Ch.11Definitions:1. Return of investment: Return of the initial amount invested.2. Return on investment: additional amount returned in excess (or less than) the amount invested.3. Annuity: A series of EQUAL cash payments made at EQUAL intervals.What is Risk?1. Risk: the chance of an unfavorable outcome.2. Inflation risk: the risk of changing price levels.3. Business Risk: Risk of a particular company going out of business.4. Liquidity Risk: Risk that an investment cannot be converted into cash we need be.How are risks and return related?1. Expected rate of return: Estimated rate of return on a investment2. Risk premium: Expected rate of return adjusted for inflation, business, and liquidity riska. Note: The greater the risk, the higher the expected rate of return.Simple versus Compound Interest:1. How to calculate simple interest:a. Note that simple interest is calculated only by the principal.i. Interest (1) = Principal * Rate * Timeii. Interest (2) = Principal * Rate * Timeb. Note that compound interest is calculated by principal plus the accumulated interest.i. Interest (1) = Principal * Rate * Timeii. Interest (2) = (Principal + Interest [1]) * Rate * TimeWhat are the time value of money components?1. FV = future value2. PV = present value3. c = compoundings/payments per year4. r = annual interest rate5. n = total number of compoundings/payments 6. ANN = annuityHere is an example of what I am talking about!• Answers the question: What amount will $1 grow to at some point in the future?• Example: If we invest $2,000 today, what will it be worth in 5 years, if we earn 8 percent interest compounded quarterly?• PV (present value) = 2,000 • r (annual interest rate) = 8 • c (compoundings/payments per year) = 4 • n (total number of compoundings/payments) = 20 • ANN (annuity) = 0, therefore:• Answer: FV = $2,971.89Formula for present value of a $1: (note that this is the step by step process for the problem above)1. PV * ($1 + r/c)n = FVa. $2,000 * ($1 + 0.08/4)20 = FVi. Your present value is $2,000ii. Your annual interest rate which is (r) is 0.08iii. Your compoundings/payments per year is 4 because there are 12 months in a year and you need to break them down into quarterly payments which means you think of 4 quarters which = 12iv. (n) is your total number of compoundings/paymentsb. $2,000 * 1.4859 = FVc. $2,971.89 = FVWhat is the present value of a dollar?• Answers the question: What is $1 at some point in the future worth today?• Example: If we receive $2,000 in 5 years, what is it worth today if we could invest it at 8 percent interest compounded quarterly?FV = 2,000 r = 8c = 4 n = 20 ANN = 0, therefore:Answer: PV = $1,345.94FV * 1/($1 + r/c)n = PV$2,000 * 1/($1 + 0.08/4)20 = PV$2,000 * 0.6730 = PV$1,345.94 = PVWhat is the future value of annuity?• Answers the question: What is a series of payments going to be worth at some point in the future?• Example: If we invest $100 every month for 10 years and earn 12 percent interest, how much money will we have in 10 years?ANN = 100 PV = 0 r = 12c = 12 n = 120, therefore: Answer: FV = $23,003.87 ANN * [($1 + r/c)n - $1]/(r/c) = FV$100 * [$1 + 0.12/12)120 - $1]/(0.12/12) = FV$100 * 230.0387 = FV$23,003.87 = FVWhat is the present value of annuity?• Answers the question: How much must be received today to generate a series of equal payments in the future?• Example: We want to buy a car for $25,000. The dealer will finance us at 10 percent annual interest for 5 years, how much will the monthly payments be?PV = 25,000 FV = 0 r = 10c = 12 n = 60, therefore:Answer: ANN = $531.18ANN * [$1 - $1/($1 + r/c)n]/(r/c) = PVANN * [$1 - $1/($1 + 0.10/12)60]/(0.10/12) = $25,000ANN * 47.0654 = $25,000ANN =