CHAPTER 4 Interst and Equivalent.ppt

7/30/2019 CHAPTER 4 Interst and Equivalent.ppt

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CHAPTER 4CHAPTER 4INTEREST & ECONOMICINTEREST & ECONOMIC

EQUIVALENCEEQUIVALENCE


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INTERESTINTEREST

Interest can be thought of as "Interest can be thought of as "rentrent of money".of money". InterestInterest is ais a feefee paid on borrowed assets.paid on borrowed assets. It is the price paid for the use of borrowed money,It is the price paid for the use of borrowed money,[1][1] Money earned by deposited fundsMoney earned by deposited funds

Interest is a rental amount charged by financialInterest is a rental amount charged by financialinstitutions for the use of money.institutions for the use of money.

It is expressed on an annual basis.It is expressed on an annual basis. For the lender, it consists, for convenience, of (1) risk ofFor the lender, it consists, for convenience, of (1) risk of

loss, (2) administrative expenses, and (3) profit or pureloss, (2) administrative expenses, and (3) profit or pure

gain.gain. For the borrower, it is the cost of using a capital forFor the borrower, it is the cost of using a capital for

immediately meeting his or her needs.immediately meeting his or her needs.
http://en.wikipedia.org/wiki/Renthttp://en.wikipedia.org/wiki/Renthttp://en.wikipedia.org/wiki/Feehttp://en.wikipedia.org/wiki/Feehttp://en.wikipedia.org/wiki/Feehttp://en.wikipedia.org/wiki/Rent


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INTEREST RATEINTEREST RATE

The percentage of money being borrowedThe percentage of money being borrowed

that is paid to the lender on some timethat is paid to the lender on some time

basisbasis

Interest Rate is a measure of the interestInterest Rate is a measure of the interest

for given loan during the loan period andfor given loan during the loan period and

usually denoted byusually denoted by iiand expressed inand expressed in

percentage (%)percentage (%)


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TIME VALUE OF MONEYTIME VALUE OF MONEY

The time-value of money is the relationship betweenThe time-value of money is the relationship between

interest and time. i.e.interest and time. i.e. Figure 1 : Time-Value of MoneyFigure 1 : Time-Value of Money

Money has time-value because the purchasing power ofMoney has time-value because the purchasing power ofa ringgit changes with time.a ringgit changes with time.

0 1 2 3

years

nn-1

NowNow

RMRMRMRM

++

InterestInterest

Figure 1Figure 1


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POWER OF MONEYPOWER OF MONEY

EARNING POWER OF MONEYEARNING POWER OF MONEY The earning power of money represents funds borrowed for theThe earning power of money represents funds borrowed for the

prospect of gain.prospect of gain. Often these funds will be exchanges for goods, services, orOften these funds will be exchanges for goods, services, or

production tools, which in turn can be employed to generate andproduction tools, which in turn can be employed to generate and

economic gain.economic gain.

PURCHASING POWER OF MONEYPURCHASING POWER OF MONEY The prices of goods and services can go upward or downward,The prices of goods and services can go upward or downward,

and therefore, the purchasing power of money can change withand therefore, the purchasing power of money can change with

time.time.

Price Reductions :Price Reductions : Caused by increases in productivity andCaused by increases in productivity andavailability of goods.availability of goods.

Price Increases :Price Increases : Caused by government policies, price supportCaused by government policies, price supportschemes, and deficit financing.schemes, and deficit financing.


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CASH FLOW DIAGRAMSCASH FLOW DIAGRAMS Cash flow diagrams are a means of visualizingCash flow diagrams are a means of visualizing

(and simplifying) the flow of receipts and(and simplifying) the flow of receipts anddisbursementsdisbursements

The diagram convention is as follows:The diagram convention is as follows: Horizontal Axis :Horizontal Axis : The horizontal axis is marked off inThe horizontal axis is marked off in

equal increments, one per period, up to the duration ofequal increments, one per period, up to the duration ofthe project.the project. Revenues :Revenues : Revenues (or receipts) are represented byRevenues (or receipts) are represented by

upward pointing arrows.upward pointing arrows. Disbursements :Disbursements : Disbursements (or payments) areDisbursements (or payments) are

represented by downward pointing arrows.represented by downward pointing arrows. Net Cash Flow :Net Cash Flow : The arithmetic sum of receipts (+) andThe arithmetic sum of receipts (+) and

disbursements (-) that occur at the same point in time.disbursements (-) that occur at the same point in time.


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CASH FLOW DIAGRAMSCASH FLOW DIAGRAMS

All disbursements and receipts (i.e. cash flows) areAll disbursements and receipts (i.e. cash flows) areassumed to take place at the end of the year in whichassumed to take place at the end of the year in which

they occur. This is known as the "end-of-year"they occur. This is known as the "end-of-year"

convention.convention.

Arrow lengths are approximately proportional to theArrow lengths are approximately proportional to the

magnitude of the cash flow.magnitude of the cash flow.

Expenses incurred before time = 0 are sunk costs, andExpenses incurred before time = 0 are sunk costs, and

are not relevant to the problem.are not relevant to the problem. Since there are two parties to every transaction, it isSince there are two parties to every transaction, it is

important to not that cash flow directions in cash flowimportant to not that cash flow directions in cash flow

diagrams depend upon the point of view taken.diagrams depend upon the point of view taken.


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ii = The interest rate per interest period.= The interest rate per interest period.

nn = The total number of interest periods.= The total number of interest periods.

PP = a sum of money at a time chosen for purposes of analysis as= a sum of money at a time chosen for purposes of analysis astime zero, sometimes referred to as thetime zero, sometimes referred to as the present valuepresent value oror

present worthpresent worth..

FF = A future sum of money at the end of the analysis period. This= A future sum of money at the end of the analysis period. Thissum may be specified assum may be specified as FnFn..

AA = An end of period payment or receipt in a uniform series that= An end of period payment or receipt in a uniform series thatcontinues forcontinues forNN periods. This is a special situation whereperiods. This is a special situation where

A1 = A2 = = ANA1 = A2 = = AN..


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RM 1000

RM 1000RM 1120

RM 1120

Borrower point of view Lender point of view

RM120

RM120

RM120

RM120

RM120

RM120

RM120

RM120

Example 1:Example 1: Figure 2 shows cash flow diagrams for a transaction spanningfive years. The transaction begins with a RM1000.00 loan. For years two,three and four, the borrower pays the lender RM120.00 interest. At year five,the borrower pays the lender $120.00 interest plus the RM1000.00 principal.

0 1 2 3 4 5

0 1 2 3 4 5


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Methods of Calculating InterestMethods of Calculating Interest

Simple Interest :Simple Interest : the practice ofthe practice ofcharging an interest rate only to ancharging an interest rate only to aninitial sum (principal amount).initial sum (principal amount).

I = Pni.I = Pni.

P = PrincipalP = Principal

i = Interest ratei = Interest raten = Number of years (or periods)n = Number of years (or periods)

I = InterestI = Interest

Example 2 : Suppose that RM 1000Example 2 : Suppose that RM 1000is borrowed at a simple interest rateis borrowed at a simple interest rate

of 8% per annum.of 8% per annum.

Principle + Interest at end ofPrinciple + Interest at end of Year 1 = 1000 * 0.08 * 1 = RM 80Year 1 = 1000 * 0.08 * 1 = RM 80 Year 2 =Year 2 = 1000 * 0.08 * 2 = RM 1601000 * 0.08 * 2 = RM 160

YearYear

Amount atstart of

year (RM)

Interestatend of

year(RM)

PrinciplePrinciple++

InterestInterest

00 1,0001,000 -- --

11 -- 8080 1,0801,080

22 -- 8080 11601160

33 -- 8080 12401240


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Methods of Calculating InterestMethods of Calculating Interest Compound InterestCompound Interest:: the practice of charging an interest rate to anthe practice of charging an interest rate to an

initial sum and to any previously accumulated interest that has notinitial sum and to any previously accumulated interest that has notbeen withdrawnbeen withdrawn

Example 3

YearYear Amount at start ofyear (RM) Interest atendof year (RM) EndingEndingBalanceBalance

11 1,0001,000 8080 1,0801,080

22 1,0801,080 86.4086.40 1,166.401,166.40

33 1,166.401,166.40 93.3193.31 1,259.711,259.71

P= RM1,000 i = 8% n = 3years


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Economic equivalenceEconomic equivalence

EE exists between cash flows that have theEE exists between cash flows that have the

same economic effectsame economic effect

and could therefore be traded for one another.and could therefore be traded for one another.

EE refers to the fact that a cash flow-whether a single payment or aEE refers to the fact that a cash flow-whether a single payment or aseries of payments-can be converted to an equivalent cash flow atseries of payments-can be converted to an equivalent cash flow atany point in time.any point in time.

Even though the amounts and timing of the cash flows may differ,Even though the amounts and timing of the cash flows may differ,the appropriate interest rate makes them equalthe appropriate interest rate makes them equal

RM 1,259.711,259.71RM1000

50

i = 8%


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Economic equivalenceEconomic equivalence Example 4: A loan of $1,000 is made at an interest of 12% for 5 years.

The interest is due at the end of each year with the principal is due at

the end of the fifth year. The following table shows the resulting

payment schedule:

Year Amount at start ofyear

Interest atend ofyear

Owed amountat end of year

Payment

11 10001000 120120 12001200 120120

22 10001000 120120 12001200 120120

33 10001000 120120 12001200 120120

44 10001000 120120 12001200 120120

55 10001000 120120 12001200 11201120

Principal P = $1000.00 Interest Rate i = 0.12. Number of years (or periods) n = 5.


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Economic equivalenceEconomic equivalence Example 5: A loan of $1,000 is made at an interest ofExample 5: A loan of $1,000 is made at an interest of

12% for 5 years. The principal and interest are due at the12% for 5 years. The principal and interest are due at theend of the fifth year. The following table shows theend of the fifth year. The following table shows theresulting payment schedule:resulting payment schedule:

YearAmount at start ofyear

Interest atend ofyear

Owed amountat end of year

Payment

11 10001000 120120 12001200 00

22 10001000 134.40134.40 1254.401254.40 00

33 10001000 150.53150.53 1404.931404.93 00

44 10001000 168.59168.59 1573.521573.52 00

55 10001000 188.82188.82 1762.341762.34 1762.341762.34


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NOMINAL AND EFFECTIVE INTEREST RATESNOMINAL AND EFFECTIVE INTEREST RATES

Nominal Interest RateNominal Interest Rate Interest rate quoted based on an annual period without adjustment for the full effect of compounding Cannot be used for calculating the interest An interest rate is called nominalif the frequency of compounding (e.g.

a month) is not identical to the basic time unit(normally a year).

Example, : 12% per year compounded monthly

What It Really Means?

Interest rate per month (i) = 12%/12 = 1%

Number of interest periods per year (N) = 12

In words,

Bank will charge 1% interest each month on

your unpaid balance, if you borrowed money.

You will earn 1% interest each month on your

remaining balance, if you deposited mone


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NOMINAL AND EFFECTIVE INTEREST RATESNOMINAL AND EFFECTIVE INTEREST RATES

Effective interest rateEffective interest rate

Actual interest earned or paid in a year or some other time period with adjustment for the full effect of compounding Application: to compare the annual interest between loans with

different compounding terms Example :

12% per year compounded monthly Effective interest rate per month = 1% Effective interest rate per year = ?????

The effective rate is calculated in the following way iiee = ( 1 + r / M )= ( 1 + r / M )

MM 1 , 1 ,

Where iiee = Effective interest rate, r = Nominal interest rate, M = number of

compounding periods For example, :

12% per year compounded monthly

Effective interest rate per year = iieyeareyear = ( 1 + r / M )= ( 1 + r / M )MM 1= (1+ 1= (1+12%/100 /12[(12%/100)/12])1212


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NOMINAL AND EFFECTIVE INTERESTNOMINAL AND EFFECTIVE INTEREST

RATESRATES

Effective Annual Rate Based on Frequency of Compounding

NominalRate

Semi-Annual

Quarterly Monthly Daily Continuous

1% 1.00% 1.00% 1.01% 1.01% 1.01%

5% 5.06% 5.10% 5.12% 5.13% 5.13%

10% 10.25% 10.38% 10.47% 10.52% 10.52%

15% 15.56% 15.87% 16.08% 16.18% 16.18%

20% 21.00% 21.55% 21.94% 22.13% 22.14%

30% 32.25% 33.55% 34.49% 34.97% 34.99%

40% 44.00% 46.41% 48.21% 49.15% 49.18%

50% 56.25% 60.18% 63.21% 64.82% 64.87%

CHAPTER 4 Interst and Equivalent.ppt

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