financial management i_chapter 3

7/27/2019 Financial Management I_Chapter 3

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Financial Management

BBPW3103

Chapter 3

Time Value of Money


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Concept of Compounding andFuture Value

Compounding concept explains that RM1 todayis more valuable than RM1 in future through theinvestment activities to generate interest and

subsequently multiple Among the reasons why the TVM make this

alternative more valuable are:- Individuals more interested use they money now

compare in the future During the inflation period, the purchasing power of

RM1 now more than the purchasing power of RM1 inthe future

Capital that be obtained now can be invested togenerate a higher return in the future


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Time Line

Refer to period of one investment.

Time 0 (t0) refer to the present time, time

1 (t1) refer to the end of the first periodand so forth.


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Compounding Interest

Types of interest

Simple Interest : Interest that will be received

based on the principal amount Compounding Interest : Interest that will be

paid not only on the principal amount but alsoon any interest payable not withdrawnthroughout the period


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Compounding Interest (Cont)

Example 3.1 : If you invested RM100 in savingaccount with the interest rate 10% per year,how much return will you received at the end of

the first year.Return (F) = Principal (P) + Interest (i)

= P + P(i)= P(1 + i)

= RM100 ( RM100 x 10%)= RM100 + RM10= RM110


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If the stated returns are not withdrawn from the savingaccount, and the interest rate for the second and thirdyear remained unchanged, how much return will you

receive at the end of the second and third year?F2 = P(1 + i)

2

= RM100(1 + 0.1)2

= RM121

F3 = P(1 + i)3

= RM100(1 + 0.1)3

= RM133.10


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When the saving period I extended to tn,the total return that will obtained in the

period (n) isFn = P(1 + i)n


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Calculating Future Value UsingSchedule

The Future Value (FVn) equivalent to theprincipal at the point of time equal 0 or

the original principal amount (PV0)multiply with the future value factor statedin the schedule of Future Value InterestFactor (FVIFi,n)

The formula of FV using the schedule isFVn = PV0 (FVIFi,n)


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Calculating Future Value UsingSchedule (Cont)

Example 3.2 : You invested RM2,000 in thesaving account at a yearly interest rate of 5%

for the period of one year. Upon the completionof one year, how much return will your receive?

FV1 = PV0(FVIFi,n)

= RM2,000 (FVIF5% , 1)= RM2,000 (1.0500)

= RM2,100.00


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Calculating Future Value UsingSchedule (Cont)

Example 3.3 : Assume you deposited RM2,000in the saving account at a yearly interest 5% for

the period 4 years. Upon the completion years,how much the return will you receive?

FV4 = PV0(FVIFi,n)

= RM2,000 (FVIF5% , 4)

= RM2,000 (1.216)

= RM2.432.00


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Graphical Illustration of FV

There are 3 basic elements which sillinfluenced the future value, these are

Principal (amount that was borrowed orinvested)

Time period (the number of frequency ofinterest payment)

Interest rate payable or interest received


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Graphical Illustration of FV (Cont)

To show the interest rate influenced the FV ofan investment, find the return for depositedRM100 at Bank A, B and C that offer interest

rate 8%, 10% and 12% per year for 3 years. FV for Bank A

FVA = PV0(FVIFi,n)

= RM100 (FVIF8% , 3)= RM100 (1.2600)

= RM126.00


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FV for Bank BFVB = PV0(FVIFi,n)

= RM100 (FVIF10% , 3)= RM100 (1.3310)= RM133.10

FV for Bank C

FVC = PV0(FVIFi,n)= RM100 (FVIF12% , 3)= RM100 (1.4050)= RM140.50


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The correlation of FV, time period andinterest rate can be shown on the graph

below


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Concept of Discounting and PresentValue (PV)

Used to ascertain the present value (PV0)of principal value for sum of the money in

the future (FVn) that is discounted at aninterest rate (i) for the valuation period(n@t)


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Calculation of PV

There are formula to calculate PV

PV0 = FV (1 + i)n

Exmaple 3.4 : Assume you expect to receivedreturns of RM2,500 a year from now. How muchthe present value if the discount rate is 8% peryear

PV0 = FV (1 + i)n

= RM2,500 (1 + 0.08)1

= RM2,314.81


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Calculation of PV (Cont)

What is the present value that you must invest ifyour expect to received RM2,500 in the period 2years and 3 years at a discount rate 8% per

year?PV0 = FV (1 + i)n

= RM2,500 (1 + 0.08)2= RM2,143.35

PV0 = FV (1 + i)n

= RM2,500 (1 + 0.08)3= RM1,984.58


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Calculation of PV Using Schedule

The way of PV using schedule is the samewith FV calculation. But calculation of PV

is using Present Value Interest Factor(PVIF)

The formula is

PV0 = FV (PVIFi,n)


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Calculation of PV Using Schedule(Cont)

Exmaple 3.5 : Assume you expect toreceive RM3,999 in 3 years from now.

How much is the PV if the discount rate is9% per year?

PV3 = FV(PVIFi,n)

= RM3,999 (PVIF9% , 3

)

= RM3,999 (0.772)

= RM3,087.23


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Calculation of PV Using Schedule(Cont)

Example 3.6 : You intend to accumulate savingmoney at the bank for RM5,712 for the 4 years.How much saving you must make now if theinterest rate is 10% per year?

PV4 = FV(PVIFi,n)

= RM5,713 (PVIF10% , 4)

= RM5,713 (0.683)

= RM3,901.98.


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Graphical Illustration of PV

Change of interest rate, time of period orthe return will changed of the present

value. Example 3.7 : You intend to obtain

return of RM1,000 in 3 years from Bank A,

B and C that offer interest 8%, 10% and12%. What id the principal value thatshould make?


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Graphical Illustration of PV (Cont)

PVA = FV(PVIFi,n)= RM1,000 (PVIF8% , 3)= RM1,000 (0.7938)

= RM793.80PVB = FV(PVIFi,n)

= RM1,000 (PVIF10% , 3)= RM1,000 (0.7513)

= RM751.30PVC = FV(PVIFi,n)

= RM1,000 (PVIF12% , 3)= RM1,000 (0.7118)

= RM711.80


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Graphical Illustration of PV (Cont)


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Single Cash Flow Money Value

Is a cash flow that only occurs once in theperiod of valuation

The FV of an amount of single cash flowinvested presently will increase from timeto time with the specific interest rate


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Series Cash Flow Money Value

Is a series receiving or payments of cashthat occur throughout the valuation

period. There are several categories of series ofcash flow that isAnnuity

Derivation Cash Flow

Perpetuity


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Annuity

Series of payments @ receiving of the sameamount at the same intervals through the period

For example, Cash flow of RM5 that receive forevery month is an example of Annuity

Types of Annuity

Ordinary Annuity : Annuity occurs at the end of each

periodAnnuity Due : Annuity at the beginning of the period


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Annuity : FV of Ordinary Annuity

That occurs at the end of each period

Future Value Annuity (FVA) is the number

of annuity payments at a specific amount(n) that will increase at a specific periodbased on a specific interest rate (i).

The formula of the FVA is= A[(1 + i)n 1)] i

OR = A(FVIFAi,n)


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Annuity : FV of Ordinary Annuity(Cont)

Example 3.8 : You had deposited RM100 at theend of each year for 3 years continuously in theaccount that pays a yearly interest rate 10%.

How much the FV of the said annuity?FVA = A[(1 + i)n 1)] i= RM100[(1 + 0.1)3 -1] 0.1= RM331

OR = A(FVIFAi,n)= RM100 (FVIFA10%,3)= RM100(3.310)

= RM331


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Annuity : FV of Ordinary Annuity(Cont)

Example 3.9 : Danon Company depositedRM5,000 at the end of each year for 3 yearsconsecutively in an account that pays a yearly

interest rate of 10%. What is the FVA?FVA = A[(1 + i)n 1)] i= RM5,000[(1 + 0.1)3 -1] 0.1= RM16,550

OR = A(FVIFAi,n)= RM5,000 (FVIFA10%,3)= RM100(3.310)

= RM16,550


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Annuity : FV of Annuity Due

The payment of annuity occurs at thebeginning of the period.

For example, at the beginning of eachmonth or each year.

The formula for FV of Annuity Due is

= [A][(1 + i)n 1)][1 + i] iOR = A(FVIFAi,n)(1 + i)


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Annuity : FV of Annuity Due (Cont)

Example 3.10 : Danon Company deposited RM5,000 atthe beginning of each year for 3 years consecutively inan account that pays a yearly interest rate of 10%. What

is the FVA?FVA = [A][(1 + i)n 1)][1 + i] i

= RM5,000[(1 + 0.1)3 -1][1 + 0.1] 0.1

= RM18,205

OR = A(FVIFAi,n)(1 + i)= RM5,000 (FVIFA10%,3)(1 + 0.1)

= RM100(3.310)(1.10)

= RM18,205


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Annuity : PV of Ordinary Annuity

Present value of ordinary annuity can beobtained using the below formula

PVA = A{1 [1 (1 + i)n

]} IOR = A(PVIFAi.n)

Example 3.11 : Taming Company expects toreceive RM3,000 at the end of each year for 3

consecutive years. How in the present value forthe annuity if the discount rate is 6% per year.


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Annuity : PV of Ordinary Annuity(Cont)

PVA = A{1 [1 (1 + i)n]} I= RM3,000{1 [1 (1 + 0.06)3]} 0.06

= RM3,000[1 0.8396] 0.06= RM481.1422 0.06= RM8,019.04

OR = A(PVIFAi.n)= RM3,000 (PVIFA6%,3)= RM3,000 (2.673)= RM8,019.00


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Annuity : PV of Annuity Due

The formula for PV of Annuity Due is (PVA)

= A{1 [1 (1 + i)n]} i x (1 + i)

OR = A(PVIFAi.n)(1 + i) Example 3.12 : Taming Company expects to

receive RM3,000 at the beginning of each yearfor 3 consecutive years. How in the present

value for the annuity if the discount rate is 6%per year.


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Annuity : PV of Annuity Due (Cont)

PVA = A{1 [1 (1 + i)n]} i x (1 + i)= RM3,000{1 [1 (1 + 0.06)3]} 0.06 x 1.06

= RM3,000[1 0.8396] 0.06 x 1.06= RM481.1422 0.06 x 1.06= RM8,500.18

OR = A(PVIFAi.n) (1 + i)= RM3,000 (PVIVA6%,3) (1 + 0.06)= RM3,000 (2.673) (1.06)= RM8,500.14


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Non-Uniform Cash Flow

Involves a mixture of cash flow or cashfloe is irregular

The calculation for future value andpresent value of an irregular cash flow is acombination concept of determining

money value for single cash flow andannuity cash flow


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FV of Derivation Cash Flow

Involves the determination of FV foe each of thecash flow and subsequently totaling all the FV.

The formula is

FVn = Pt(1 + i)n-1

Example 3.13 : Bikin Fulus Company made adecision to deposit RM2,000 at the end of the 1st

and 2

nd

year, withdrawing RM3,000 at the endof the 3rd year and depositing RM4,000 at theend of 4th year. How much is this future valuecash flow at the end of the 4th year if the annualinterest rate is 10% per year?


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FV of Derivation Cash Flow (Cont)

FVn = Pt(1 + i)n-1

= (RM2,000)(1 + 0.1)4-1

+ (RM2,000)(1 + 0.1)4-2

- (RM3,000)(1 + 0.1)4-3

+ (RM4,000)(1 + 0.1)4-4

= RM5,782


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PV of Derivation Cash Flow

Involves the determination of PV foe each of thecash flow and subsequently totaling all the PV.

The formula is

PV0 = Pt[1 (1 + i)n]

Example 3.14 : Bikin Fulus Company expectsto receive RM1,000 at the end of 1st year and

2nd year, RM2,000 at the end of 3rd year andRM4,000 at the end of 4th year. How much is thepresent value cash flow if the yearly interest rateis 10% per year?


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PV of Derivation Cash Flow (Cont)

PV0= Pt[1 (1 + i)n]

= RM1,000[1 (1 + 0.1)1]

+ RM1,000[1 (1 + 0.1)2]

+ RM2,000[1 (1 + 0.1)3]

+ RM4,000[1 (1 + 0.1)4]

= RM5,970.22


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Perpetuity

Is the annuity that have infinity period

Cannot be used in decision making

because every investment have valuationperiod.

The formula is

PVp = P i


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Perpetuity (Cont)

Sukehati Company issued securities thatpromised a payment of RM100 per year atthe yearly interest rate of 8% to theholders of that security. How much thepresent value for that cash flow?

PVp = P i

= RM100 0.08= RM1,250


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Compounding and DiscountingMore Than Once A Year

Sometimes, the payment or receiving of returnoccurs more than once a year. For example,twice a year, quarterly and monthly.

For this, the period (n) must times with thenumber of payment or receiving (m) and theinterest rate (i) must be divided with the numberof payment or receiving (m) as shown below:

FV = PV x [1 + (i m)]nm

OR = PV [FVIF(im)(nm)]


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Compounding and DiscountingMore Than Once A Year (Cont)

Example 3.16 : The future value of RM1 nowfor 6 years, using the interest rate of 10% peryear with the different compounding frequencies

Compounding Nm i/m FVOnce a year 6 x 1 = 6 0.1 1 = 0.1 RM1(1 + 0.1)6 = RM1.772Twice a year 6 x 2 =

12 0.1 2 = 0.05 RM1(1 + 0.05)12 = RM1.796

Four times a

year 6 x 4 =24 0.1 4 = 0.025 RM1(1 + 0.025)24 = RM1.809

Every month 6 x 12 =72 0.1 12 =0.0083 RM1(1 + 0.0083)

72 =

RM1.817


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Compounding and DiscountingMore Than Once A Year (Cont)

Example 3.17 : The present value of RM1received in 6 years from now, discounting at theinterest rate of 10% per year with differentdiscounting frequencies

Discounting Nm i/m PVOnce a year 6 x 1 = 6 0.1 1 = 0.1 RM1 (1 + 0.1)6 = RM0.564Twice a year 6 x 2 = 12 0.1 2 = 0.05 RM1 (1 + 0.05)12 =

RM0.557Four times a

year 6 x 4 = 24 0.1 4 = 0.025 RM1 (1 + 0.025)24 =

RM0.553Every month 6 x 12 =

720.1 12 =

0.0083RM1 (1 + 0.0083)72 =

RM0.550


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Continuous Compounding andDiscounting

Some cases of the time value of money,interest must be compounded or

discounted continuously or at eachmicrosecond.

The formula is

FV = PV(ein)PV =FV (ein)


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Continuous Compounding andDiscounting (Cont)

Example 3.18 : What is the future valuefor RM100 that is invested now for 6 years

with an interest rate of 8% per year andcompounded continuously?

FV = PV(ein)

= RM100(e(0.08)(6))= RM161.61


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Continuous Compounding andDiscounting (Cont)

Example 3.19 : What is the presentvalue for RM161.61 that will received in 6

years from now with an interest rate of8% per year and discounted continuously?

PV =FV (ein)

= RM161,61 (e(0.08)(6))= RM100

financial management i_chapter 3

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