Thread Modes. eBook for Accounting and finance for Bankers IIBF. ramnivas Offline Junior Member *. Posts: Threads: 7. Joined: Nov Accounting and Finance for Bankers - JAIIB Course material by sure2k. JAIIB- MACMILLAN EBOOK-Principles and Practices of ronaldweinland.info · Accounting. eBook - INFORMATION TECHNOLOGY. eBook - ADVANCED BANK MANAGEMENT. eBook - BANK FINANCIAL MANAGEMENT. eBook - ACCOUNTING.

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This book is a practical handbook that takes the reader through accounting and financial techniques in an easy-to-follow, progressive way. In this new. ronaldweinland.info - Ebook download as PDF File .pdf), Text File .txt) or read book online. The recalled questions of the previous examinations have been made available in question – answer form as well as MCQs. JAIIB FAST 3: MCQs ON LEGAL & REGULATORY ASPECTS OF BANKING - Pass in Just 4 days. Accounting and Finance for Bankers For JAIIB and Diploma in Banking &.

Money supply change is a technique of controlling inflationary or deflationary situations in the economy. All these policies are among the important macroeconomic policies that influence various businesses in the country. RBI issues monetary and credit policies annually. These are discussed below. As you know, demand liabilities of a bank represent its deposits which are payable on demand of the depositors viz. In order to meet these liabilities in time i.

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.

He should accept b Rs. PartB 1. 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 sumof-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. 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. 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 first pillar sets out the minimum capital requirement. 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. 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. 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. 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. Credit Risk. 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'.

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. 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. These are largely in alignment with the 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. With the prospect of greater inflows under a fuller CAC regime, it may be necessary for tightening the provisioning requirements, to enhance the shock absorbing capacity of the banks and thus, enhance their resilience.

As a result, this gives rise to the scope for a borrower to keep the nonperforming portion of his exposures in one particular bank and keep the other exposures as performing, though the exposure to the banking system when viewed at an aggregated level might have become 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:. Age of delinquency Provisioning per cent Substandard 90 days to 15 months. Secured advances 10 per cent of total outstanding.

Unsecured advances - 20 per cent. Age of delinquency Provisioning per cent Secured Portion Unsecured Portion Substandard a secured advances b unsecured advance. Capital Adequacy Banks in India are at present adopting the capital adequacy framework as required under the Basel I. Banks are maintaining capital for both credit risk and market risk exposures. The minimum CRAR required to be maintained by the banks in India is 9 per cent as against the 8 per cent norm prescribed by the Basel.

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.

Migration to a fuller CAC is likely to throw up numerous challenges to the banks' risk management systems. Migration to Basel II at the minimum approaches would be making the banks' capital adequacy framework more risk sensitive than under the Basel I.

The capital adequacy framework, even under. The system should move forward to a differential capital regime. The 'complex' banks as defined in Paragraph 7. As of March , 86 banks were maintaining capital in excess of the regulatory minimum and 2 banks were falling short of. Reserve Bank has advised banks in India to implement the revised capital adequacy framework popularly known as Basel II with effect from 31st March, Banks will be maintaining capital for operational risks under the Basel II in addition to the credit risks and market risks.

The Indian banking system will be adopting the standardised approach for credit risk, standardised duration method for market risk and the basic indicator approach for operational risk. On a quick broad assessment, it is expected that the impact of Basel II on banks' CRAR will be adverse to the extent of to basis points. It may be raised to at least 66 per cent. Further, almost 90 per cent of banks' credit portfolio is unrated.

The risk- weight structure under the Basel II provides a perverse incentive for high risk 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. 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. 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 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 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. 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.

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.

Therefore, the intrinsic value or the present value of a bond is. The required rate of return on the bond is 10 per cent. What is the value of this bond? 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. 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: Years to Maturity. 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.

For two bonds X and Y having 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. A bond of face value of Rs.

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 is less than the term to maturity Bond's duration will be equal to its term to maturity if and only if it is zero coupon bonds. Longer a coupon paying bond's term to maturity, the greater the difference between its term to maturity and duration Duration and YTM are inversely related Larger the coupon rate, smaller the duration of a bond. An increase in the frequency of coupon payments decreases the duration, while a decrease in frequency of coupons increases it. Duration of a bond declines as the bond approaches maturity.

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. Percentage change in price for bond in period t Percentage change in yield to maturity for bond [ It implies, a 10 per cent change in YTM would cause a 5. Let us now run through the illustration 1.

Consider the following annuity cash flow schedule:. In order to calculate the future value of the annuity, we have to calculate the future value of each cash flow. Let us assume that you are receiving Rs. The following diagram shows how much you would have at the end of the five-year period:. I I I I Payment paid or received at end of each period.

Since, we have to add the future value of each payment, you may have noticed that, if you have an ordinary annuity with many cash flows, it would take a long time to calculate all the future values and then add them together. Fortunately, mathematics provides a formula that serves as a short cut for finding the accumulated value of all cash flows received from an ordinary annuity:. Each of the values of the first calculation must be rounded to the nearest paise.

The more you have to round numbers in a calculation the more likely rounding errors will occur. Therefore, the above formula not only provides a short cut to finding FV of an ordinary annuity but also gives a more accurate result. If you would like to determine today's value of a series of future payments, you need to use the formula that calculates the present value of an ordinary annuity.

You would use this formula as part of a bond pricing calculation. The PV of ordinary annuity calculates the present value of the coupon payments that you will receive in the future. For the illustration 2, we will use the same annuity cash flow schedule as we did in the illustration 1. To obtain the total discounted value, we need to take the present value of each future payment and, as we did in the illustration 1, add the cash flows together.

End of each period. Again, calculating and adding all these values will take a considerable amount of time, especially if we expect many future payments. As such, we can use a mathematical shortcut for PV of ordinary annuity. Cash flow per period www. Here is the calculation of the annuity represented in the diagram for Illustration 2: Beginning of each period.

Payment paid or received at the beginning of each period. Since, each payment in the series is made one period sooner; we need to discount the formula one period later.

A slight modification to the FV-of-an-ordinary-annuity formula accounts for payments occurring at the beginning of each period. In the following Illustration 3, let's illustrate why this modification is needed when each Rs. Notice that when payments are made at the beginning of the period, each amount is held for longer than at the end of the period. For example, if Rs.

The future value of annuity formula would then read:. For the present value of an annuity due, we need to discount the formula one period forward, as the payments are held for a lesser amount of time. When calculating the present value, we assume that the first payment made was today. We could use this formula for calculating the present value of your future rent payments as specified in a lease you sign with your landlord. Let us say for the illustration that you make your first rent payment at the beginning of the month and are evaluating the present value of your five-month lease on that same day.

Your present value calculation would work as follows:. Therefore, 1. The present value of an ordinary annuity is less than that of an annuity due because the further back we discount a future payment, the lower is its present value: Now you can see how annuity affects and how you calculate the present and future value of any amount of money. Remember that the payment frequencies, or number of payments, and the time at which these payments are made whether at the beginning or end of each payment period , are all variables you need to account for in your calculations.

Illustration Find the compound amount of Rs. Solution Using formula, we could find the value of compound amount.

However, in these kinds of problems, generally we use compound interest for the full interest period and simple interest for the fractional interest period. Here we find the compound interest for 13 interest periods and simple interest for 1 month.

Find i the rate of interest, ii the principal, iii the difference between the C. Solution i Let the principal be Rs. P and rate of interest be R per centp. If the present population is 1 million, estimate the population five years hence.

Also, estimate the population three years ago. Illustration Avichal Publishers download a machine for Rs. The rate of depreciation is 10 per cent. Find the depreciated value of the machine after 3 years.

Also, find the amount of depreciation. What is the average rate of depreciation? In this chapter, we shall discuss different methods of repaying interest-bearing loans, which is one of the most important applications of annuities in business transactions. The first and most common method is the amortisation method. By using this method to liquidate an interest-bearing debt, a series of periodic payments, usually equal, are made.

Each payment pays the interest on the unpaid balance and repays a part of the outstanding principal. As time goes on, the outstanding principal is gradually reduced and interest on the unpaid balance decreases. When a debt amortises, by equal payments at equal payment intervals, the debt becomes the discounted value of an annuity.

The common commercial practice is to round the payment up to the next rupee. Thus, an annuity is a sequence of payments made at regular periods over a given time interval e.

The total time, is called the term of the annuity. The regular periods, where the repayments are made, are called the payment periods. Annuities, where the payments are made at the end of the payment period, are called ordinary annuities. When the payments are made at the beginning of the payment period, the process is called an annuity due. The present value of the annuity involves 'moving' each of the payments R to the present. Not an easy task, for the monthly payments of a 25 year loan.

Hence, the following mathematical formula can help: R per payment period, for n periods, at the rate r per period. For an illustration, if the plan is to get paid Rs. What will be the monthly repayments at 18 per cent compounded monthly?

Both loans require a repayment of equal monthly payments made at the end of the month for the next five years. What is the monthly payment? Assume 10 per cent compounded monthly Bring everything back to the present value.

It turns out that we can calculate this; using a loan amortisation formula. We can think of Arlene as lending the bank Rs. When a loan is repaid in equal instalments, part of the payment covers interest and the rest covers principal.

The formula for paying back a loan in equal instalments is known as the amortisation formula. Plugging in Rs. This says that by lending investing her Rs. If there were no inflation, then Arlene would receive exactly Rs. If there is inflation of, say, 2 per cent per year, then the nominal interest rate will be 5 per cent and the real interest rate will be 3 per cent.

Arlene will receive Rs. That is, each year, her annuity payment will rise 2 per cent, in order to keep up with inflation. Adjusting for inflation is what makes this a real annuity. In the real world, there are some complications. First, not all annuities are adjusted for inflation. Although inflation is important, all too often the elderly live on fixed incomes, which are annuities that do not adjust for inflation.

Second, insurance companies need to earn a profit. If the insurance company earns 0. This will www. If Arlene dies early, say in 5 years, she will not have collected her annuity and the insurance company earns a windfall gain. Conversely, if she defies the actuarial tables and lives for 25 years, the insurance company may take a loss, because the Rs.

When interest-bearing debts are amortised by means of a series of equal payments at equal intervals, it is important to know how much goes for interest from each payment and how much goes for the reduction in principal. For an illustration, this may be a necessary part of determining one's taxable income or tax deductions.

We construct an amortisation schedule, which shows the progress of the amortisation of the debt. Illustration A debt of Rs. Make out an amortisation schedule showing the distribution of the payments as to interest and the repayment of principal.

Solution The interest due at the end of the first quarter is 2. The first payment of Rs. Thus, the outstanding principal after the first payment is reduced to Rs. The interest due at the end of the second quarter is 2. The second payment of Rs. The outstanding principal now becomes Rs. This procedure is repeated and the results are tabulated below in the amortisation schedule.

It should be noted that the fifth payment is only Rs. The totals at the bottom of the schedule are for checking purposes.

The total amount of principal repaid must equal the original debt. In addition, the total of the periodic payments must equal the total interest and the total principal returned. Note that the entries in the principal repaid column except the final payment are in the ratio. This formula, can also be rewritten as. Investing this way to meet some future obligation is commonly called sinking fund.

In problems 1 - 3 , you deposit Rs. How much will you have in the bank after 7 years? How much will you have in the bank after 25 years? How long will it take to have Rs. In problems 4 and 5, you deposit Rs. How much will you have in the bank after one year? After four years? In problems 6 and 7, you deposit Rs. If you deposit Rs. Suppose that you deposit Rs. How much will you have after you make your deposit at the start of the tenth year? Suppose that you want to have Rs. How much will you have to deposit each year?

In the problems , suppose that you have Rs. What is the annuity payment? Suppose that the inflation rate is 2 per cent per year. What is the real interest rate that would be used to calculate a real annuity payment?

Calculate the real annuity payment assuming that inflation is 2 per cent per year. 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. 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.

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: SLR has three objectives: To restrict expansion of banks' credit, To increase banks' investment in approved securities and To ensure solvency of banks. The effect of an increase in SLR by RBI is the reduction in the lending capacity of banks by pre-empting blocking a certain portion of their DTL for government or other approved securities.

It has therefore a deflationary impact on the economy, not only by reducing the supply of loanable funds of banks, but also by increasing the lending rates in the face of an increasing demand for bank credit.

The reverse phenomena happens in case of a cut in SLR. It is the basic cost of rediscounting and refinance facilities from RBI. The Bank Rate is therefore used by RBI to affect the cost and availability of refinance and to change the loanable resources of banks and other financial www. Change in the Bank Rate by RBI affects the interest rates on loans and deposits in the banking system across the board in the same direction, if not to the same extent.

After deregulation and banking reforms since , RBI has gradually loosened its direct regulation of deposit and lending rates and these are left to banks to decide through their boards, with only a few exceptions. However, RBI can still affect the interest rates via changes in its Bank Rate, whenever the situation of the economy warrants it. RBI's objective in issuing Selective Credit Control SCC directives is to prevent speculative holding of essential commodities and the resultant rise in their prices.

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