Chapter 4 time value of money

• Future cash flows are best depicted through the use of a timeline:The Role Of Time Value Cash Flows On Top Time On Bottom...  Annuity: Series of cash flows of equal amount, received

Learning Goals:

• Discuss the role of time value in finance and the basic patterns of cash flows.

• Understand present and future value.

• Describe annuities, and perpetuities.

• Find future/present values of a stream of cash flows.

• Understand the effect of frequently compounding interest.

• Determine amortisation parameters.

The Role Of Time Value

things being equal, a dollar today is worth more than a dollar that will be received at some future date.

by considering:

• Future cash flows are best depicted through the use of a timeline:

The Role Of Time Value

Cash Flows On

Top

Time On Bottom

Compounding & Discounting

Page 147

Useful Calculation Tools

Tables.pdf

Financial TablesFinancial

Tables.pdf

Page 148

Basic Cash Flow Patterns

 Single Amount: One lump sum.

 Annuity: Series of cash flows of equal amount,

received at equal time intervals.

 Mixed Stream: Series of cash flows that are not

equal or a series of cash flows that are not

received at equal time intervals.

Future Value Of A Single

Amount

 Future Value: the value of a present amount at a

future date (Go to excel sheet)

 Calculated by applying compound interest over a specified period of time.

 Future Value Interest Factor (FVIF): the multiplier

used to calculate FV at a given discount rate.

• Written as FVIF i,n

• FVIF i,n = (1 + i) n [Equation 4.5] Financial

Tables.pdf

• FV n = PV x FVIF i,n [Equation 4.6]

Future Value Of A Single

Amount

 Example: Jane Farber places $800 in a savings

account paying 6% interest compounded annually She wants to know how much money will be in the account at the end of five years Formula Sheet.pdf

Future Value Relationship

Page 153

Present Value Of A Single

Amount

 Present Value: the current value of a future

amount.

specified period of time.

 Present Value Interest Factor (FVIF): the multiplier

used to calculate PV at a given discount rate.

• Written as PVIF i,nFinancial Tables.pdf

Present Value Of A Single

Amount

 Example: Pam Valentine wishes to find the

present value of $1,700 that will be received

eight years from now Pam’s opportunity cost is 8%

 Formula:

(1 + i) n

= 1,700 (1 + 0.08) 8

= $918.46

Present Value Of A Single

Amount

Present Value Relationship

 Annuity: a stream of equal periodic cash flows

over a specified time period.

1 Ordinary Annuity: Cash flow occurs at the

end of each period.

2 Annuity Due: Cash flow occurs at the

beginning of each period.

annuity refers to ordinary annuities.

Future Value Of An Ordinary

Annuity

cash flows

Present Value Of An Ordinary

Annuity

cash flows.Financial Tables.pdf

Future Value Of An Annuity

Due

annuity, as the cash flows occur at the start of the

period.

[Equation 4.17]

Present Value Of An Annuity

Due

first period, the annuity must be discounted back one less year than for an ordinary annuity.

[ Equation 4.18]

Mixed Streams

particular pattern

 Future Value Of A Mixed Stream: Calculated by

adding together the future values of each cash flow at the specified future dates.

 Present Value Of A Mixed Stream: Calculated by

adding together the present values of each future cash flow.

Future Value Of A Mixed

Stream

 Example: Shrell Industries, a cabinet manufacturer, expects to

receive the following mixed stream of cash flows over the next five years from one of its small customers:

End Of Year Cash Flow

If Shrell expects to earn 8% on its investments, how much will accumulate by the end of year 5 if

it immediately invests the cash flows when they are received?

Future Value Of A Mixed

Present Value Of A Mixed

Stream

 Example: Frey Ltd, a shoe manufacturer, has been

offered an opportunity to receive the following mixed stream of cash flows over the next five years:

End Of Year Cash Flow

If the firm must earn at least 9% on its investments, what is the most it should pay for this opportunity?

Present Value Of A Mixed

Compounding More Frequently

 Compounding can be done:

 The more frequent the compounding the larger the

amount of money accumulated.

 Is calculated with the following formula:

is compounded.

Compounding More Frequently

Continuous Compounding

continuous compounding can be calculated by:

 Example: Fred Moore wished to find the future value

at the end of two years of $100 invested at 8%

interest compounded continuously.

FV = 100 x 1.1735

FV = $117.35

Continuous Compounding

Nominal & Effective Rates Of Interest

allow comparison.

 Nominal Interest Rate: The contractual annual rate

of interest charged by the lender or promised by a borrower.

Must be disclosed by financial providers to

consumers on credit cards and loans

 Effective Annual Rate (EAR): The annual rate of

interest actually paid or earned.

Must be disclosed by financial providers on savings products

 Annual Percentage Rate (APR): the nominal annual

rate charged on loan products.

 Annual Percentage Yield (APY): the effective annual

rate a savings product pays.

Nominal & Effective Rates Of Interest

Applications Of Time Value

Finding the deposit/s need to accumulate a specified future sum e.g house deposit

PMT = FVA n

FVIFAi, n [Equation 4.25]



2 Loan amortisation: Finding the equal periodic

loan payments needed to meet the lender’s

required interest rate and repayment date.

A loan amortisation schedule shows the

allocation of each payment to principal and

3 Interest rate determination: Finding the

compound annual interest/growth rate of a

series of cash flows.

PVIFA i, n = PVA n

PMT [Equation 4.28]

4 Period determination: Finding an unknown

number of periods needed to generate a given amount of cash flow from an initial amount.

PVIFA i, n = PVA n

PMT

Applications Of Time Value