BUSFIN1 (Business Finance) 4th QUARTER (Second Sem, SY 2020-2021) Be reminded of our class preliminaries! VIRTUAL CLASSROOM RULES/REMINDERS!!! CHAPTER 4. Basic Long-Term Financial Concepts LESSON. Time Value of Money OBJECTIVES: At the end of the lesson, you should be able to: explain the concept on time value money; compute problems concerning the time value of money; and apply the concepts in real-life scenarios Recap of previous lesson To be able to acquire assets, our funds must have come somewhere. If it is acquired using cash from our pockets/stockholders, it is financed by ____________. On the other hand, if we used money from our borrowings, the asset bought is financed by ___________. Recap of previous lesson Debt which is scheduled to mature in more than one year but in less than years. Debt which is scheduled to mature in more than ten years. Debt scheduled to be paid within a year. Introduction Time Value of Money The idea that the MONEY available NOW is worth MORE THAN the same amount that will be available at some FUTURE date. “The connecting piece or link between present (today) and future is the Interest Rate.” Interest The rate which is charged or paid for the use of money. Excess of resources (usually cash) received or paid over the amount of resources loaned or borrowed which is called the principal. SIMPLE INTEREST vs COMPOUNDED INTEREST 2 Types of Interest (1) Simple Interest – occurs when there is no interest earned on top of interest that was earned in the previous periods. SIMPLE INTEREST I = P x r x T EXERCISE 1 I = P x r x T You invested Php10,000 for 3 years at 9% and the proceeds from the investment will be collected at the end of 3 years. Calculate the simple interest. 2 Types of Interest (2) Compound Interest – occurs when interest is earned on the interest that was earned from the previous periods. *m is the compounding frequency Compounding Frequency - the number of times interest is computed on a certain principal in one year. COMPOUND INTEREST Compound Interest Year Principal Interest (P x r) Cumulative Interest Total 1 Php 500,000.00 Php 40,000.00 Php 40,000.00 Php 540,000.00 2 540,000.00 43,200.00 83,200.00 583,200.00 3 583,200.00 46,656.00 129,856.00 629,856.00 4 629,856.00 50,388.48 180,244.48 680,244.48 5 680,244.48 54,419.56 Php 234,664.04 Php 734,664.04 EXERCISE 1 You invested P 10,000 for 3 years at 9% and the proceeds from the investment will be collected at the end of 3 years. Calculate the compound interest. TIME LINES is a graphical representation of the timing of cash flows. period PRESENT VALUE (PV) vs FUTURE VALUE (FV) • also known as discounting where, (𝟏 + 𝒊) −𝒏 = Present value interest factor (PVIF)* or discount factor • value of the present value after n time periods FUTURE VALUE (FV) Using the formula, find the future values of P 1,000 compounded at a 10% annual interest at the end of one year? two years? and five years? OTHER COMPOUNDING PERIODS If compounded annually: Apply the given formula to get the future value of money worth Php 1,000.00 that was deposited in an interest bearing account. The annual interest rate is 6% and the money will stay in the account for 5 years. FV = Php 1,338.23 OTHER COMPOUNDING PERIODS Apply the given formula to get the future value of money worth Php 1,000.00 that was deposited in an interest bearing account. The annual interest rate is 6% and the money will stay in the account for 5 years. What if the 6% interest rate is compounded semi-annually? What will be the future value? a. Divide the interest rate by 2 (semi-annual), making it 3%. b. Multiply the number of periods by 2, making it 10 FV = Php 1,343.92 Exercise Determine the compound amount on an investment at the end of 2 years if Php 20,000 is deposited at 4% compounded (a) semi-annually and (b) quarterly. PRESENT VALUE (PV) vs FUTURE VALUE (FV) • also known as discounting where, (𝟏 + 𝒊) −𝒏 = Present value interest factor (PVIF)* or discount factor • value of the present value after n time periods PRESENT VALUE (PV) Jack would like to buy a car two years from now using the proceeds of a 20% investment that is compounded semiannually. If the projected price of the car is P 1,400,000.00 how much money must be invested today to earn the price of the car? EXERCISE: You need PHP25,000 to buy a laptop when you enter college 2 years from now. How much must you invest now if the interest rate is at 6% per annum. PV = 25,000/(1.1236) = PHP22,249.91 You need to invest PHP22,249.91 to have PHP25,000 by the end of 2 years. REAL LIFE APPLICATION c/o Group 3 ANNUITIES A series of equal payments at fixed intervals for a specified number of periods (normally in years). ORDINARY ANNUITY The type of annuity wherein payments occur at the end of the period. Period 1 0 2 3 Php 300 Php 300 5% Payments Php 300 ANNUITY DUE The type of annuity wherein payments occur at the beginning of each period. Period 1 0 2 3 5% Payments Php 300 Php 300 Php 300 Php 0 FUTURE VALUE OF ORDINARY ANNUITY Given: t = 3 ; r = 5% R/PMT/Cash Flow (annuity payment) = Php 300 FVA = ordinary Php 945.75 FUTURE VALUE OF ORDINARY ANNUITY EXAMPLE (Ordinary Annuity): Mr. Mendoza wishes to determine how much will be the value of his savings in 5 years if he will put PHP1,000 per year in a bank that provides 7% interest per annum. FV = 1,000 x (FVA factor: 5.7507 t=5, r=7%) FVA = ordinary Php 5,750.70 FUTURE VALUE OF ANNUITY DUE Given: t=3 r = 5% R/PMT/Cash Flow (annuity payment) = Php 300 FVAdue= FVA (1 + r) ordinary FVA due = Php 945.75 (1+0.05) FVAdue= Php 993.04 PRESENT VALUE OF ORDINARY ANNUITY Given: t = 3 ; r = 5% PMT/Cash Flow (annuity payment) = Php 300 PVA = Php 817.20 PRESENT VALUE OF ORDINARY ANNUITY Mr. Yusoph wants to buy a pair of shoes worth P10,500. He has the option of paying it today for PHP10,500 or buying in installment where he has to pay a down payment of PHP4,000 today, and the balance will be paid in two equal payments of PHP4,000 each for the next two years. Given an interest rate of 10%, which is the better option? PV = 4,000 + 4000 x (PVA factor: 1.7355 t=2, r=10%) PV = PHP10,932.00 for buying on installment vs. PV PHP10,500 for buying today. PRESENT VALUE OF ANNUITY DUE If a supplier would allow you to pay P 50 000 annually at 10% for 3 years with the first payment due immediately, how much would be the present value? PVA = Php 136,776.00 i = i/m n = mt EFFECTIVE ANNUAL RATE The annual rate of interest actually being earned. Equivalent Annual Rate (EAR) EFF% 1 + r m m -1 Nominal Rate – the rate stated or quoted in a contract. m – number of compounding periods per year EFFECTIVE ANNUAL RATE What is the effective annual rate of a 10% nominal interest rate compounded semi-annually? annually? 1 + r m 2 m -1 = (1 + .1) – 1 2 = (1 + .05) – 1 = 0.1025 = 0.05 EFF% = 10.25% EFF% = 5% LOAN AMORTIZATION • The payment of a loan in installments over a specified period of time. AMORTIZED LOAN • A loan that is to be repaid in equal payments over a specified period of time. Example: A home improvement loan in the amount of Php 100,000 has an interest rate of 6%. The term of the loan is for 5 years. Equal payments at the end of every year should be made until the loan (including the interest) is paid off. AMORTIZATION SCHEDULE A home improvement loan in the amount of Php 100,000 has an interest rate of 6%. The term of the loan is for 5 years. Equal payments at the end of every year should be made until the loan (including the interest) is paid off. PMT IS Php 23,739.64. AMORTIZATION SCHEDULE Amount Borrowed: Php 100,000 Years: 5 Interest Rate: 6% PMT: Php 23,739.64 Year Beginning Payment Amount Interest Repayment of Principal Ending Balance 1 Php100,000 Php23,739.64 Php6,000.00 Php17,739.64 Php82,260.36 2 82,260.36 Php23,739.64 4,935.62 18,804.02 63,456.34 3 63,456.34 Php23,739.64 3,807.38 19,932.26 43,524.08 4 43,524.08 Php23,739.64 2,611.44 21,128.20 22,395.89 5 22,395.89 Php23,739.64 1,343.75 22,395.89 0.00 EXERCISE 1