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MGFB10H3 (19)
Chapter 5

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Sultan Ahmed

Chapter 5: Time Value of Money 5.1 Accounting Principles  Time value of money: the idea that money invested today has more value than the same amount invested later  Money represents our ability to buy goods and services (operates as a medium of exchange)  The opportunity cost of money is the interest rate that would be earned by investing it (if put money under mattress instead of bed, lose the opportunity of earning interest) o Interest rate is the price of money  Market interest rate=required rate of return=discount rate=investor’s opportunity cost 5.2 Simple Interest  Simple interest: interest paid or received on only the initial investment (the principle) o Interest is not earned on the accrued/earned interest  Value (time n)= Principal + (number of periods in years × Principal × interest rate) 5.3 Compound Interest Compounding (Computing Future Values)  Compound interest: interest that is earned on the principal amount invested and on any accrued interest (compound amount increases every year)  Growth is directly related to the length of the period as well as to the level of return earned  In the first year, compound interest is the same as simple interest (in other words, starting principle + the interest) o E.g. $1000 + ($1000 × 0.1) = $1100= $1000 × (1×0.1) or P0 =(1+i) o PV = the present value today 0  In the second year, $1100 is re-invested. We don’t spend the $100 interest o Interest earned increases to $110 ($100 interest on starting principal plus $10 interest earned on the $100 of interest reinvested at the end of the first year o Formula: FV =PV (1+i) n n 0 n o FV n the future value at time n and (1+i) = compound value interest factor (CVIF) o Compound value interest factor (CVIF): a term that represents the future value of an n investment at a given rate of interest and for a stated number of periods (1+i)  The compound rate of return can also be called the geometric mean  Basis Point: 1/100 of 1 percent Discounting (Computing Present Values)  Discounting: finding the present value of a future value by accounting for the time value of money making it easier to compare future values  E.g. $1 million in 40yrs is not worth $1 million today, so you discount or take something off, to get it to its true value  1/(1+i) is called the discounting factor or present value interest factor (PVIF)  Present value interest factor (PVIF): a formula that determines the present value of $1 to be received at some time in the future, n, based on a given interest rate, i o The PVIF is always less than one (as long as i >0). This means that future dollars are worth less than the same dollars today o Discount factors are the reciprocals of their corresponding compound factors and vice versa (PVIF= 1/CVIF) Determining Rates of Return or Holding Periods n  FVn=PV 01+i)  Equation has four variables. Therefore, if we know 3 variables, we can solve for the last one.  4 different types of finance problems can be solved: o Future value problems: How much will I have in w years at x percent if I invest $y today? o Present Value problems: What is the value today of receiving $z in w years if the interest rate is x percent? o IRR problems: What rate of return will I earn if I invest $y today for w years and get $z? o Period problems: How long do I have to wait to get $z if I invest $y today at x percent? 5.4 Annuities and Perpetuities Ordinary Annuities  Annuity: series of payments or receipts, which we will simply call cash flows, that are the same amount and paid at the same interval (e.g. annually or monthly) over a period of time (e.g. loan)  Cash flows: the actual cash generated from an investment  Ordinary annuities: equal payments that are made at the end of each period o values involved w/ ordinary annuity: FV, PV, n, i and PMT (for the regular annuity payment or receipt)  Ordinary annuity equation:  This formula is usually called the compound value annuity formula or CVAF to distinguish it from the single-sum CVIF  The formula for present value annuity formula or PVAF is (formula is for ordinary annuity): Annuities Due  Annuity due: an annuity (such as a lease) for which the payments are made at the beginning of each period  Lessee: a person who leases an item  The FV annuity due formula is:  The PV annuity due formula is: Perpetuities  Perpetuities: special annuities that provide payments forever (n goes to infinity in the annuity equation)  Perpetuities= cash payment or receipt/ interest rate  The annuity and perpetuities discussed for Chapter 5 illustrate constant annuities and perpetuities (i.e. where the cash flows remain t
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