false

Textbook Notes
(368,241)

Canada
(161,733)

University of Toronto Scarborough
(18,510)

Finance
(37)

MGFB10H3
(19)

Sultan Ahmed
(8)

Chapter 5

by
OneClass3113

Unlock Document

Finance

MGFB10H3

Sultan Ahmed

Winter

Description

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

More
Less
Related notes for MGFB10H3

Join OneClass

Access over 10 million pages of study

documents for 1.3 million courses.

Sign up

Join to view

Continue

Continue
OR

By registering, I agree to the
Terms
and
Privacy Policies

Already have an account?
Log in

Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.