1. LESSON 2 – SUMMARY – TIME VALUE OF MONEY The concept of Real Interest Rate The costs associated with financial transactions The notion of costs The All-in cost rate: one-period analysis The EGAR The EAR (or AER) The concept of Annuity The standard case: constant flow and frequency The cases of perpetuity and constant growth 13 FF - LFC/LG/LGM - 2Sem_2014/2015

2. THE REAL INTEREST RATE (1/2) The concept of real interest rate comes from taking the inflation into account. A positive real interest rate represents a situation where the interest rate is higher than the rate of inflation. Therefore, a negative one happens when the interest rate is lower than the inflation rate. If the real interest rate is positive there is an incentive to save (you gain purchase power with savings rather than using the money) and a disincentive to the use of credit, for the opposite reason. If the real interest rate is negative there is a symmetrical situation from the previous one. 14 FF - LFC/LG/LGM - 2Sem_2014/2015

3. THE REAL INTEREST RATE (2/2) Analytically, the real interest rate is calculated as follows: r – stated interest rate; i – inflation rate RIR = (1+r) / (1+i) - 1 When the difference between interest rates and inflation is not significant, we can easily get the real interest rate by making the difference between the two, since the output turns out to be very similar and the calculation is simpler. 15 FF - LFC/LG/LGM - 2Sem_2014/2015 Example : r = 3%; i = 2% Real Interest Rate= 1.03/1.02 -1 = 0,98% ≈ 1% = 3%-2%

4. COSTS ASSOCIATED WITH FINANCIAL TRANSACTIONS In a loan contract, in addition to the interest, there are often other costs that who ever gets the funding must support : Stamp Tax ( retained by the lender and then delivered to the IRS) Fees of various kinds, charged by the lender Mandatory Insurance policies Other Thus, stating that the cost of a funding is its interest rate may represent a significant bias in relation to the dimension of the true whole cost of the operation. 16 FF - LFC/LG/LGM - 2Sem_2014/2015

5. ALL-IN COST RATES: EGAR (1/6) To protect the less informed client about the true cost of a loan, the one that includes all charges associated with the transaction, it is mandatory in most cases to compute and give knowledge of the EGAR: Effective Global Annual Rate This rate is intended to reflect the true final cost to the borrower, giving him a better sense of what the financial transaction can represent for him and a way of comparing with other alternatives. 17 FF - LFC/LG/LGM - 2Sem_2014/2015

6. ALL-IN COST RATES: EGAR (2/6) The EGAR can be calculated for two distinct types of operations : One-period operations, in which there are only two moments: the first in which the loan is granted and in which there may exist the payment of other charges, and at the end in which the loan is paid back, and also the interest and any other charges; multi-period operations in which there are interest periodic payments and a variety of possible ways of paying back the principal (annuity, amortizing, bullet…). 18 FF - LFC/LG/LGM - 2Sem_2014/2015

7. ALL-IN COST RATES: EGAR (3/6) 19 FF - LFC/LG/LGM - 2Sem_2014/2015 EXAMPLE : EGAR for one-period operations Amount of funding – 20,000 € Term - 91 days Stated interest rate - 6% Stamp Tax – 4% Fee for granting the loan – 100 € (paid at the time of the loan contract) Commission for collecting the principal - 50 € (paid when the principal is paid back)

8. ALL-IN COST RATES: EGAR (4/6) 20 FF - LFC/LG/LGM - 2Sem_2014/2015 EXAMPLE : EGAR for one-period operations (cont.) Interest calculation = Stamp tax on interest = Net amount received: 20,000 – 100 = 19,900 Amount payable at the end: 20,000 + 303.3 + 12.1 + 50 = 20,365.4 The global rate driven by the previous values is obtained by the following equation: 19,900 = 20,365.40 / (1+EGAR)^(91/360)

9. ALL-IN COST RATES: EGAR (5/6) Thus, EGAR = 1.0234^(360/91) -1 = 0.0958 = 9.58% 21 FF - LFC/LG/LGM - 2Sem_2014/2015

10. ALL-IN COST RATES: EGAR (6/6) Generalizing, the calculation of the EGAR for one-period operations is as follows: IC – Initial Capital IE – All costs incurred at time zero –Initial expenses I – Interests FE – All costs incurred at the end of the loan (excluding interest) – Final Expenses N – # of days of the operation IC-IE = (IC+FE+I) / (1+EGAR)^(N/360) 22 FF - LFC/LG/LGM - 2Sem_2014/2015

11. ALL-IN COST RATES: EAR (1/2) Another rate that can also be calculated is the one that reflects the effective yield to the lender: a rate of interest and also all other revenues obtained by the financial institution, therefore excluding taxes. This is the EAR – Effective Annual Rate (or Annual Equivalent Rate) In practice there is one difference between the EGAR and the EAR: The EAR does not include the fiscal dimension, since although taxes are a cost to the borrower, they are not a revenue for the financial institution but for the Government (the financial institution delivers them to the IRS). 23 FF - LFC/LG/LGM - 2Sem_2014/2015

12. ALL-IN COST RATES: EAR (2/2) In the previous example the EAR would be: In general, the EGAR is higher than the EAR as the first includes the fiscal costs and the other no. 24 FF - LFC/LG/LGM - 2Sem_2014/2015

13. ANNUITY CONCEPT (1/4) Sometimes when we are facing a problem of determining a present value, we may have to deal with a set of financial flows over a period of time (imagine, for example, the monthly installments of a five years loan). From the conceptual point of view, the present value is determined by calculating the sum of the present values ​​ of each future cash flows. However, there are some particular cases where such a calculation can be made ​​ much easier: When the receivable / payable periodic value is the same, and When the frequency of the flows ​​ is constant (monthly, quarterly, yearly, etc.) In these situations we can use the concept of annuity. 25 FF - LFC/LG/LGM - 2Sem_2014/2015

14. ANNUITY CONCEPT (2/4) Example: Over the next three years, at the end of each year, it will occur a revenue of € 1,000 and it is intended to determine the present value of this set of flows, considering an annual interest rate of 10%. According to the discounting principle, the present value (PV or VA) of that set of flows would be: In other way: 26 FF - LFC/LG/LGM - 2Sem_2014/2015

15. ANNUITY CONCEPT (2/4) Example: Over the next three years, at the end of each year, it will occur a revenue of € 1,000 and it is intended to determine the present value of this set of flows, considering an annual interest rate of 10%. According to the discounting principle, the present value (PV or VA) of that set of flows would be: In other way: 26 FF - LFC/LG/LGM - 2Sem_2014/2015

16. ANNUITY CONCEPT (3/4) 27 FF - LFC/LG/LGM - 2Sem_2014/2015 The present value will naturally be the same as the one obtained previously: This discount factor of a constant flow with the same frequency over time has this symbol: where r represents the interest rate for the frequency period of the flow and n the number of constant flows. Generically,

17. ANNUITY CONCEPT (4/4) 28 FF - LFC/LG/LGM - 2Sem_2014/2015 Two particular cases of annuity: Perpetuity of a constant flow When n tends to infinity the expression for calculating the annuity becomes: Perpetuity with constant growth Where g represents the constant growth rate of the periodic flow.