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The annuity payment in the first year is equal to the real annuity payment. Calculate the annuity payment for the second year and for the third year. Suppose that you have Rs. If the inflation rate is 5 per cent, calculate the real annuity.

Calculate the actual annuity payments for each of the four years. Show that the annuity works. That is, for each year, fill out a table with the beginning balance, interest earned, annuity paid, and ending balance. Show that after four years the ending balance is exactly zero. Do the same calculations as in the problem The formula for finding the monthly payment on a mortgage or an auto loan is the same as the formula for an annuity. However, the interest rate is the annual interest rate divided by 12, and the number of periods, n, is the number of years times Find the monthly payment on a thirty year mortgage with a Rs.

Find the monthly payment on a five year auto loan with a Rs. When a specified amount of money is needed at a specified future date, it is a good practice to accumulate systematically a fund by means of equal periodic deposits.

Such a fund is called a sinking fund. Sinking funds are used to pay-off debts, to redeem bond issues, to replace worn-out equipment, to download new equipment, or in one of the depreciation methods.

Since the amount needed in the sinking fund, the time the amount is needed and the interest rate that the fund earns are known, we have an annuity problem in which the size of the payment, the sinking-fund deposit, is to be determined. A schedule www. Illustration 1. If you wish an annuity to grow to Rs. An annuity consists of monthly repayments of Rs.

How much money will a student owe at graduation if she borrows Rs. A construction company plans to download a new earthmover for Rs. Determine the annual savings required to download the earthmover if the return on investment is 12 per cent.

A common method of paying off long-term loans is to pay the interest on the loan at the end of each interest period and create a sinking fund to accumulate the principal at the end of the term of the loan. Usually, the deposits into the sinking fund are made at the same times as the interest payments on the debt are made to the lender. The sum of the interest payment and the sinking-fund payment, is called the periodic expense or cost of the debt.

It should be noted that the sinking fund remains under the control of the borrower. At the end of the term of the loan, the borrower returns the whole principal as a lumpsum payment by transferring the accumulated value of the sinking fund to the lender.

When the sinking-fund method is used, we detain the book value of the borrower's debt at any time as the original principal, minus the amount in the sinking fund. The book value of the debt, may be considered as the outstanding balance of the loan.

Illustration In 10 years, a Rs. A new machine at that time is expected to sell for Rs. In order to provide funds for the difference between the replacement cost and the salvage value, a sinking fund is set up into which equal payments are placed at the end of each year. If the fund earns 7 per cent compounded annually, how much should each payment be? Simple Interest: When money is lent, the borrower usually pays a fee to the lender. This fee is called 'interest' 'simple' interest or 'flat rate' interest.

The amount of simple interest paid each year is a fixed percentage of the amount borrowed or lent at the start. Compound Interest: When interest is added to the account against returning it immediately to the customer, the interest itself earns interest during the next time period for computing interest. This is compounding of interest or more simply stated compound interest.

Compounding Period: The time interval, between the moment at which interest is added to the account is called compounding period. The rule allows us to determine the number of years it takes your money to double whether in debt or investment. Here is how to do it. Divide the number 72 by percentage rate you are paying on your debt or earning on your investment Annuities: They are essentially a series of fixed payments required from you or paid to you at a specified frequency over the course of a fixed period of time.

Sinking Fund: When there is a need for a specified amount of money at a specified future date, it is a good practice to accumulate systematically a fund by means of equal periodic deposits.

Sinking funds are used to pay-off debts, to redeem bond issues, to replace worn- out equipment, to download new equipment, or in one of the depreciation methods. Part A 1. A person invests Rs. A man saves every year Rs. Calculate the total amount of his savings at the end of the third year.

The simple interest on a certain sum for 3 years is Rs. Find the rate of interest and the principal. A sum of money is lent out at compound interest for two years at 20 per cent p. If the same sum of money is lent out at a compound interest at the same rate per cent per annum, C. Calculate the sum of money lent out. A man borrowed a certain sum of money and paid it back in 2 years in two equal instalments.

If the rate of compound interest was 4 per cent per annum and if he paid back Rs. A sum of Rs. Find the annual payment. A loan of Rs. The interest is compounded annually at 10 per cent.

Find the value of each instalment. A man borrows Rs. He repays Rs. Calculate the amount outstanding at the end of the third payment. Give your answer to the nearest Re. Find the amount which he has to pay at the end of the fourth year.

Divide Rs. The rate of compound interest is 5 per cent per annum. Two partners A and B together invest Rs. After 3 years, A gets the same amount as B gets after 5 years. Find their shares in the sum of Rs.

A debtor may discharge a debt by paying a Rs. If money is worth 5 per cent compounded semi-annually to him, which alternative should he accept? At the birth of a daughter, a father wishes to invest sufficient amount to accumulate at 12 per cent compounded semi-annually to Rs. How much should he invest?

In downloading a house, X pays Rs. At 6 per cent compounded semi-annually, find the cash value of the home. The cost of a refrigerator is Rs.

If it depreciates at 10 per cent per annum, find its value 3 years hence. The present value of a machine is Rs. If its value depreciates 6 per cent in the first year, 5 per cent in the second and 4 per cent in the third year, what will be its value after. If rate of interest is 15 per cent compounded annually, what is the present worth of the mobike? If the rate of depreciation is 10 per cent, what will be the resale value after 7 years?

A person downloads a land at Rs. Assuming that land appreciates at 20 per cent annually and building depreciates at 20 per cent for first 2 years and at 10 per cent thereafter, find the total value of property after 5 years from date of download of land. The rate of interest charged is 20 per cent annually. Find the amount of each instalment. The population of a town increased from 2 lakh to 8 lakh in last 10 years. If the same trend continues, in how many years will it become 1.

Find the nominal rate compounded monthly equivalent to 6 per cent compounded semi-annually. Also find the effective rate of interest. The machinery of a certain factory is valued at Rs. If it is supposed to depreciate each year at 8 per cent of the value at the beginning of the year, calculate the value of the machine at the end of and If Mr. X takes a housing loan of Rs. Find out EMI if loan is Rs. Answers 1. He should accept b A couple is saving a down payment for a home.

They want to have Rs. How much must be deposited in the fund at the end of each year? Make out a schedule showing the growth of the fund. A company wants to save Rs. Make out schedule for this problem. What quarterly deposit is required in a bank account to accumulate Rs. Prepare a schedule for this problem.

What quarterly deposits for the next 5 years will cause the fund to grow to Rs. How much is in the fund at the end of 3 years? A cottagers' association decides to set up a sinking fund to save money to have their cottage road widened and paved. What annual deposit is required per cottager if there are 30 cottages on the road? Show the complete schedule. Find the quarterly deposits necessary to accumulate Rs. Find the amount in the fund at the end of 9 years and complete the rest of the schedule.

A city needs to have Rs. Make out the rest three and last three lines of the schedule. What monthly deposit is required to accumulate Rs. A couple wants to save Rs. They can save Rs. How many years to the nearest quarter will it take them, and what is the size of the final deposit?

In its manufacturing process, a company uses a machine that costs Rs. The company sets up a sinking fund to finance the replacement of the machine, assuming no change in price, with level payments at the end of each year.

Find the value of the sinking fund at the end of the 1 Oth year. PartC 1. A homeowners' association decided to set up a sinking fund to accumulate Rs. What monthly deposits are required if the fund earns 5 per cent compounded daily? Show the first three and the last two lines of the sinking-fund schedule.

Consider an amount that is to be accumulated with equal deposits R at the end of each interest period for 5 periods at rate i per period. Hence, the amount to be accumulated is Rs. Do a complete schedule for this sinking fund. Verify that the sum-of-the-interest column plus the sum- of-the-deposit column equals the sum of the increase-in-the-fund column, and both sums equal the final amount in the fund. If the fund contains Rs. PartD 1. A borrower of Rs. How much is in the sinking fund at the end of 4 years?

A city borrows Rs. What is the total annual expense of the debt? A company issues Rs. Find a the semi-annual expense of the debt; b the book value of the company's indebtedness at the end of the fifteenth year.

Find a the semi-annual expense of the debt; b the book value of the city's indebtedness at the beginning of the sixteenth year. On a debt of Rs. Recommendations on Capital Charge 2. To provide a bird's-eye view on background of Basel II accord recommendations of Basel II accord its influence on Indian banking scenario.

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The interdependence of the world's major banking systems and the lack of formal machinery for co- ordinating the national regulatory arrangements were brought into sharp focus by the Herstatt crisis of The distinctive feature of the Herstatt failure was the way it disrupted the clearing mechanism for spot foreign exchange transactions, which in turn, had damaging effects on the international interbank market.

There were widespread losses affecting several West German banks as well as Italian and Japanese banks whose own national authorities at that time were poorly placed to provide emergency dollar support. Consequently, in , a standing committee of Bank Supervisors, 'Committee on Banking Regulation and Supervisory Practices' now known as Basel Committee on Banking Supervision , was set up under the auspices of the Bank for International Settlements, Basel 'not to harmonise national laws and practices but rather to interlink disparate regulatory regimes with a view to ensuring that all banks are supervised according to certain broad principles', Cooke The third world debt crisis of the early s also exposed the fragility of the international banking system and the urgency of preventing capital erosion and strengthening banks' balance sheets.

Against this background, the initiative for global regulation and supervision was taken by regulators of two Central Banks: The G supervisors joined in, resulting in the historic Basel Capital Accord agreement of July , viz. Basel I was originally designed to apply only to internationally active banks in the G countries. It was, however, increasingly adopted as a standard for banks across the development spectrum because of its focus on the level of capital in the major banking systems and a 'level playing field'.

The Basel committee on banking supervision had come out with a new consultative paper on 'New Capital Adequacy Framework' in June, After much discussion, revisions and comments, the new framework called the international Convergence of Capital Measures and Capital Standards: It came into effect by end By end, the most advanced approaches to risk measurement were to become effective.

The new standards are mandatory for Internationally active banks. The ability of a bank to absorb unexpected shocks and losses rests on its capital base. Basel II norms are centred on sustained economic development over the long haul and include.

The new proposal is based on three mutually reinforcing pillars that allow banks and supervisors to evaluate properly the various risks that banks face and realign the regulatory capital more closely with the underlying risks. Each of these three pillars has risk mitigation as its central plank. The new risk sensitive approach seeks to strengthen the safety and soundness of the industry by focusing on: Risk-based capital Pillar 1 - assessment of minimum capital requirement for banks Risk-based supervision Pillar 2 - supervision to review bank's capital adequacy and internal assessment process Risk disclosure to enforce market discipline Pillar 3 - use of market discipline for greater transparency and disclosure and encouraging best international practices.

Basel II Framework. The new framework maintains the minimum capital requirement of 8 per cent of risk assets. In this, the calculation is based on credit, market and operational risk. It sets the minimum ratio of capital to risk weighted assets and in doing so, maintains the current definition of capital.

What is Capital Adequacy? Basel II focuses on improvement in measurement of risks.

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The revised credit risk measurement methods are more elaborate than the current accord. It proposes, for the first time, a measure for operational risk, while the market risk measure remains unchanged. Influence of level ofNPAs - High non-performing assets exacerbate the pressure on bank's capital by reducing the ratio of capital to risk-weighted assets the absolute value of capital and leaking revenue availability of less free capital.

The Second Pillar - Supervisory Review Process Supervisory review process has been introduced to ensure, not only that banks have adequate capital to. Thus, it deals with 'Operational control and compliance with Pillar 1 Requirements'.

The process has four key principles: The Third Pillar - Market Discipline Market discipline imposes strong incentives to banks to conduct their business in a safe, sound and effective manner. It is proposed to be effected through a series of disclosure requirements on the capital, risk exposure, etc. These disclosures should be made at least semi-annually and more frequently if appropriate. Qualitative disclosures such as risk management objectives and policies, definitions, etc.

The requirements under this pillar are common to all regulated firms. Credit Risks The first pillar of the accord sets forth the minimum capital requirements.

To ensure that risks e. Credit Loss within the entire banking group are considered, improvements in the measurement of credit risks have been made in Basel II.

For the measurement of credit risk, Basel II proposes three principle options: Standardised approach, or Internal rating-based approach IRB. The IRB method proposes two approaches: Securitisation frame work.

Alternative methods for computing capital requirement for credit risk are depicted below. Operational Risks Operational risks are, e. Three approaches have been proposed for the measurement of operational risks: Approaches for measurement of operational risk. Operational Risk. Market Risks RBI has issued detailed guidelines for computation of capital charge on market risk in June The guidelines address the issues involved in computing capital charge for interest rate related instruments in the trading book, equities in the trading book and foreign exchange risk including gold and precious metals in both trading and banking books.

Trading book includes: Securities included under the 'Held for Trading' category Securities included under the 'Available for Sale' category 'Open Gold' position limits 'Open Foreign Exchange' position limits Trading position in derivatives and derivatives entered into for hedging trading book exposures.

As per the guidelines, the minimum capital requirement is expressed in terms of two separately calculated charges: Specific risk, and b. General market risk Specific Risk: Capital charge for specific risk is designed to protect against an adverse movement in price of an individual security due to factors related to the individual issuer.

This is similar to credit risk. The specific risk charges are divided into various categories such as investments in Govt securities, claims on banks, investments in mortgage backed securities, securitised papers, etc. General Market Risk: Capital charge for general market risk is designed to capture the risk of loss arising from changes in market interest rates.

The Basel committee suggested two broad methodologies for computation of capital charge for market risk, i. As banks in India are still in a nascent stage of developing internal risk management models, in the guidelines, it is proposed that to start with, the banks may adopt the 'Standardised Method'. Again, under Standardised Method, there are two principle methods for measuring market risk - maturity method and duration method.

As the duration method is a more accurate method of measuring interest rate risk, RBI prefers that banks measure all of their general market risk by calculating the price sensitivity modified duration of each position separately. For this purpose, detailed mechanics to be followed, time bands, assumed changes in yield, etc. Methods of calculating General Market Risks. A unique feature of the Indian financial system is the diversity of its composition.

We have the dominance of Government ownership coupled with significant private shareholding in the public sector banks, which in turn, continue to have a dominant share in the total banking system.

We also have cooperative banks in large numbers, which also pose a challenge because of the multiplicity of regulatory and supervisory authorities. There are also the Regional Rural Banks with links to their parent commercial banks.

Foreign bank branches operate profitably in India and, by and large, the regulatory standards for all these banks are uniform. The process of providing financial services is changing rapidly from traditional banking to a one-stop shop of varied financial services, as the old institutional demarcations are getting increasingly blurred.

Approach to Prudential Norms The Reserve Bank's approach to the institution of prudential norms has been one of gradual convergence with international standards and best practices, with suitable country-specific adaptations. The aim has been to reach global best standards in a deliberately phased manner, through a consultative process evolved within the country.

This has also been the guiding principle in the approach to the new Basel Accord, e. On the other hand, banks in India are still in the process of implementing capital charge for market risk, prescribed in the Basel document as Basel norms take into account only the trading portfolio. Ensuring that the banks have a suitable risk management framework, oriented towards their requirements; dictated by the size and complexity of business, risk philosophy, market perceptions and the expected level of capital.

The framework adopted by banks would need to be adaptable to changes in the business, size, market dynamics and to introduction of innovative products by banks in future. Encouraging banks to formalise their 'Capital Adequacy Assessment Programme' CAAP , in alignment with the business plan and performance budgeting system. This, together with adoption of risk-based supervision, would aid in factoring the Pillar II requirements under Basel II. Enhancing the area of disclosures Pillar III , so as to have greater transparency of the financial position and risk profile of banks.

Improving the level of corporate governance standards in banks. Following table provides an insight into the existing provisioning requirements and capital adequacy norms, and the changes proposed thereto by RBI in the light of Basel II Accord. Banks are required to follow strict With the prospect of greater inflows a RBI should require banks to prudential norms with regard to under a fuller CAC regime, it may make provisions for their non-fund identification of the NPAs and be necessary for tightening the based commitments in the NPA making provisions thereof.

These provisioning requirements, to accounts with reference to the are largely in alignment with the enhance the shock absorbing credit equivalent amounts. RBI international best practices. The non-fund based exposures to entities, whose fund based exposures are classified as NPAs do not attract a provisioning requirement as per the present RBI regulations.

In terms of AS Provisions, contingent liabilities and contingent assets; banks will be required to subject their contingent liabilities to an impairment test and if there is a likelihood of the bank incurring a.

As a result, this system, such that if an exposure to gives rise to the scope for a a counter party becomes NPA in borrower to keep the non- any bank, all banks having an performing portion of his exposure to that counter party exposures in one particular bank should classify the exposure as and keep the other exposures as NPA.

The provisioning requirements on substandard assets may be increased to 20 per cent for secured advances and 30 per cent for unsecured advances. The age of delinquency may also be reviewed to ensure that all working capital exposures beyond a delinquency of 36 months are fully provided.

The proposed schedule for provisioning should be as under: Category Category Age of delinquency Age of delinquency Provi- Provisioning per cent sioning per cent Substandard Secured Portion 90 days to 15 months.

Unsecured Portion Secured advances 10 per cent of Substandard total outstanding.

The working capital exposures in the NPA accounts will attract a per cent provisioning requirement on both the secured and unsecured portions, when the delinquency exceeds 36 months. Capital Adequacy before 31 st March Banks in India are at present Migration to a fuller CAC is likely a It will not be adequate to have adopting the capital adequacy to throw up numerous challenges a uniform 9 per cent norm for all framework as required under the to the banks' risk management banks.

The system should move Basel I. Banks are maintaining systems. The 'complex' banks as market risk exposures. The minimum approaches would be defined in Paragraph 7. The capital all other banks may be moved over norm prescribed by the Basel adequacy framework, even under to this regime over the next 5. Committee on Banking Basel II, will need strengthening years. This may be dovetailed to the Reserve Bank has advised banks in Pillar II requirement under the India to implement the revised Basel II, which requires banks to capital adequacy framework have in place an internal capital popularly known as Basel II with adequacy assessment process effect from 31st March, Banks will be maintaining capital c Consider the introduction of a for operational risks under the higher core capital ratio than the Basel II in addition to the credit default 50 per cent of total capital risks and market risks.

The Indian funds at present. It may be raised banking system will be adopting to at least 66 per cent. Further, almost 90 per cent basic indicator approach for of banks' credit portfolio is operational risk.

On a quick broad unrated. The risk- weight structure assessment, it is expected that the under the Basel II provides a impact of Basel II on banks' perverse incentive for high risk CRAR will be adverse to the borrowers to remain unrated.

In view of this and since the system may not be able to rank risk objectively, the risk weighting system should be economic risk undertaken by the banks. Hence, unrated or high-risk sectors should be subject to a per cent or higher risk weights.

Considering the fact that retail exposures include a much wider weaker segment, the risks to which the banks are actually exposed to under retail exposures is not low. Hence, the risk weight for this sector should also be appropriately increased. They should be required to set off losses against capital funds, including certain capital instruments other than equity shares, on an on-going basis.

RBI should decide on the methodology for setting off the losses against capital funds. Pillars of Basel II Framework Three mutually reinforcing pillars, that allow the banks and supervisors to evaluate properly the various risks that the banks face and realign the regulatory capital more closely with the underlying risks, are the three Pillars of the Basel II framework.

Capital Adequacy It is the cushion against the unexpected losses and refers to the minimum capital requirement expressed in terms of percentage of the risk assets. Credit Risk Risk associated with the lending of loans. Operational Risk Risk associated with unexpected disasters and events. Market Risk Risk associated with interest and other returns. What are the three pillars of Basel II framework? How is the capital adequacy measured? Explain the types of risks and name the methods prescribed for measuring them.

The objectives of this unit are to understand: DEBT means a sum of money due by certain and expresses agreement. In a less technical sense, it means a claim for money. In a still more enlarged sense, it denotes any kind of a just demand; such as the debts of a bankrupt. Debts arise or are proved by matter of record, as judgment debts; by bonds or specialities; and by simple contracts, where the quantity is fixed and specific, and does not depend upon any future valuation to settle it.

Debts are also divided into active and passive. The former means, what is due to us, the latter, what we owe. By a liquid debt, we understand, one, the payment of which may be immediately enforced, and not one, which is due at a future date, or is subject to a condition; hypothecation debt means, one which has a lien over an estate, and a doubtful debt is one the payment of which is uncertain. Debts are discharged in various ways, but principally by payment. In the payment of debts, some are to be paid before others.

In cases of insolvent estates; firstly, in consequence of the character of the creditor; e. Loans from banks or financial institutions are one of the popular forms of debt.

Loans are granted by the banks or institutions based on the records and documentary evidences and, of course, with security. The mode and time of repayment are clearly expressed in the documents. When the debtor fails to meet the conditions of repayment as per the contract of loan, the lender gets the right to charge penal interest for defaulted payments, compound the loan and to realise the loan through the liquidation of securities. In India, the grant of loans, charge of interest, penal interest, compounding, etc.

Debt capital consists of mainly bonds and debentures. The holder of debt capital does not receive a share of ownership of the company when they provide funds to the firm. Rather, when a company first issues debt capital, the providers of debt capital download a debenture, which involves lending money. In return for loaning this money, bondholders have a right to certain guaranteed payments. For an illustration; a company issued a bond of a face value of Rs.

This entitles the bondholder to receive Rs. At the end of tenth year, the bondholder is also entitled to receive back the invested amount of Rs. Irrespective of the level of profits or losses, which company makes during that period of ten years, the bondholder is entitled to receive the coupon interest during that period. If the company fails to pay the coupon interest or the redemption value, at the end of term, the bondholder can force the company into bankruptcy as per the procedure of law.

Thus, from the viewpoint of the provider of the debt capital, debt capital is less risky and therefore, earns a lower rate of return in comparison to other forms of capital. In addition to the fact that debt is cheaper than equity capital because there is less risk, it has a further advantage over equity capital from the point of view of the firm.

This advantage relates to the differential tax treatment of interest payments on debt and dividend payments on equity. The interest payments on debt are said to be tax-deductible, which means that the interest payments are deducted from total income to arrive at the taxable income of the company. In contrast, dividend payments are not tax-deductible. Thus, two companies with identical operating incomes, but which differ in terms of their level of debt, will have different taxable incomes and therefore, different After Tax Income computation.

This tax deducibility of debt payments means that the debt capital provides a 'tax-shield' which is not provided by the equity capital and, thus, further lowers the after-tax cost of debt from the point of view of the firm.

With the dividends now being taxed on the companies, equity has become even more expensive. The fact that debt capital has a lower cost than equity capital, has raised the question of whether a firm can lower its overall cost of capital and hence, its discount rate for investment appraisal purposes, by changing the mix of debt and equity which it uses. The mix of debt and equity is known as the capital structure of the firm. Bonds are negotiable promissory notes that can be used by individuals, business firms, governments or government agencies.

Bonds issued by the government or the public sector companies are generally secured. Private sector companies can issue secured or unsecured bonds. In case of a bond, the rate of interest is fixed and is known to the investors. A bond is redeemable after a specific period. The expected cash flows consist of annual interest payments plus repayment of principal. Following are the general terms associated with a bond: Face Value: Also known as the par value and stated on the face of the bond.

It represents the amount borrowed by the firm, which it promises to repay after a specified period. Coupon rate: A bond carries a specific rate of interest, which is also called as the coupon rate. A bond is issued for a specified period.

It is to be repaid on maturity. Redemption Value: The value, which the bondholder gets on maturity, is called the redemption value. A bond is generally issued at a discount less than par value and redeemed at par.

Market Value: A bond may be traded on a stock exchange. Market value is the price at which the bond is usually bought or sold in the market. Market value may be different from the par value or the redemption value.

Therefore, the value of any security can be defined as the present value of these future cash. It is quite clear that the holder of a bond receives a fixed annual interest payment for a certain value equal to par value at the time of maturity. The required rate of return on the bond is 10 per cent. What is the value of this bond?

If the bond carries a semi-annual interest, as the amount of the half-yearly interest can be reinvested, the value of such bonds would be more than the value of bonds with an annual interest payment. Hence, by multiplying the numbers of years to maturity by two and dividing the i annual interest payment, ii discount rate by two we can modify bond valuation formula as follows: Illustration A bond, whose par value is Rs.

The required rate of return on bond is 10 per cent. It measures the rate of return earned on a bond, if it is downloadd at its current market price and if the coupon interest is received. It is the rate of return earned by an investor, who downloads a bond and holds it until the maturity. Illustration Consider a Rs.

The bond carries a coupon rate of 8 per cent and has the maturity period of nine years. What would be the rate of return that an investor earns if he downloads the bond and holds until maturity?

Using it, we find that kd is equal to the following: When the required rate of return is equal to the coupon rate, the value of the bond is equal to its par value. When the required rate of return kd is greater than the coupon rate, the value of the bond is less than its par value.

When the required rate of return is less than the coupon rate, the value of the bond is greater than its par value. When the required rate of return kd is greater than the coupon rate, the discount on the bond declines as maturity approaches. When the required rate of return kd is less than the coupon rate, the premium on the bond declines as maturity approaches. A bond price is inversely proportional to its yield to maturity. For a given difference between YTM and coupon rate of the bonds, the longer the term to maturity, the greater will be the change in price with a change in YTM.

It is because, in the case of long maturity bonds, a change in YTM is cumulatively applied to the entire series of coupon payments and the principal payment is discounted at the new rate for the entire number of years to maturity. Given the maturity, the change in bond price will be greater with a decrease in the bond's YTM than the change in bond price with an equal increase in the bond's YTM. That is, for equal sized increases and decreases in the YTM, price movements are not symmetrical.

For any given change in YTM, the percentage price changes, in case of bonds of a high coupon rate, will be smaller than in the case of bonds of a low coupon rate, other things remaining the same.

In tabulated form it can be represented as follows:. From the above table it is clear, that for a required rate of return of 13 per cent, the value of the bond will increase with the passage of time until its maturity. Consider a bond having a face value of Rs. Let the YTM be 10 per cent. Market price of the bond will be equal to Rs.

A 1 per cent increase in YTM to 11 per cent changes price to Rs. A decrease of 1 per cent YTM to 9 per cent changes the price to Rs. Thus, an increase in bond's yield caused a price decrease that is smaller than the price increase caused by an equal size decrease in yield. The market value of the bond will be Rs. Consider another identical bond Y but with differing YTM of 20 per cent. The market value of this bond will be Rs. If the YTM increase by 20 per cent, i.

YTM of bond X rises to 12 per cent 10 x 1.

Bond ABC: When the interest rates rise, there is a gain in reinvestment and a loss on liquidation. The converse is true when the interest rates fall. For any bond, these two effects exactly balance each other for a holding period. What is lost on reinvestment, is exactly compensated by a capital gain on liquidation and vice versa. For this holding period, there are no interest rate risks. The holding period for which the interest rate risk disappears, is known as the duration of the bond.

There is a simple way of computing the desired holding period duration , which is as follows: Determine the cash flows from holding the bond. Determine the present value of these cash flows by discounting the flows with discount rate YTM. Multiply each of the present values by respective numbers of years left before the present value is received.

Sum these products up and divide by the present value to get the duration of the bond. Consider a The expected market rate is 15 per cent. The duration of this bond can be computed as follows: It indicates that interest rate risk will disappear if the holding of bond will be for 3.

The concept was first introduced by F Macaulay and thus, is called by his name as the Macaulay Duration. It is also possible to compute the duration of an entire portfolio of bonds. It is the weighted average of. For an Investor a bond will be risky if the holding period of the bond is different from its duration. Duration of a bond declines as the bond approaches maturity.

The sensitivity of the bond price to changes in the interest rates is called 'Bond Volatility'. Bond prices and YTM are inversely related. Therefore, instantaneous changes in market yields cause prices to change in the opposite direction. The extent of change in the bond prices for a change in YTM measures the interest rate risk of a bond. The interest rate risk is a function of the interest rate elasticity.

Interest rate elasticity IE can be defined as:. Bond price elasticity can also be computed with the help of following mathematical formula: Anything that causes the duration of a bond to increase will also increase the bond's interest rate elasticity.

Illustration Consider a bond having a face value of Rs. Calculate the Macaulay Duration, Modified Duration of a bond for company A, if the coupon rate is given to be 8 per cent, the YTM is 6 per cent and the time to maturity is five years.

The face value of the bond is Rs. The interest payments are made annually. Also, calculate the percentage change in price of the bond if the YTM falls by basis points or 1 per cent from 6 per cent to 5 per cent.

Duration 4. Consider two bonds A and B. They have the following characteristics. Face value Rs. What did you notice regarding the percentage price change in case of Bonds A and B identical in all respects, except term to maturity? What did you observe when the interest rate rose by 1 per cent and fell by the same amount in case of the Bond A? Solution a Since the bonds are available at their respective face values, the YTM of the Bond A and B will be equal to their coupon rates, i.

We observe that percentage price change in case of increase or decrease in interest rate is asymmetrical. A bond with a face value of Rs. It has a term to maturity of four years. The holder of this bond has an applicable income tax rate of 33 per cent and a capital gain tax rate of 15 per cent.

Assuming that interest is paid annually, you are required to calculate: The percentage price change when the interest rate rose by basis point is computed below: It is also known as par value and stated on the face of the bond.

It represents the amount borrowed by the firm, which it promise to repay after a specified period of time. Coupon Rate: A bond carries a specific rate of interest which is also called as the coupon rate. A bond is issued for a specified period of time.

It is repaid on maturity. The value which bondholder gets on maturity is called redemption value. A bond may be redeemed at par, at premium more than par value or at discount less than par value. A bond may be traded in a stock exchange. Market value may be different from par value or redemption value. Intrinsic Value: Therefore, the intrinsic value is the present value of the cash flow over the redemption period.

It can be computed as follows: It is the rate of return earned by an investor who downloads a bond and holds it till maturity. Duration of Bond: The holding period for which interest rate risk disappears knows as the duration of the bond.

Define debt. What are the salient features of debt? Investors are assured about the fixed return on investment in bonds.


However, there are various risks involved in bond investment. Recommend the techniques to reduce the risk involved in bond investment. Bonds are less risky than equity but are not entirely risk free. Explain the factors affecting the price of bond. Explain the concept duration. How duration of bond helps to reduce interest rate risk?

The objectives of this unit are: Money has the time value, i. To illustrate, consider an investor, who is evaluating an investment opportunity that requires an immediate outlay of Rs. In deciding whether to go ahead with the investment, the investor will be concerned with how much income generation will be in the future.

A rational investor will be unwilling to undertake the investment if he knows that he will receive less than what he can earn as interest.

This illustration clarifies the importance of the timing of the receipt or expenditure of cash flows and that it is not sufficient to treat the money to be received in the future as having the same value as the money to be received immediately.

If the decision maker is to be able to make a choice about whether to go ahead with an investment or is to be able to rank the investment opportunities where there is more than one alternative, then a way must be found to allow money to be received at different points of time to be compared. One way of making the comparison is to use the approach adopted above; namely to work out what the value of money to be received now will be at any point in the future.

Future value of Rs. Future value is a useful concept and helps to capture the principle that underlines the time value of money. However, when considering an investment opportunity, the decision maker is typically faced with a stream of cash inflows and outflows, rather than just comparing money to be expended now with a single money to be received at some point in the future, So, we need to convert all cash flows, received at different points of time, to a common reference point, to allow a direct comparison.

While it would be possible to convert all the sums of money to the future values, for the time period associated with the most distant cash flow resulting from the investment opportunity, it is easier to think in terms of what the future cash flows are worth now, thus using the present time as a common reference point. This simply requires a reversal of the way in which the future values were calculated. For example, if two projects are to be compared, one that has an expected life of five years and the other having an expected life of nine years, it is easier to convert the cash flows to their present values than to a future value.

Taking a future sum of money and calculating its present value in this way is known as discounting. Following example illustrates the method: The illustration demonstrates that it is essential to take into account the time value of money and to discount the future sums to their present value, before making a decision on whether a particular investment opportunity is worth pursuing.

The concept of time value is of vital importance when considering investment opportunities. It is through the concept of the present values that the decision makers can make a trade-off between the money receivable at different points of time.

Failure to take account of the time value of money may well lead the decision makers to make incorrect judgements about the desirability or otherwise of an investment opportunity. It is very tedious to calculate the present values of the multiple streams of cash flows without the aid of a computer or a programmable calculator. However, in the absence of such devices, discount tables are of great use.

The discount tables are of two types: Down the left hand side of the table, is the number of years. The main body of the table gives the present values of Re. The figures are called as discount factors.

For an illustration, if the time in which Re. Thus, if the money to be received in the year ten is 1,, then its present value is x. Table B is similar in layout to the Table A and is used in exactly the same way.

However, the figures in. For an illustration, an annuity of Re. Thus, an annuity of Rs. This chapter sets out the two main discounting techniques of investment appraisal namely the net present value NPV method and the internal rate of return JRR methods.

Two main assumptions that are made in discussing the two techniques, are as follows: With the above two caveats, both the methods are scientific methods of investment appraisal. Explicitly, the NPV method involves comparing the present value of the future cash flows of an investment opportunity with the cash outlay that is required to finance the opportunity.

In this way, we can determine whether the investment opportunity provides a surplus, when the cash flows are measured in present value terms.

The stages involved in using the NPV method are as follows: Estimate all future net cash flows revenue minus cost associated with an investment opportunity; 2. Convert these net cash flow figures to their present value equivalents by discounting at the appropriate discount rate; 3. Add all the present value figures of future cash flows; 4. Subtract from this value, the initial cost of investment. The resulting figure from these calculations is the net present value.

Mathematically, the NPV is calculated by using the following formula: Above formula calculates the surplus that is made as a result of undertaking the project, in excess of that which could be made by investing at the marginal rate of return. If the NPV is negative, the surplus is actually a deficit and undertaking the investment would reduce the wealth of the shareholders.

Thus, under condition of certainty, the NPV method provides a definite decision advice for independent investment projects: Similarly, when projects are mutually exclusive, NPV provides a definite ranking advice: The use of NPV can be explained using an illustration. Consider, a firm wants to set up toy making plant. Production of the toys requires new factory space and equipment. Either the firm can construct a factory on a site it has identified or it can refit a factory that it owns and that is currently lying idle.

The initial investment in constructing a factory is more; however, the running cost may be less due to design that is more appropriate. The firm is faced with a choice of mutually exclusive investment opportunities. The net cost associated with the new built factory Project A and that of the renovated factory Project B are shown in Tables 1 and 2 respectively, as are the present values of the cash flows for a discount rate of 10 per cent. Table 4. For Project B. A 1 1 1.

If projects A and B were independent projects, rather than mutually exclusive investment opportunities, then the firm would maximise the increase in shareholder wealth by undertaking both projects, funds permitting. The IRR method is one more method for an investment appraisal. Srinivasan Module A , R. Malayarasan Module B , V.

Rao, Asst. Glossary prepared by Mr. This book is meant for educational and learning purposes. FOREWORD The world of banking and finance is changing very fast and banks are leveraging knowledge and technology in offering newer services to the customers.

Banks and technology are evolving so rapidly that bank staff must continually seek new skills that enable them not only to respond to change, but also to build competence in handling various queries raised by customers.

Therefore, there is a need for today's bank employees to keep themselves updated with a new set of skills and knowledge. The Institute, being the main provider of banking education, reviews the syllabus for its associate examinations, viz. The latest revision has been done by an expert group under the Chairmanship of Prof.

Candidates to the course will get extensive and detailed knowledge on banking and finance and details of banking operations. The Diploma is offered in the distance learning mode with a mix of educational support services like provision of study kits, contact classes, etc. The key features of the Diploma is that it aims at exposing students to real-life banking environment and that it is equivalent to JAIIB.

Marketing of Bank products have been covered in length. Aspects such as insurance, mutual funds, credit cards, etc.

The flow of transactions in a centralised computerised operating environment and delivery of services through multiple channels have been given adequate coverage to make the participants aware of the latest banking environment and practices. The Institute acknowledges with gratitude the valuable services rendered by the authors in preparing the courseware in a short period of time.Few of the methods are as follows: Basel II Framework.

The use of NPV can be explained using an illustration. They are just extract of t Macmillan books. A cut in the CRR enhances loanable funds with banks and reduces their dependence on the call and term money market.

For any bond, these two effects exactly balance each other for a holding period. When the debtor fails to meet the conditions of repayment as per the contract of loan, the lender gets the right to charge penal interest for defaulted payments, compound the loan and to realise the loan through the liquidation of securities.

If it depreciates at 10 per cent per annum, find its value 3 years hence.