4561_Illustration Slides

8/7/2019 4561_Illustration Slides

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Interest Rate

&Time Value of Money


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Illustration - 1

Pritam has deposited Rs 20,000 with SBI for 4 years

The bank pays simple interest at the rate of 15% perannum

What is amount Pritam is going to receive at the end of

4th

year FV = P(1+rN)

FV = 20000 (1+0.15*4) = 20000 (1+.6) = Rs. 32,000

What is amount Pritam is going to receive at the end of4.5 years (every thing else remain the same)?

FV = 20000 (1+0.15*4.5) = 20000 (1+.675) = Rs. 33,500


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Illustration - 2

Pritam has deposited Rs 20,000 with SBI for 4 years The bank pays 15% per annum interest rate compounded annually

What is amount Pritam is going to receive at the end of 4th year

FV = P(1+r)N

FV = 20000 (1+0.15)4 = 20000 * 1.749 = Rs. 34,980

What is amount Pritam is going to receive at the end of 4.5 years(every thing else remain the same)?

FV = 20000 (1+0.15)4.5 = 20000 (1+.975) = Rs. 37,512

What amount Pritam is going to receive at the end of 4.5 years if hegets compounding rate till the 4th year and simple rate for the next 6months (every thing else remain the same)?

FV = 34980 + 34980 * (0.15/2) = 34980 + 2623.5 = Rs. 37,603


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Illustration - 3

ICICI Bank is quoting 9% per annumcompounded annually and HDFC Bank isquoting 8.75% per annum compoundedquarterly.

Where would you invest?

In the case of ICICI The nominal rate is 9% per annum

The effective rate is also 9% per annum

In the case of HDFC The nominal rate is 8.75% per annum

The effective rate is (1+0.0875/4)4 = 9.0413% perannum


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Illustration - 4

Suppose HDC Bank wants to offer an effective annual

rate of 10% with quarterly compounding

What should be the quoted nominal rate

ICICI Bank is offering 9% per annum with semi-annual

compounding.

What should be the equivalent rate offered by HDFC

Bank if it intends to compound quarterly.


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Illustration - 6

Pritam has deposited Rs 10,000 for 5 years at 10% compoundedannually.

What is the Future Value?

Thus F.V. = 10,000 x 1.6105 = Rs 16,105

Pritam has deposited Rs 10,000 for 4 years at 10% per annum

compounded semi-annually.

What is the Future Value? 10% for 4 years is equivalent to 5% for 8 half-years

Thus F.V. = 10,000 x 1.4775 = Rs 14,775


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Illustration - 7

LIC has collected a one time premium of Rs 10,000 fromPritam and has promised to pay her Rs 30,000 after 10years.

The company is in a position to invest the premium at 10%compounded annually.

Can LIC meet its obligation? The future value of Rs 10,000 after 10 years is

FV = 10,000 x FVIF (10,10) = 10000 * (1.1)10 = 10000 *2.5937 = Rs 25,937

The FV is lesser than the liability of Rs 30,000

Therefore LIC can not meet its commitment, and to meetits commitment it has to either increase the premium orincrease the effective rate of return


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Illustration -8 Syndicate Bank is offering the following scheme

An investor has to deposit Rs 10,000 for 10 years

Interest for the first 5 years is 10% compounded annually

Interest for the next 5 years is 12% compounded annually

What is the Future Value?

The first step is to calculate the future value after 5

years:

The next step is to treat this as the principal and

compute its terminal value after another 5 years


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Illustration - 9

Pritam would like to have Rs. 12000 after 4 years

What amount Pritam need to invest if he gets a

10% simple rate of return

PV = FV / (1+rN) = 12000 / [1+0.1*4] = Rs. 8571

What amount Pritam need to invest if he gets a

10% return compounded quarterly

PV = FV / (1+r)N = 12000 / (1+0.1/4)16 = Rs.

8084


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SBI is offering an instrument that will payRs 10,000 after 5 years.

The price that is quoted is Rs 5,000.

If the investor wants a 10% rate of return,should he invest.

The problem can be approached in three

ways.

Illustration 10: Evaluating an Investment


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The Future Value Approach

Assume that the instrument is bought for5,000.

If the rate of return is 10% the future valueis 5,000 x FVIF (10,5) = 5000 * 1.6105 =Rs 8,052.50

Since the instrument promises a terminalvalue of Rs 10,000 which is greater thanthe required future value, the investment isattractive.



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The Present Value Approach

The present value of Rs 10,000 using a discountrate of 10% is;

10,000 * PVIF(10,5) = 10000 * 0.6209 = Rs 6,209 Therefore to get a 10% return over 5 years the

investor would have to pay Rs 6,209

In this case the investment is Rs 5,000 which is

less than Rs 6,209 The investment is attractive



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The rate of return is the solution to the following

equation:

Illustration - 11: The Internal Rate of Return

The solution to this equation is called the

Internal Rate of Return (IRR)

It can be obtained using the IRR function inEXCEL.

In this case, the solution is 14.5189%


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Annuities


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Illustration - 12

LIC is offering an instrument that will pay Rs 10,000 per year fornext 20 years, beginning one year from now.

If the rate of interest is 10%, what is the present value?

PV = 10,000xPVIFA(10,20) = 10,000 x 8.5136 = Rs 85,136

If the rate of interest is 10%, and payment is for 25 years what is thepresent value?

PV = 10,000xPVIFA(10,25) = 10,000 x 9.0770 = Rs 90,770


PV = 10,000xPVIFA(8,20) = 10,000 x 9.8181 = Rs 98,181

If the rate of interest is 8%, and payment is for 25 years what is thepresent value?

PV = 10,000xPVIFA(8,25) = 10,000 x 10.6748 = Rs 106,748

The Present Value of Annuity would Decrease if the Interest Rate

Goes Up and Increases with the # of Years of Payment


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Illustration - 13

Pritam is expecting to receive Rs 10,000 per year for next 20 years,beginning one year from now.

If the cash flow can be invested at 10%, what is the future value?

FV = 10,000xFVIFA(10,20) = 10,000 x 57.275 = Rs 572,750

If the rate of interest is 10%, and Pritam is going to receive thepayment for 25 years, what is the future value?

FV = 10,000xFVIFA(10,25) = 10,000 x 98.3471 = Rs 983,471

If the rate of interest is 8%, what is the future value?

FV = 10,000xFVIFA(8,20) = 10,000 x 45.7620 = Rs 457,620

If the rate of interest is 8%, and Pritam is going to receive thepayment for 25 years, what is the future value?

PV = 10,000xPVIFA(8,25) = 10,000 x 73.1059 = Rs 731,059

The Future Value of Annuity would Increase if the Interest Rate

Goes Up and Increases with the # of Years of Payment


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Illustration - 14

Pritam bought a insurance policy, which requires him to pay Rs.10,000 per year as insurance premium for next 20 years.


PV = 10,000xPVIFAAD(10,20) = 10,000 x 9.3649 = Rs 93,649

Which is equal to Rs. 85,136 * (1+r) = Rs. 93,649

Pritam bought a insurance policy, which requires him to pay Rs.10,000 per year as insurance premium for next 20 years.

If Pritam would have invested the amount he would have got 10% perannum, what is the future value of the cash he invested in theinsurance policy?

FV = 10,000xFVIFAAD(10,20) = 10,000 x 63.0025 = Rs 630,025 Which is equal to Rs. 572,750 * (1+r) = Rs. 630,025


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Illustration - 15

A financial instrument promises to pay Rs 10,000 per year forever. If the investor requires a 10% rate of return, how much should he be

willing to pay for it?

The value of the perpetuity is: 10,000 / 0.1 = 100,000

If the investor requires a 20% rate of return, how much should he be

willing to pay for it?


If the payment from the instrument increases to Rs.12,000 and

investor requires a 10% rate of return, how much should he be willing

to pay for it?


The Value of the Perpetuity would Decrease if the Required Rate of

Return Increases and Value would Increase if the Payment Increases


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Amortization


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Illustration - 16

Pritam has borrowed Rs 10,000 from SBI andhas to pay it back in five equal annualinstallments.

The interest rate is 10% per annum on theoutstanding balance.

What is the installment amount?


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Illustration 16: Amortization Schedule

At time 0, the outstanding principal is 10,000

After one period an installment of Rs 2,637.97 is made.

The interest due for the first period is 10% of 10,000 or Rs 1,000

So the excess payment of Rs 1,637.97 is a partial repayment of principal.

After the payment the outstanding principal is Rs 8,362.03

After another period a second installment is paid.

The interest for this period is 10% of 8,362.03 which is Rs 836.20. The balance of Rs 1,801.77 constitutes a partial repayment of principal.

The value of the outstanding balance at the end should be zero.

After each payment the outstanding principal keeps declining.

Since the installment is constant

The interest component steadily declines

While the principal component steadily increases


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Amortization with a Balloon Payment

Pritam has taken a loan of Rs 100,000 from SBI. She has to pay in 5 equal annual installments along with a terminal

payment of Rs 25,000

The terminal payment which has to be made over and above thescheduled installment in year 5 Is called a BALLOON payment.

If the interest rate is 10% per annum, the annualinstallment may be calculated as


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Amortization Schedule


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Types of Interest Computation Financial institutions employ a variety of different techniques to calculate the interest on the loans

made by them. The interest that is effectively paid on the loan may be very different from the rate that

is quoted. Thus what you see is not what you get.The Simple Interest Method

In this technique, interest is charged for only the period of time that a borrower has actually used the

funds.

Each time principal is partly repaid, the interest due will decrease.

The Add-on Rate Approach

In this case interest is first calculated on the full principal.

The sum of interest plus principal is then divided by the total number of payments in order todetermine the amount of each payment.

In Alfreds case if he repays in one annual installment, there will be no difference with this approach

as compared to the simple interest approach.

The Discount Method Approach

In this approach the total interest is first computed on the entire loan amount.

This is then deducted from the loan amount.

The balance is lent to the borrower.

The Compensating Balance Approach

Many banks require that borrowers keep a certain percentage of the loan amount with them as a

deposit.

This is called a Compensating Balance.

It raises the effective interest rate

Since the borrower cannot use the entire amount that is sanctioned


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Illustration 17: Simple Interest Method Pritam has borrowed 5,000 from the bank for a year.

The bank charges simple interest at the rate of 8% per annum.

If the loan is repaid at the end of one year:

Interest payable = 5000x0.08 = 400

Total amount repayable = 5,400

Assume the loan is repaid in two equal semi-annual installments. After six months principal of 2,500 is repaid.

Interest will however be charged on 5,000.

Amount repayable = 2500 + 5000x0.08x.5 = 2700

For the next six months interest will be charged only on 2,500.

The amount payable at the end of the second six-monthly period= 2500 + 2500x0.08x.5 = 2,600

Total outflow on account of principal plus interest = 2700 + 2600 = 5300

Obviously the more frequently the principal is repaid the lower is theinterest.


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What if he repays in two installments?

Interest for the entire year = 400 This will be added to the principal and divided by 2.

Thus each installment = (5000 + 400) / 2 = 2700

The quoted rate is 8% per annum.

But the actual rate will be higher.

The actual rate is given by

The solution is i = 10.5758%

Illustration 18: Add-on Rate Approach


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Illustration 19: The Discount Method

Approach Prtam borrows 5000 at 8% for a year.

The interest for the year is 400.

So Pritam will be given 4600 and will have torepay 5000 at the end.

The effective rate of interest

= [(5000 4600) / 4600 ] * 100 = 8.6957%


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Illustration 20: The Compensating Balance

Approach

Pritam is sanctioned 5,000 at the rate of 8%.

But he has to keep 10% of the loan amount with thebank for the duration of the loan.

So while he pays an interest of 400, the usable amountis only 5000x0.9 = 4500

The effective interest cost is [400 / 4500] * 100 =8.8889%

Quite obviously The higher the compensating balance, the greater will

be the effective interest rate.


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Risk-Return


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Illustration - 21

A company has 2MM shares outstanding The stock price is Rs.40

The debt is quoted at 90% of face value and the face value of debt is10 MM

The YTM for the debt is 10%

The risk-free rate is 5%

The market risk premium is 10% and the beta is .75 The tax rate is 30%

RE = 5 + .75 x 10 = 12.5% and RD = 10%

The value of equity is 2 x 40 = 40MM

Value of debt is 0.90 x 10 = 9MM

Total value V = 49MM WACC = 40/49 x 12.5 + 9/49 * 10 x (1-0.3) = 11.49%

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