Chapter 2, Module 2 Notes
FIN 502 – Personal Financial Planning
Chapter 1 – Module 2
Time value of money * How to compare monetary amounts you pay or receive at different times * The arithmetic with which we convert money between periods, or calculate what rate of return is implied by a given set of cash flows
Single Period – Rate of Return * N = amount of years * I% = x (what we’re trying to find) * PV = How much it’s worth today * FV = How much it’s worth at maturity date
* Discount bonds pay no interest during it’s life, the interest you receive is part of the final payment (FV) * The interest rate is also known as the discount rate * The rate that makes us indifferent between present and future amounts (in any pattern). If we use the appropriate discount rate to calculate the present of a future amount, we don’t care whether we receive the present value now or the future value at a later date
Multiperiod – Rate of Return * Annual rate is always implied when we speak about rate of return * Sometimes interest is given monthly, etc. These need to be converted to annual rate of returns
Arithmetic & Geometric Rates of Return
If we invest $100 for 2 years and at the end of 2 years we receive $120
* Arithmetic (Mutual funds often quote their past rates of return using this method) * $20 / 2 years = 10%
* Geometric (This is correct because it allows for compounding) * TVM = 9.5445%
Arithmetic Mean & Geometric Mean Return
Year | Return (%) | 1990 | 17 | 1991 | 8 | 1992 | 2 | 1993 | 15 |
* Arithmetic Average * .17 + .8 + .2 +.15 / 4 = .105 = 10.5% * Use this in analyzing investments when we want to estimate an average of expected return across different investments in the same period.
* Geometric Average * Lower than or equal to the arithmetic mean * nth root of 1.17 x 1.08 x 1.02 x 1.15 – 1 = 10.34 * OR *
Chapter 1 – Module 2
Time value of money * How to compare monetary amounts you pay or receive at different times * The arithmetic with which we convert money between periods, or calculate what rate of return is implied by a given set of cash flows
Single Period – Rate of Return * N = amount of years * I% = x (what we’re trying to find) * PV = How much it’s worth today * FV = How much it’s worth at maturity date
* Discount bonds pay no interest during it’s life, the interest you receive is part of the final payment (FV) * The interest rate is also known as the discount rate * The rate that makes us indifferent between present and future amounts (in any pattern). If we use the appropriate discount rate to calculate the present of a future amount, we don’t care whether we receive the present value now or the future value at a later date
Multiperiod – Rate of Return * Annual rate is always implied when we speak about rate of return * Sometimes interest is given monthly, etc. These need to be converted to annual rate of returns
Arithmetic & Geometric Rates of Return
If we invest $100 for 2 years and at the end of 2 years we receive $120
* Arithmetic (Mutual funds often quote their past rates of return using this method) * $20 / 2 years = 10%
* Geometric (This is correct because it allows for compounding) * TVM = 9.5445%
Arithmetic Mean & Geometric Mean Return
Year | Return (%) | 1990 | 17 | 1991 | 8 | 1992 | 2 | 1993 | 15 |
* Arithmetic Average * .17 + .8 + .2 +.15 / 4 = .105 = 10.5% * Use this in analyzing investments when we want to estimate an average of expected return across different investments in the same period.
* Geometric Average * Lower than or equal to the arithmetic mean * nth root of 1.17 x 1.08 x 1.02 x 1.15 – 1 = 10.34 * OR *