time value of money2

8/9/2019 Time Value of Money2

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Time Value of MoneyTime Value of Money18-03-201018-03-2010


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Fill in the blanksFill in the blanks

Money has ---------- value.Money has ---------- value. Future value relies on ----------- toFuture value relies on ----------- to

measure the value of the futuremeasure the value of the future

amounts.amounts.

The formula for compounding moreThe formula for compounding morethan once a year is --------------than once a year is --------------

Present value represents --------- ofPresent value represents --------- offuture value.future value.

-------------- is the process that links-------------- is the process that linksrisk and returns to determine therisk and returns to determine the

worth of an asset/security.worth of an asset/security.


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AnswersAnswers

Time valueTime value

Compound interestCompound interest

A = P(1+i/m)A = P(1+i/m)nmnm

An oppositeAn opposite

ValuationValuation


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Amortization of LoansAmortization of Loans

The determination of equal periodicThe determination of equal periodicloan payments necessary to provideloan payments necessary to provide

a lender with specified interest returna lender with specified interest return

and to repay the loan principal overand to repay the loan principal overa specified perioda specified period

Loan amortization schedule: ALoan amortization schedule: A

schedule of equal payments to repayschedule of equal payments to repaya loan. It shows the allocation ofa loan. It shows the allocation of

each loan payment to interest andeach loan payment to interest and

principalprincipal


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Answer the followingAnswer the following

Company A is establishing a sinking fundCompany A is establishing a sinking fundto retire a Rs. 5,00,000, 8 per centto retire a Rs. 5,00,000, 8 per centdebentures 10 years from today. Thedebentures 10 years from today. Thecompany plans to put a fixed amount intocompany plans to put a fixed amount into

the fund each year for 10 years. The firstthe fund each year for 10 years. The firstpayment will be made at the end of thepayment will be made at the end of thecurrent year. The company anticipatescurrent year. The company anticipates

that the funds will earn 6 per cent a year.that the funds will earn 6 per cent a year.What equal annual contributions must beWhat equal annual contributions must bemade to accumulate the required amountmade to accumulate the required amount, 10 years from now., 10 years from now.


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SolutionSolution

Annuity factor for 10 years at 6 perAnnuity factor for 10 years at 6 per

cent is 13.181cent is 13.181

Amount required Rs.5,00,000Amount required Rs.5,00,000

To get the amount to be paid intoTo get the amount to be paid into

the sinking fund:the sinking fund:

Amount required/ CVIFAAmount required/ CVIFA 5,00,000/13.1815,00,000/13.181

Rs. 37,933.39Rs. 37,933.39


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Company B wants to replace an asset fiveCompany B wants to replace an asset five

years from now whose value at that pointyears from now whose value at that point

of time would be Rs. 25,00,000. Theof time would be Rs. 25,00,000. The

company plans to establish a sinking fundcompany plans to establish a sinking fundto by putting a fixed amount into the fundto by putting a fixed amount into the fund

each year. The company anticipates theeach year. The company anticipates the

funds will earn 10 per cent a year. Whatfunds will earn 10 per cent a year. What

equal annual payments must be made toequal annual payments must be made tothe fund to accumulate the requiredthe fund to accumulate the required

amount, 5 years from now.amount, 5 years from now.


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SolutionSolution

Amount required: Rs. 25,00,000Amount required: Rs. 25,00,000

CVIFA:6.105CVIFA:6.105

The equal amount to be paid to theThe equal amount to be paid to thesinking fund to obtain the requiredsinking fund to obtain the required

amount : 25,00,000/6.105amount : 25,00,000/6.105

Rs.409500.4095Rs.409500.4095


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Practical Applications of Present Value andPractical Applications of Present Value and

Compounding Techniques - 2Compounding Techniques - 2

Determining the annual amount ofDetermining the annual amount of

annual installment of loan to beannual installment of loan to be

repaid to financial institutions orrepaid to financial institutions or

commercial bankscommercial banks


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A limited company borrows from aA limited company borrows from a

commercial bank Rs.10,00,000 at 12commercial bank Rs.10,00,000 at 12

per cent rate of interest to be paid inper cent rate of interest to be paid in

equal annual end-of-yearequal annual end-of-yearinstallments. What would be the sizeinstallments. What would be the size

of the installment be? Assume theof the installment be? Assume the

repayment period is 5 years.repayment period is 5 years.


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SolutionSolution

Amount Borrowed: Rs. 10,00,000Amount Borrowed: Rs. 10,00,000

Interest rate: 12Interest rate: 12

Years of payment: 5 yearsYears of payment: 5 years PVAF: 3.605PVAF: 3.605

Amount to be paid each year: Rs.Amount to be paid each year: Rs.

2,77,3932,77,393


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A firm borrows from a FinancialA firm borrows from a Financial

institution Rs.50,00,000 at 15 perinstitution Rs.50,00,000 at 15 per

cent rate of interest to be paid incent rate of interest to be paid in

equal annual end-of-yearequal annual end-of-yearinstallments. What would be the sizeinstallments. What would be the size

of the installment be? Assume theof the installment be? Assume the

repayment period is 15 years.repayment period is 15 years.


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SolutionSolution

Amount Borrowed: Rs. 50,00,000Amount Borrowed: Rs. 50,00,000

Interest rate: 15Interest rate: 15

Years of payment: 15 yearsYears of payment: 15 years PVAF: 5.847PVAF: 5.847

Amount to be paid each year: Rs.Amount to be paid each year: Rs.

855139.3877855139.3877


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Compounding Techniques - 3Compounding Techniques - 3

Investors can find the rate of growthInvestors can find the rate of growth

in dividend paid by a company over ain dividend paid by a company over a

period of time.period of time.

Why growth in dividends has aWhy growth in dividends has a

significant bearing on the price ofsignificant bearing on the price of

sharesshares


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SolutionSolution

Amount of dividend received in yearAmount of dividend received in year5: 8.355: 8.35

Amount of dividend received in yearAmount of dividend received in year

1: 5.51: 5.5 The CVIFA is arrived at by 8.35/ 5.5The CVIFA is arrived at by 8.35/ 5.5 i.e.(1.518)i.e.(1.518)

The interest rate that corresponds toThe interest rate that corresponds tofour years and the found CVIFA isfour years and the found CVIFA is11 per cent11 per cent


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Mrs. Y wants toMrs. Y wants to

determine the rate ofdetermine the rate of

growth of thegrowth of the

following streams offollowing streams of

dividend from adividend from acompanycompany

Year Dividend (per share)

1Rs 15.5

2Rs 18.85

3Rs 23.75

4Rs 27.45

5Rs 38.35

6Rs 49.75

7Rs 50.85

8Rs 62.00

9Rs 75.45

10Rs 80.00


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Compounding Techniques - 4Compounding Techniques - 4 To determine the current value ofTo determine the current value of

debenturesdebentures Cash flow from debentures consists ofCash flow from debentures consists of

two parts: Interest flow at periodictwo parts: Interest flow at periodic

intervals and the repayment of theintervals and the repayment of theprincipal on maturity.principal on maturity.

Calculate present value of the annuityCalculate present value of the annuitytype of interest inflowstype of interest inflows

Calculate the present value of the faceCalculate the present value of the facevalue of the debenture if redeemed atvalue of the debenture if redeemed atface valueface value

Add both the valuesAdd both the values


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A debenture pays interest at 8 perA debenture pays interest at 8 percent per annum. The debenture is tocent per annum. The debenture is tobe paid after ten years at a premiumbe paid after ten years at a premiumof 5 per cent. The face value of theof 5 per cent. The face value of thedebenture is Rs 1000. Interest isdebenture is Rs 1000. Interest ispaid after every six months. What ispaid after every six months. What isthe current worth of the debenturethe current worth of the debenture

assuming the appropriate marketassuming the appropriate marketdiscount rate on debentures ofdiscount rate on debentures ofsimilar risk and maturity is equal tosimilar risk and maturity is equal tothe debentures coupon rate i.e. 8the debentures coupon rate i.e. 8

per cent.per cent.


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SolutionSolution

Interest compounded semi-annually for tenInterest compounded semi-annually for tenyears, relevant compounding period is 20years, relevant compounding period is 20

and the discount rate will be one half of theand the discount rate will be one half of the

yearly interest of 8 per centyearly interest of 8 per cent PVIFA for 20 years and 4 per cent is 13.59PVIFA for 20 years and 4 per cent is 13.59

The annuity of interest flow will be Rs 40The annuity of interest flow will be Rs 40

Present value for the interest cash flows isPresent value for the interest cash flows is40*13.59 = Rs 543.6040*13.59 = Rs 543.60


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SolutionSolution

The debenture is redeemed at a premiumThe debenture is redeemed at a premiumof 5 per cent and hence the present valueof 5 per cent and hence the present value

to be calculated on Rs 1050to be calculated on Rs 1050

The period concerned is 20 years andThe period concerned is 20 years and

the applicable interest rate is 4 per centthe applicable interest rate is 4 per cent

Present value for 20 years at 4 percentPresent value for 20 years at 4 percent

for Re.1 is .456for Re.1 is .456

The present value of the debenture onThe present value of the debenture on

maturity is 1050*.456=478.8maturity is 1050*.456=478.8


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SolutionSolution

The total value of the debentureThe total value of the debenture

would be Rs 543.6+ Rs 478.8 = Rswould be Rs 543.6+ Rs 478.8 = Rs

1022.41022.4


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A debenture pays interest at 12 per cent perA debenture pays interest at 12 per cent per

annum. The debenture is to be paid after tenannum. The debenture is to be paid after ten

years at a premium of 10 per cent. The faceyears at a premium of 10 per cent. The face

value of the debenture is Rs 2000. Interest isvalue of the debenture is Rs 2000. Interest ispaid after every three months. What is thepaid after every three months. What is the

current worth of the debenture assuming thecurrent worth of the debenture assuming the

appropriate market discount rate onappropriate market discount rate on

debentures of similar risk and maturity isdebentures of similar risk and maturity isequal to the debentures coupon rate i.e. 12equal to the debentures coupon rate i.e. 12

per cent.per cent.


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SolutionSolution

Interest compounded quarterly for fifteenInterest compounded quarterly for fifteenyears, relevant compounding period isyears, relevant compounding period is10*4=40 and the discount rate will be one10*4=40 and the discount rate will be onefourth of the yearly interest of 12 per centfourth of the yearly interest of 12 per centi.e.3 per centi.e.3 per cent

PVIFA for 40 years and 3 per cent isPVIFA for 40 years and 3 per cent is23.11523.115

The annuity of interest flow will be Rs 60The annuity of interest flow will be Rs 60 Present value for the interest cash flows isPresent value for the interest cash flows is

60*23.115 = Rs 1386.960*23.115 = Rs 1386.9


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SolutionSolution

The debenture is redeemed at a premium ofThe debenture is redeemed at a premium of

10 per cent and hence the present value to10 per cent and hence the present value to

be calculated on Rs 2200be calculated on Rs 2200

The period concerned is 40 years and theThe period concerned is 40 years and theapplicable interest rate is 3 per centapplicable interest rate is 3 per cent

Present value for 40 years at 3 percent forPresent value for 40 years at 3 percent for

Re.1 is .307Re.1 is .307

The present value of the debenture onThe present value of the debenture onmaturity is 2200*.307=675.6maturity is 2200*.307=675.6


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SolutionSolution

Rs 675.6 + Rs 1386.9 = Rs 2062,5Rs 675.6 + Rs 1386.9 = Rs 2062,5

time value of money2

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