Course: Financial Operation Analysis Unit 1: Introductory Concepts and Basic Operations MATERIAL OF SESSION 1 Teacher: Lucía Boedo Vilabella Materials made by Lucía Boedo Vilabella The use of them is forbidden without the permission of the author INDEX 1. Economic activity and financial activity 2. Financial capital 3. Rate of interest 4. Financial transaction or financial operation 5. Financial projection and financial rule 6. A first approach to simple interest and compound interest (capitalization) 1. Economic activity and financial activity (I) Economic goods are those that satisfy human needs in the sense that they provide utility to society. The economic goods are scarce, their supply is less in relation to their demand by economic agents (by people, companies or non-profit entities). Examples: a cake, a theatre ticket, a 100-euro bill or a deposit of money in a checking account or a loan from the bank. Economic goods are classified: 1) According to the position of the economic agent with respect to them: a) Rights: when the position is creditor (the economic agent has the right to receive the good in the future) b) Liabilities: when the position is debtor (the economic agent has the obligation to provide the good in the future) 2) According to the time perspective: a) Present goods: those whose availability is immediate. b) Future goods: those whose availability is not immediate. • • • For example: If I now have 5,000 €, I have a present asset that I spend or use now. If six months ahead, my company will pay me a bonus of 5,000 €, This is for me future good. I am in creditor position (they owe me the money) and my company is in a debtor position (it must do this payment in the future). If the bank lends me 5,000 euros and in return I must pay back two future quantities of 3,000 euros each (at the end of each of the next two years), I have a present good and I am in a debtor position. The bank has a future good and it is in a creditor position. 1. Economic activity and financial activity (II) Economic activity is the human activity that consists of the exchange of economic goods. Economic agents prefer present goods to future goods (equal in quantity and quality). This hypothesis is known as the principle of underestimation of future needs with respect to present ones. As the availability of a good is further in time, the less useful or satisfying it produces. Its value is lower. Financial activity arises when the exchange of goods is not simultaneous in time. The financial activity requires that exchanged goods must be measured in monetary units and that the moment of time that those goods are available is considered. For example: I buy a car (and so I receive a good now) and I pay it monthly during the next year (I will provide another good, money in this case, in the future). Financial capital: measure of an economic good expressed in terms of its quantity and referred to its time of availability. 2. Financial capital (I) It is a amount of money, expressed in a currency (dollar, euros, pesos, ruppe..) available at a specific moment in time (when do I have to provide it or when I receive it) It’s a bidimensional magnitude (C,t) in which C is the quantity t is the moment of time when this quantity is available (its maturity). Amount of Money (expressed in a currency). QUANTITY (C,t) Specific moment in time when this amount is available MATURITY This is because MONEY has a time value. The maturity of the money is as important as the quantity. 2. Financial capital (II) What do you prefer, 100€ available now or 100 € available a year from now (at the end of the first year)? 100 100 t=0 t=1 A euro available now has more value than if it is available in the future. WHY? INFLATION (cost of living) In normal conditions I can buy more thigs today with 10€ than after a year because the cost of living increases. RISK and uncertainty about the future. RATE OF INTEREST Money is a commodity that can be bought and can be sold SO IT HAS TO HAVE A PRICE. 6 2. Financial capital (III) We usually represent it in a time- line 10 20 0 Co 8 1 37 2 C1 3 C2 ….. ….. n (10 € ; 0) (20 € ; 1) (8 € ; 2) (37 € ; 3) 10€ available now… 8€ available at the end of the second year (two years from now) Cn C 0 1 2 n (400 €; 3) Cartesian axis in which the moment in time is represented on the X axis and the amount on the Y axis t 2. Financial capital (IV) Financial capital can be considered from two perspectives: • Objective perspective: refers to its intrinsic value. From this point of view, C is always positive (or null), because every good has a value for the person that can have or use it. • Subjective perspective: considers the position of the agent with respect to the capital. C ≥ 0 when the agent has a creditor position and C ≤ 0 when the agent has a debtor position. For example, financial capital (100 €, 1) If it is expressed from a subjective perspective, I will write (100 €, 1) if I will receive that money a year from now (someone owes me the money) and as (-100 €, 1) if I have to provide than money (I have this debt, I owe that money to someone). 3. The rate of interest 100 100 + 10% (100) =100 + 10 = 110 • It is the Exchange relation between two capitals referred to different moments of time. • It can be understood as the Price of money • We use the interest rate to express the time value of money. • It is expressed as a percentage and with annual reference. It may have other time reference (monthly, quarterly,…) in order to perform financial operations that do not have annual periodicity. • In order to operate, it is necessary to transform de percentage format into decimal format ⇒ 10 % → 10/100 = 0,10 10% It can be a cost or a profitability 9 4. Financial transaction or financial operation (I) Financial operation: Non-simultaneous exchange of financial capitals. An agreement between 2 parties to exchange capitals over time. Here we are lending money for free 100 100 100 This is not a financial operation, there is not an exchange of financial capitals. 10 4. Financial transaction (II) Lender or creditor: person or Company that provides the first capital PROVISION: Capital o set of capital given by the lender 1000 1 0 3 1300 2 1000 Borrower or debtor: person that receives that first capital CONSIDERATION: capital or set of capital granted by the borrower The LENDER or CREDITOR lends money or extents credit to another party. 1 367,21 2 367,21 3 367,21 The BORROWER or DEBTOR is the person or entity that owes the money. It is the person or entity to whom the money has been granted There is a lender (creditor) and a borrower (debtor) in every financial transaction 11 5. Financial rule • The consideration of a financial operation is not set arbitrarily, but in accordance with a INTEREST RATE and with the use of a mathematical formula→ Financial rule • Financial rule is a formula than transforms one capital available at a specific point in time into another capital available another point in time. • The two capitals are equivalent, what it means that they are interchangeable, according to a certain financial law and according to a certain interest rate. • We are going to study two financial rules: SIMPLE INTEREST RULE and COMPOUND INTEREST RULE 12 6. Simple interest rule (capitalization) • Only the initial amount we deposit in the savings account produces interest. 100 € 0 1 0,10*100 10 € 2 0,10*100 10 € 120 € C0 0 1 i·C0 2 i·C0 3 i·C0 C0 + i·C0 + i·C0 + i·C0 C0 + 3·i·C0 𝐶𝐶𝑛𝑛 = 𝐶𝐶0 + 𝑛𝑛 · 𝑖𝑖 · 𝐶𝐶0 C0 · (1+ 3·i) 𝐶𝐶𝑛𝑛 = 𝐶𝐶0 · (1 + 𝑛𝑛 · 𝑖𝑖) • The interest is not added to the principal to jointly produce new interest. It is as if the interest were transferred to another account. • Each year the growth of money is constant: i·C0 • The operation is signed for a specific duration and we cannot have the interest period by period. • We have the interest (and the principal) jointly together at the end of the operation. 6. Compound interest rule (capitalization) 100 € 0 1 0,10*100 10 € 2 0,10*110 11 € 110 € 121 € • The interest earned each period is added to the principal, so the accumulated amount over a period becomes the principal for the next period. • The principal doesn´t remain constant. It growths. C0 0 1 i·C0 C0 + i· C0 C0 ·( 1+ i ) C1 2 i·C1 C1 + i·C1 C1 · (1 + i) C0 ·( 1+i ) · (1+i) = C0· (1+i)2 C2 𝐶𝐶𝑛𝑛 = 𝐶𝐶0 · (1 + 𝑖𝑖)𝑛𝑛 Simple interest and compound interest 100 € 0 C0 100 € 0 C0 100+0,10·100 110+0,10·100 120+0,10·100 130+0,10·100 110 120 130 140 1 C1 C0 + i·C0 C0 · (1+i) 2 C2 C1+i·C0 = C0 + i·C0 + i·C0 C0 · (1+2·i) 3 C3 C2 + i·C0 = C0 + i·C0 + i·C0 + i·C0 C0 +3·C0·i = C0 · (1+3·i) 4 C4 C3+i·C0 = C0 + i·C0 + i·C0 +i·C0 + i·C0 C0 +4·C0·i = C0 · (1+4·i) 100+0,10·100 110+0,10·110 121+0,10·121 133,1+0,10·133,1 110 121 133,1 146,41 1 C1 C0 + i·C0 2 C2 C1 + i·C1 = C1·(1+i) C0 · (1+i)·(1+i)= C0·(1+i)2 3 C3 C2 + i·C2= C2 ·(1+i) C0 ·(1+i)2·(1+i)= C0 ·(1+i)3 4 C4 C3+i·C3 = C3 · (1+i) C0 ·(1+i)3·(1+i)= C0 ·(1+i)4 C0 · (1+i) Example. We understand the Simple interest rule We invest 100 € at 10% p.a. (simple interest) and we plan to hold this investment for 6 years. C6 = C0 + C0·(6-0)·i = = C0 (1+6·i) C6 = 100 (1+6·0,10)= 160 C6 =100+100·6·0,10= 10+60= 160 100 0 1 2 3 4 5 6 At maturity 10 10 10 10 10 10 = 60 Interest =100 Initial capital 160 Final ammount We understand the operation: •The starting capitalor PRINCIPAL is 100 € and its maturity is the present time (t=0). •Each year, the investment produces 10 € of interest (0,10*100). AMOUNT OF INTEREST OF EACH YEAR •The interest is accrued or produced each year, but they are not available until the maturity of the operation (at t=6). We don´t receive 10 € each year, we receive 60 € at t=6. •The TOTAL INTERESTS ARE 60 € (6*10). They are accrued for the total Interval of 6 years that the operation lasts ⇒ Is the increase of the capital in the Interval (0,6). IS THE AMOUNT OF INTEREST OF THE OPERATION •The accumulated amount of the operation is 160 € ⇒ It is available at maturity. THIS IS THE FINAL CAPITAL or FINAL AMOUNT. •(100;0) is financially equivalent to (160;6) according to SIMPLE INTEREST RULE and at 10% p.y. Example. We understand the compound interest rule We invest 100 € at 10% p.a. (compound interest) and we plan to hold this investment for 6 years. 100 0 1 10 110 2 11 121 3 4 5 6 12,1 13,331 14,641 16,1051 133,1 146,41 161,051 177,1561 We understand the operation: •The starting capital or PRINCIPAL is 100 € and its maturity is the present time (t=0). • The amount of interest of each year is added to the principal and the accumulated amount becomes the principal for the next period. •Each year the capital growths (1+0,10). •The accumulated amount is 177,16 €. This amount is available at t=6. •177,16 - 100 = 77,16 IS THE AMOUNT OF INTEREST OF THE OPERATION •(100;0) is financially equivalent to (177,16;6) according to COMPOUND INTEREST RULE and at 10% p.y. The final amount is available at the end of the operation In both cases (simple interest and compound interest) we have to wait until to the maturity of the operation to receive the money. This is important in simple interest rule because if we could withdraw the money before, we could transform the simple interest into compound interest. • Suppose we put 100 € IN savings account at 10% (simple interest) per annum for one year. Then we withdraw the interest and put it for one year in another account paying simple interest at 10%. How much do we have in the end? 𝐶𝐶1 = 100 · 1 + 1 ∗ 010 = 100 + 10 𝐶𝐶2 = 10 · 1 + 1 ∗ 0,10 = 11 100 + 10 + 11 = 121 € If we could obtain the interest each period, we could invest them in another bank account, and therefore they became productive as in compound interest and, on the practical there wouldn´t be a distinction between simple and compound method. EXERCISES 1) Calculate the equivalent of 5.000 € deposited today in a savings account that pays a interest rate per year (per annum) of 6% for a period of 3 years. (simple and compound interest rule) 2) Find the interest of a savings account of 5.000 € at a rate of 6% p.a. for a period of 3 years. (simple and compound interest rule) 3) Calculate the interest of the third year of a savings account of 5.000 € at a rate of 6% p.a. and a duration of 3 years (simple and compound interest rule) 4) John deposited 5.000€ at 6% simple interest rate per year. If the final amount of the savings account was 5.900 €, How long was the money invested? 5) John invested 5.000€ in a savings account for 3 years. If the final amount of the account was 5.900 €, What was the annual interest rate applied in simple interest? 6) John invested 5.000€ in a savings account for 3 years. If the final amount of the account was 5.955,08 €, What was the annual interest rate applied in compound interest?
