BSTM TM 101 The Future Value of Money and the Present Value of Money 2002 | The Future Value of Money and the Present Value of Money

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Business FinanceCHAPTER 5 Basic Long-term Financial ConceptsThe Future Value of Money and the Present Value of MoneyTime Value of Money ØThe value of P1.00 today is not the same as the value of... P1.00 tomorrow or many years after! ØValue of Money fluctuates over time! ØMoney today may either be spent or invested.The Concept of Interest What is the FORMULA for computing INTEREST? where: I = Interest P = Principal R = Interest Rate per annum T = Time Period Interest is earned or incurred for the use of the principal amount over the relevant time period.The Concept of Interest EXAMPLE: An individual borrowed ₱1,000 from a local bank at an interest rate of 9% over a one-year period. Ø In the example, the ₱1,000 amount borrowed is the principal of the loan; 9% is the applicable interest rate; and the relevant time period is one year. Ø The interest on the loan is computed as: I = ₱1,000 x 9% x 1 year I = ₱90 Ø Thus, the interest on the loan is ₱90. This ₱90 is the COST of using the ₱1,000 borrowed for one year.The Concept of Interest EXAMPLE: Aldric borrowed ₱10,000 from BPI at an interest rate of 8% per annum for 6 months. Ø The interest on Aldric’s loan is computed as: I = ₱10,000 x 8% x 6/12 I = ₱400 Ø IF the period is a fraction of a year, use à m/12. Ø IF the period is in years, use number of years (no need to divide by 12).Self-Test Questions 1. What is the basic formula for the computation of interest? 2. What is the cost for the use of money?Exercise 1 Direction: Identify the (a) principal, (b) interest rate, and (c) time period in the examples below: 1. Your mother invested ₱18,000 in government securities that yield 6% annually for two years. 2. Your father obtained a car loan for ₱800,000 with an annual rate of 15% for 5 years. 3. Your sister placed her graduation gifts amounting to ₱25,000 in a special savings account that provides an interest of 2% for 8 months. 4. Your brother borrowed from your neighbor ₱7,000 to buy a new mobile phone. The neighbor charged 11% for the borrowed amount payable after three years. 5. You deposited ₱5,000 from the savings of your daily allowance in a time deposit account with your savings bank at a rate of 1.5% per annum. This will mature in 6 months.Simple Interest If the interest earned or incurred is always based on the original principal, then simple interest is assumed. http://www.fundation.com/wp-content/uploads/2015/10/simple-interestloans.jpgSimple Interest EXAMPLE: You invested ₱10,000 for 3 years at 9% and the proceeds from the investment will all be collected at the end of 3 years. Ø Using a simple interest assumption, interest will be computed as follows: Ø Interest, in this example, is always calculated based on the original principal of ₱10,000. Under this assumption, the interest for every year is the same, in this case, ₱900 annually. The total interest for the three-year period is ₱2 700 (₱900
3 years).Self-Test Questions 1. On which principal amount simple interest is always calculated? 2. Why does the interest applicable to every period stay the same using a simple interest assumption?Exercise 2 Direction: Using the situations provided in Exercise 1, compute the annual interest, total interest, and amount to be received or paid at the end of the term for each scenario below using a simple interest assumption: 1. Your mother invested ₱18,000 in government securities that yield 6% annually for two years. 2. Your father obtained a car loan for ₱800,000 with an annual rate of 15% for 5 years. 3. Your sister placed her graduation gifts amounting to ₱25,000 in a special savings account that provides an interest of 2% for 8 months. 4. Your brother borrowed from your neighbor ₱7,000 to buy a new mobile phone. The neighbor charged 11% for the borrowed amount payable after three years. 5. You deposited ₱5,000 from the savings of your daily allowance in a time deposit account with your savings bank at a rate of 1.5% per annum. This will mature in 6 months.Compound Interest Compound interest is simply earning interest on interest. This means that the basis for the computation of the applicable interest for a certain period is not only the original principal but also any interest earned in the previous period assuming all cash flows would be paid or received in lump sum upon maturity. http://www.fundation.com/wp-content/uploads/2015/10/simpleinterest-loans.jpgCompound Interest EXAMPLE: Using the previous example where you invested ₱10,000 for 3 years at 9% and the proceeds from the investment will all be collected at the end of 3 years, we illustrate the computation of compound interest. Ø Using a compound interest assumption, interest will be computed as follows: Ø Interest, in this example, is increasing per period because the principal is also increasing by the amount of interest earned in the previous year. Under this assumption, the interest for every year is no longer the same but is higher as it nears maturity. The total interest for the three-year period is ₱2,950.29. This is the sum of the increasing interest for the 3- year period (₱900 + ₱981 + ₱1,069.29). ₱12 950.29Self-Test Questions 1. What is the difference between simple interest and compound interest? 2. Why does interest applicable to the succeeding period increase using a compound interest assumption? -- - - - - - - - - - - - - - - - - - - Multiple Cash flows Scenario B – pay P25k annually at end of year for 3 yrs PV = (P25,000 x 0.9524)+(P25,000 x 0.9070) + (P25,000 x 0.8638) = P23,810 + P22,675 + P21,595 PV = P68,080, cheaper than paying P70,000 now ---- Better option!!! You regularly invest your savings in a TD that gives annual interest of 5%.Chapter 5 (continuation) Annuities • Annuity – series of equal cash flows over many periods • To compute: use Present Value Interest Factor for an Ordinary Annuity (PVIFA) • Formula for Present Value of an Annuity = IF cash flow stream lasts forever or is indefinite, it is called a Perpetuity • Formula for Present Value of a Perpetuity = Perpetuity R Perpetuity is common for pension plansChapter 5 Annuity vs Perpetuity • ANNUITY – series of equal cash flows over many periods (fixed number of periods) • PERPETUITY – series of cash flows that lasts forever or is indefinite (everlasting) Perpetuity is common for pension plans.Effective Annual Interest rate • Nominal Rate – rate quoted • Effective Rate – real or actual rate paid on a loan, investment or financial product due to the result of compounding • Note: Effective rate increases as the frequency of compounding increasesEffective Annual Interest Rate • Interest rates are quoted as per annum (per year) rates. However, lenders may require interest payments to be made more frequently – either monthly, quarterly or semi-annually. • Hence, due to compounding, the effective annual interest rate may be higher. Remember: more frequent interest payments give effectively higher interest amount [Show More]

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