Textbook Notes (290,000)

CA (170,000)

UTSG (10,000)

Rotman Commerce (1,000)

RSM230H1 (30)

Ray Daroga (1)

Chapter 5

Department

Rotman CommerceCourse Code

RSM230H1Professor

Ray DarogaChapter

5This

**preview**shows pages 1-2. to view the full**6 pages of the document.**Ch. 5: Time Value of Money

LO 5.1 Explain the importance of the time value of money and how it is related to an

investor's opportunity costs

Opportunity Cost

Time value of money: idea that a dollar today is worth more than a dollar in the future

Medium of exchange: something that can be used to facilitate transactions

• Money represents our ability to buy goods and services, and has no value in and of itself

• Opportunity costs such as investing the dollar to earn a return are what produce the time

value of money

• The opportunity cost of money is the interest rate that would be earned by investing it

o Call the interest rate the "price of money"

o Knowing this rate helps us determine the value of money received at different times

Required rate of return (discount rate): the market interest rate (k) or the investor's

opportunity cost

LO 5.2 Define simple interest and explain how it works

Simple interest: interest paid or received on only the initial investment (principal)

P = principal

n = number of periods

P x k = interest

LO 5.3 Define compound interest and explain how it works

Compound interest: interest that is earned on the principal amount invested and on any accrued

interest

• The amount of compound interest earned increases every year

FVn = future value at time n

(1 + k)n = future value interest factor (FVIF)

Compound return represents the average annual growth rate in the value of $1 invested at the

start of the period

• Involves the same reinvestment rate assumption as compound interest rate

• Often referred to as the geometric return

Basis point: 1/100 of 1%

Only pages 1-2 are available for preview. Some parts have been intentionally blurred.

• Earning just a few basis points more on one investment causes the future value of the

portfolio to compound much faster, however the search for additional returns often leads

investors to underestimate the associated risks

Discounting (Computing Present Values)

Discounting: finding the present value of a future value by accounting for the time value of

money

1 / (1 + k) n, is called the discount factor or present value interest factor (PVIF)

PVIP = 1/FVIP

• The greater the discount rate, the greater the FVIF (and future value) and the smaller the

PVIF (and present value) and vice versa

o E.g low interest rates and pension payments. Pension funds estimate the present value

of future pension payouts to plan members (their liabilities) based on discounting

these future pension payments using current interest rates

• As a result of low interest rates, the present value of these pension liabilities

have increased dramatically

Determining Rates of Return or Holding Periods

FVn = PV0 (1 + k)n

• Future value problems: How much will I have in n years at x percent if I invest $y today?

• Present value problems: What is the value today of receiving $z in n years if the interest

rate is x percent?

• IRR problems: What rate of return will I earn if I invest $y today for n years and get $z?

• Period problems: How long do I have to wait to get $z if I invest $y today at x percent?

LO 5.4 Differentiate between an ordinary annuity and an annuity due, and explain how

special constant payment problems can be valued as annuities and in special cases, as

perpetuities.

Ordinary Annuities

Annuity: regular payments on an investment that are for the same amount and are paid at the

same interval of time

• Ex: Car loan, mortgage payment

Cash flows: actual cash generated from an investment

Ordinary annuity: equal payments that are made at the end of each period of time

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