static
- Dynamic
Static methods do not considers a fixed value of money.
CSSTIAE exam covers pay-back, NPV, IRR and PI in topic 2023.42.
Metrica v3 methodology, used in Spain public sector, considers return of investment (RoI) and net present value (NPV) methods to analyze the economical viability of a project.
It also explains the concepts of pay-back and break-even, but they are not used as an analysis tool. You can read more on this external link.
Static
Static methods:
- Pay-back
- Total cash flow per committed monetary unit
- Average Annual Cash Flow Method per Committed Monetary Unit
- Expense comparison
- Accounting rate of return
Pay-back
Pay-back means calculating the time when you get back the invested amount.
Break Even Point (BEP) is the date where the cash flow is equal to the initial investment.
Total Cash Flow per Committed Monetary Unit
Total Cash Flow per Committed Monetary Unit (flujo de caja total por unidad monetaria comprometida) means adding all cash flows and dividing by the initial investment.
Average Annual Cash Flow per Committed Monetary Unit
Average Annual Cash Flow per Committed Monetary Unit (in Spanish, flujo de caja medio anual por unidad monetaria comprometida) means adding all cash flows and dividing by the initial investment times the number of year.
Expense comparison
Expense comparison (in Spanish, comparación de gastos or comparación de costes) means comparing different investment alternatives.
Accounting Rate of Return
Accounting Rate of Return (ARR) (in Spanish, tasa de rendimiento contable) means calculating the average benefit and the average investment.
This methods uses the benefit instead the cash flow.
Dynamic
There is a formula to calculate the initial capital in n years:
C0 = Cn / (1 + k)^n
k is the interest rate.
The discount rate is the value of a single monetary unit (C0 = 1) in N year.
r = 1 / (1+k)^n
Dynamic methods:
- Net present value
- Internal rate of return
- Present value rate
- Profitability index
Net Present Value
Net Present Value (NPV) (in Spanish, Valor Actual Neto, VAN) calculates the present value of future cash flows generated by an investment, minus the initial investment cost.
It helps determine the profitability of a project.
Internal Rate of Return
IRR (Internal Rate of Return (IRR) (in Spanish, TIR, Tasa Interna de Retorno) is the value discount rate that makes the NPV of all cash flows from a project equal to zero.
It represents the expected annualized return of an investment.
IRR can be represented graphically to compare investments. In case there are doubts, NPV comparison is recommended.
Present Value Rate
Present value rate (PVR) (in Spanish, tasa de valor actual)
T = NPV / Q0.
Profitability Index
Profitability Index (PI) (in Spanish, IR, Índice de Rentabilidad) is the ratio of the present value of future cash flows to the initial investment.
It measures the relative profitability of an investment.
PI = current value collection / current value payments
Investment Comparison Methods
Investment comparison methods:
- Equivalent annual annuity
- Replacement chain
Equivalent annual annuity
Equivalent annual annuity (EAA) (in Spanish, anualidad equivalente) smoothes out all cash flows and generates a single average cash flow for all periods that (when discounted) equal the project’s NPV.
Replacement chain
Replacement chain (in Spanish, cadena de reemplazo) takes into consideration the different life spans of alternative plans, as well as their expected cash flows.
Example
Example 1
For a project that requires an initial outlay of €1M and generates a cash inflow of €1.2M at the end of the third year, considering a cost of capital equal to the current €STR reference rate of the European Central Bank (ECB) at 3.63%.
Calculate pay-back, NPV and IRR.
Pay-back is 3 years.
Apply these values to the NPV and IRR formulae:
Ct = 1.2M (cash inflow in year 3)
C0 = 1M (initial investment)
r = 3.63% = 0.363 (discount rate)
t = 3
The NPV is 0.078M.
The IRR is 6.26%.
External References
- Manuel Cilllero; “Análisis Coste/Beneficio en Métrica v3“; mcillero.es
- Equivalent annual annuity
- Tim Vipond; “Equivalent annual annuity“; CFI