This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Investment Tools: Quantitative Methods 1.A.: Time Value of Money a: Calculate the future value (FV) and present value (PV) of a single sum of money. Future Value: FV = PV(1 + I/Y) N Where PV = the amount of money invested today, I/Y = the rate of return, and N = the length of the holding period. ? Example: Using a financial calculator, here's an example of how you would find the FV of a $300 investment (PV), given you earn a compound rate of return (I/Y) of 8% over a 10year (N) period of time: N = 10, I/Y = 8, PV = 300; CPT FV = $647.68 (ignore the sign). ? Present Value: PV = FV / (1 + I/Y) N ? Example: Using a financial calculator, here's an example of how you'd find the PV of a $1,000 cash flow (FV) to be received in 5 (N) years, given a discount rate of 9% (I/Y). N = 5, I/Y = 9, FV = 1,000; CPT PV = $649.93 (ignore the sign). b: Calculate an unknown variable, given the other relevant variables, in singlesum problems. Example 1: Solving for I/Y In this example, you want to find the rate of return (I/Y) that you'll have to earn on a $500 investment (PV) in order for it to grow to $2,000 (FV) in 15 years (N). This very same problem could also be set up in terms of growth rates  e.g., what rate of growth (I/Y) is necessary for a company's sales to grow from $500 per year (PV) to $2,000 per year (FV) in 15 years (N).? ? N = 15, PV = 500, FV = 2,000; CPT I/Y = 9.68% ? Example 2: Solving for N In this example, you want to find out how many years (N) it will take for a $500 investment (PV) to grow to $1,000 (FV), given that we can earn 7% annually (I/Y) on your money. ? I/Y = 7, PV = 500, FV = 1,000; CPT N = 10.24 years. c: Calculate the FV and PV of an regular annuity and an annuity due. Calculate the FV of an ordinary annuity: Example: Find the FV of an ordinary annuity that will pay $150 per year at the end of each of the next 15 years, given the investment is expected to earn a 7% rate of return. ? N = 15, I/Y = 7%, PMT = $150; CPT FV = $3,769.35 (ignore the sign). ? Calculate the FV of an annuity due: ? Example: Find the FV of an annuity due that will pay $100 per year for each of the next three years, given the cash flows can be invested at an annual rate of 10%.? Note: When solving for a FV of an annuity due, you MUST put your calculator in the beginning of year mode (BGN), otherwise you'll end up with the wrong answer. ? N = 3, I/Y = 10%, PMT = $100; CPT FV = $364.10 (ignore the sign). ? Calculate the PV of an ordinary annuity: Example: Find the PV of an annuity that will pay $200 per year at the end of each of the next 13 years, given a 6% rate of return. ? N = 13, I/Y = 6, PMT = 200; CPT PV = $1,770.54 ? Calculate the PV of an annuity due: ?...
View Full
Document
 Fall '08
 PeterPellat

Click to edit the document details