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with computations about the tvm

Everdina IcawaloSeguir

- 1. TIME VALUE OF MONEY JULY23, 2016
- 2. INTRODUCTION “A Peso Received Today Is Worth More Than a Peso Received in The Future”. The time value of money impacts business finance, consumer finance, and government finance. Time value of money results from the concept of interest. - is a cost of using money over time or the sum of money paid for the use of money
- 3. Interest and Time Value of Money are considerations in decisions involving expenditures for business investments and the acquisition of operating assets. Time Value of Money involves 2 major concepts: Future Value Present Value 3 factors considered by both of the 2 concepts: Principal Interest Rate Time Period
- 4. SIMPLE INTEREST it is the interest paid or earned on the initial principal only. Interest (I) is a sum of money for the use of money. Principal (P) Rate of interest (r) Length of time (t) Formula: I = P r t
- 5. Example: Venus deposited P5,000 in a bank at 6.5% simple interest for 2 years. How much will she earns after 2 years, assuming that no withdrawals were made? solution: P = P5,000 r = 6.5% or 0.065 t = 2 years I = ? I = P r t = (P5,000) (0.065) (2) = P650.00 (interest)
- 6. To find also the rate, r, the time, t, and the principal, P, and also the future amount, F, we use the following formula: r = I / P t t = I / P r P = I / r t or P = F / 1 + r t F = P (1 + r t)
- 7. Compound interest It is the interest paid on both the principal and the amount of interest accumulated in the prior period. Compounding is the process called for determining future value when compound interest is applied. Formula: F = P (1 + i ) n
- 8. Example: Venus deposited P5,000 in a bank at 6.5% compounded annually for 2 years. How much will she earns after 2 years, assuming that no withdrawals were made? solution: F = P (1 + i ) n = P5,000 ( 1 + 0.065) 2 = P5,671.125
- 9. Simple interest compared with compound interest Example: ABC Corporation leaves its P10,000 on deposits for five years in a bank paying 10% annual interest. Simple Interest Compound Interest Year Beginning amount Simple interest Ending amount Beginnin g amount Compound interest Ending amount 1 P10,000 P1,000 P11,000 P10,000 P1,000 P11,000 2 P10,000 P1,000 P12,000 P11,000 P1,100 P12,100 3 P10,000 P1,000 P13,000 P12,100 P1,210 P13,310 4 P10,000 P1,000 P14,000 P13,310 P1,331 P14,641 5 P10,000 P1,000 P15,000 P14,641 P1,464.10 P16,105.10 Total interest P5,000 P6,106.10
- 10. Future value (annual compounding) Formula: FVn = PV ( 1 + i)n FV n -- future value PV -- initial principal amount i -- interest rate (compounded) n -- periods
- 11. Example: The future value of P10,000 compounded at a 10% annual interest rate at the end of one year, two years and five years are computed as follows: Year Calculation Future Vale 1 FV1 = (P10,000)(1+0.10)1 P11,000 2 FV2 = (P10,000)(1+0.10)2 = (P10,000)(1,21) P12,100 5 FV5 = (P10,000)(1+0.10)5 =(P10,000)(1.61051) P16,105.10
- 12. FUTURE VALUE ( WITH INTRAPERIOD COMPOUNDING) It is compounding that occurs more than once a year. Formula: FVn = PV (1 + i/m)mn FV n -- future value PV -- initial principal amount i -- interest rate (compounded) n -- periods m --number of compounding period per year
- 13. Example: Instead of placing P1,000 in Atlanta Bank that pays 10% interest annually, the financial manager decides to put the money in National Bank that pays 10% interest compounded semi-annually. Between the two banks, there would be a difference in the future value of your investment after one year. Atlanta Bank Annual Compounding National Bank Semi-annual Compounding FV1 = (P1,000)(1 + 0.10)1 = (P1,000)(1.10) =P1,100 FV1 = (P1,000)(1 +0.10/2)(2)(1) = (P1,000)(1.1025) = P 1,102.50
- 14. Nominal interest rate compared to effective interest rate Nominal Interest Rate is simply the stated rate while the Effective Interest Rate or also called Annual Percentage Rate (APR) is the true interest rate and may differ from nominal rate depending on the frequency on compounding. Formula; APR = (1 + i/m )m - 1
- 15. Example: Disney Incorporated deposits money in a bank that pays 10% nominal interest and compounds interest semi-annually. APR = (1 + 0.10/2)2 – 1 = (1.05)2 -1 = 1.1025 – 1 = 0.1025 or 10.25%
- 16. Comparison or results of different compounding periods for P1,000 invested at a 10% interest rate for one year Initial Investment Compounding Period Future Value Annual Percentage Rate P1,000 Annually P1,100 10% P1,000 Semi-annually P1,102.50 10.25% P1,000 Quarterly P1,103.81 10.38% P1,000 Monthly P1,104.71 10.47%
- 17. Determination of the future value of a stream of payments Future Value Determination Involving a Stream of Unequal Payments In calculating the future value of an unequal stream of payments, find the future value of each payment at a specified future date and then sum it up.
- 18. Example: A firm plans to deposit P2,000 today and P1,500 one year from now at Mount Carmel Rural Bank. No future deposits or withdrawals are made and the bank pays 10% interest compounded annually. The future value of the account at the end of four years is computed to be: FV4 = (P2,000)(1.10)4 + (P1,500)(1.10)3 = (P2,000)(1.464) + (P1,500)(1.331) = P2,928 + P1,996.50 = P4,924.50
- 19. Future Value Determination Involving a Stream of Equal Payments A stream of equal payments made at regular time intervals is an annuity There are two types of fixed annuities: Ordinary Annuity Annuity Due
- 20. 1. Ordinary annuity It is one in which payments or receipts occurs at the end of each period. Formula: FVOA n = A ((( 1 + i ) n – 1) / i ) FVOA n - future value of ordinary annuity A - amount of fixed annuity payment
- 21. Let's now run through Example 1. Consider the following annuity cash flow schedule:
- 22. To calculate the future value of the annuity, we have to calculate the future value of each cash flow. Let's assume that you are receiving $1,000 every year for the next five years, and you invested each payment at 5%. The following diagram shows how much you would have at the end of the five-year period:
- 23. this is formula that serves as a shortcut for finding the accumulated value of all cash flows received from an ordinary annuity: FVOA n = A ((( 1 + i ) n – 1) / i ) = $1,000 ((( 1 + .05) 5 -1 ) / .05) = $5,525.63
- 24. Example: Crystal Corporation deposits P1,000 at the end of each of three years in a bank account paying 10% interest compounded annually. The value of the account at the end of the third year is computed by: FVOA3 = (P1,000) (((1+0.10)3 -1)/0.10) = (P1,000)(3.310) = P3,310
- 25. 2. Annuity due It is one which payments or receipts occur at the beginning of each period. Formula: FVAD n = A ((1 + i )n – 1) / i)(1 + i) FVAD n - future value of an annuity due A - amount of fixed annuity payment
- 26. When you are receiving or paying cash flows for an annuity due, your cash flow schedule would appear as follows:
- 27. Example: $1,000 payment is made at the beginning of the period rather than at the end (interest rate is still 5%):
- 28. The future value of this annuity can use this formula: FVAD n = A ((1 + i )n – 1) / i)(1 + i) = $1000 (( 1 + .05) 5 – 1) / i) ( 1+.05) =$ 5801.91
- 29. Example Instead of depositing P1,000 at the end of the year for three consecutive years, the firms makes deposits at the beginning of each year. Interest is compounded annually at 10%. How much will the firm have in account after three years? FVOA3 = (P1,000)(3.310) (1.10) = (P1,000)(3.641) = P3,641
- 30. Present value It is the current value of a future amount of money, or series of payments, evaluated at an appropriate discount year. Discount rate is the rate of the interest that is used to find present values.
- 31. Discounting It is the process of determining the present value of the future amount. Formula: PV = FVn / (1 + i)n PV = FVn (1 + i)-n
- 32. Example Blueberry Company expects to receive P1,100 one year from now. What is the present value of this amount if the discount rate is 10%? PV = FVn / (1 + i)n PV = P1,100 / (1 + 0.10)1 = P1,100 / 1.10 = P1,000
- 33. Determination of the present value of a stream of payments Present Value Determination Involving a Stream of Unequal Payments To find the present value of an unequal or mixed stream of payments, simply calculate the present value of each future amount separately and then add these present values together.
- 34. Example: MNM Company expects to receive payments of P1,000, P1,500 and P2,000 at the end of one, two and three years, respectively. The present value of this stream of payments discounted at 10% is computed as follows: PV = (P1,000)(0.909) + (P1,500)(0.826) + (P2,000)(0.751) = P909 + P1,239 + P1,502 = P3,650
- 35. Present Value Determination Involving a Stream of Equal Payments The present value of an equal payments is found by using the equation below. PVOA n = A { ∑ 1 / (1 + i) t } This equation, the annuity payment, A, is multiplied by the term in bracket, which is the sum of the individual present value interest factors.
- 36. Example: Summer Corporation expects to receive P1,000 at year’s end for the next 3 years. The present value of this annuity discounted at 10% is computed as follows: PVOA n = (P1,000) { ∑ 1 / (1 + i) t } = (P1,000) (0.909 + 0.826 + 0.751) = (P1,000) (2.486) = P2,486.00
- 37. Determination of the present value of a perpetuity Perpetuity – is an annuity with an infinite life: that is, the payments continue indefinitely. The present value of perpetuity is found by using the equation below: PV of a perpetuity = annuity / discount rate
- 38. Example: Honey Dew Corporation wants to deposit an amount of money in the bank account that will allow it to withdraw P1,000 indefinitely at the end of the year without reducing the amount of initial deposit. If a bank guarantees to pay the firm 10% interest on its deposits, the amount of money the firm has to deposits is computed as follows: PV of a perpetuity = P1,000 / 0.10 = P10,000
- 39. BOTTOM LINE Time literally is Money - the value of the money you have now is not the same as it will be in the future and vice versa. So, it is important to know how to calculate the time value of money so that you can distinguish between the worth of investments that offer you returns at different times.