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Illustration Your friend borrows Rs. The extra step here is that she will owe you less in principal each month. The principal payment each month will be Rs. The extra step here is that the interest rate of 8 per cent is the annual rate and this needs to be divided by 12 to get a monthly rate. Because the principal amount remained the same for each month. I want to pay the same amount every month and not have to look up this table.
Table 1. Third month: And so on for the twelve months. The formula for calculation of EMI given the loan. Add up the twelve monthly payments Rs. Under this system.
Easy to see why calculators and computers are used. The EMI is fixed based on the loan amount. The EMI payment loans are heavily tilted towards the interest payments at the start and principal repayments towards the end of the loan tenure. For example. The interest is calculated on a monthly reducing basis. Though it is an unequal combination of the principal repayment and interest cost. Fixed Rates 2. Ordinary Annuity: Payments are required at the end of each period.
Since the present and future value calculations for ordinary annuities and annui ties due are slightly www. It may increase or decrease.
If the loan is under an EMI system. Floating Rates also called as variable rates. Floating Rate: In the floating rate or variable rate. The most common payment frequencies are yearly once a year.
Rent is an illustration of annuity due. It will not change during entire period of the loan. Annuities 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. The fixed rate is. They are 1.
Depending on the prevailing market conditions. If you understand the time value of money and have an understanding of the future and present value. Annuity Due: Payments are required at the beginning of each period. These are called annuities. You are usually required to pay rent when you first move in at the beginning of the month.
At some point in your life. Fixed Rate: In the fixed rate. There are two basic types of annuities: Let us now run through the illustration 1. Consider the following annuity cash flow schedule: End of each period 1. The following diagram shows how much you would have at the end of the five-year period: End of each period 1 1.
Let us assume that you are receiving Rs. If you are making payments on a loan. Each of the values of the first calculation must be rounded to the nearest paise. As such. For the illustration 2.
The more you have to round numbers in a calculation the more likely rounding errors will occur. The PV of ordinary annuity calculates the present value of the coupon payments that you will receive in the future. To obtain the total discounted value. You would use this formula as part of a bond pricing calculation. A slight modification to the FV-of-an-ordinary-annuity formula accounts for payments occurring at the beginning of each period.
Beginning of each period 1 1. End of each period 0 1 1. Here is the calculation of the annuity represented in the diagram for Illustration 2: In the following Illustration 3. 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.
When calculating the present value. The future value of annuity formula would then read: 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: End of each period 2 1 1. Find i the rate of interest. Solution Using formula. Illustration Find the compound amount of Rs.
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. Here we find the compound interest for 13 interest periods and simple interest for 1 month. Solution i Let the principal be Rs.
According to the first condition of the question. P and rate of interest be R per centp. The present value of an ordinary annuity is less than that of an annuity due because the further back we discount a future payment. Find the depreciated value of the machine after 3 years. What is the average rate of depreciation? Illustration Avichal Publishers buy a machine for Rs. Solution Present population.
If the present population is 1 million. Rate of depreciation. The rate of depreciation is 10 per cent. The total time. Each payment pays the interest on the unpaid balance and repays a part of the outstanding principal. Not an easy task. As time goes on. When a debt amortises. The first and most common method is the amortisation method.
When the payments are made at the beginning of the payment period. The common commercial practice is to round the payment up to the next rupee.
The regular periods. By using this method to liquidate an interest-bearing debt. R per payment period. Arlene can live for 15 years on Rs. Monthly repayment If Arlene thinks in terms of living exactly 15 years from today. This will www. Although inflation is important.
That is. Plugging in Rs. We can think of Arlene as lending the bank Rs. This says that by lending investing her Rs. What is the monthly payment? Assume 10 per cent compounded monthly Bring everything back to the present value. The formula for paying back a loan in equal instalments is known as the amortisation formula. It turns out that we can calculate this. If there were no inflation.
If the insurance company earns 0. If there is inflation of. Arlene will receive Rs. When a loan is repaid in equal instalments. Both loans require a repayment of equal monthly payments made at the end of the month for the next five years. What will be the monthly repayments at 18 per cent compounded monthly? A is the initial loan balance. Adjusting for inflation is what makes this a real annuity. The outstanding principal now becomes Rs. Solution The interest due at the end of the first quarter is 2.
The first payment of Rs. In addition. The total amount of principal repaid must equal the original debt. Illustration A debt of Rs. We construct an amortisation schedule. The interest due at the end of the second quarter is 2. The totals at the bottom of the schedule are for checking purposes. When interest-bearing debts are amortised by means of a series of equal payments at equal intervals.
Note that the entries in the principal repaid column except the final payment are in the ratio That is. Make out an amortisation schedule showing the distribution of the payments as to interest and the repayment of principal. This procedure is repeated and the results are tabulated below in the amortisation schedule.
The second payment of Rs. If Arlene dies early. In problems 6 and 7. This formula. How long will it take to have Rs. How much will you have in the bank after 7 years? If you deposit Rs. How much will you have in the bank after one year? After four years?
C in the bank. Investing this way to meet some future obligation is commonly called sinking fund. In problems 4 and 5.
JAIIB-MACMILLAN eBook-Accounting and Finance for Bankers | Present Value | Compound Interest
How much will you have in the bank after 25 years? In the second year. Find the monthly payment on a thirty year mortgage with a Rs. How much will you have to deposit each year? The formula for finding the monthly payment on a mortgage or an auto loan is the same as the formula for an annuity. B is the initial balance. The annuity payment in the first year is equal to the real annuity payment.
A schedule www. What is the real interest rate that would be used to calculate a real annuity payment? Calculate the annuity payment for the second year and for the third year.
Suppose that the inflation rate is 2 per cent per year. Suppose that you have Rs. What is the annuity payment? How much will you have after you make your deposit at the start of the tenth year? Since the amount needed in the sinking fund. If the inflation rate is 5 per cent. Do the same calculations as in the problem Suppose that you want to have Rs.
In the third year. Suppose that you deposit Rs. Calculate the real annuity payment assuming that inflation is 2 per cent per year. In the problems Sinking funds are used to pay-off debts. Show that the annuity works. Show that after four years the ending balance is exactly zero. Find the monthly payment on a five year auto loan with a Rs.
Such a fund is called a sinking fund. Calculate the actual annuity payments for each of the four years. If you wish an annuity to grow to Rs. Determine the annual savings required to purchase the earthmover if the return on investment is 12 per cent.
An annuity consists of monthly repayments of Rs. A construction company plans to purchase a new earthmover for Rs. How much money will a student owe at graduation if she borrows Rs. Illustration 1. A new machine at that time is expected to sell for Rs. If the fund earns 7 per cent compounded annually. This fee is called 'interest'— 'simple' interest or 'flat rate' interest. When the sinking-fund method is used. The sum of the interest payment and the sinking-fund payment.
The amount of simple interest paid each year is a fixed percentage of the amount borrowed or lent at the start. At the end of the term of the loan. It should be noted that the sinking fund remains under the control of the borrower. The book value of the debt. When money is lent. In order to provide funds for the difference between the replacement cost and the salvage value. Illustration In 10 years. Type To solve the previous two problems using Excels' built-in functions: Compounding Period: The time interval.
He repays Rs. The interest is compounded annually at 10 per cent. A person invests Rs. The rule allows us to determine the number of years it takes your money to double whether in debt or investment. A loan of Rs. Find the value of each instalment. Calculate the amount outstanding at the end of the third payment. Calculate the total amount of his savings at the end of the third year. If the rate of compound interest was 4 per cent per annum and if he paid back Rs.
A man borrowed a certain sum of money and paid it back in 2 years in two equal instalments.
This is compounding of interest or more simply stated compound interest. When interest is added to the account against returning it immediately to the customer.
Sinking Fund: When there is a need for a specified amount of money at a specified future date. A man borrows Rs. Calculate the sum of money lent out. Find the annual payment. If the same sum of money is lent out at a compound interest at the same rate per cent per annum.
A sum of money is lent out at compound interest for two years at 20 per cent p. The simple interest on a certain sum for 3 years is Rs.
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. Find the rate of interest and the principal. A man saves every year Rs. A sum of Rs. Give your answer to the nearest Re. Find the nominal rate compounded monthly equivalent to 6 per cent compounded semi-annually. If money is worth 5 per cent compounded semi-annually to him..
How much should he invest? Divide Rs. The machinery of a certain factory is valued at Rs. A debtor may discharge a debt by paying a Rs. If its value depreciates 6 per cent in the first year.
Answers 1. The rate of interest charged is 20 per cent annually. In buying a house. The present value of a machine is Rs. A gets the same amount as B gets after 5 years. At 6 per cent compounded semi-annually. The population of a town increased from 2 lakh to 8 lakh in last 10 years. A person buys 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. If rate of interest is 15 per cent compounded annually.
Also find the effective rate of interest. Find out EMI if loan is Rs. If it is supposed to depreciate each year at 8 per cent of the value at the beginning of the year. Find the amount which he has to pay at the end of the fourth year. After 3 years. Two partners A and B together invest Rs. Find the amount of each instalment. The cost of a refrigerator is Rs. At the birth of a daughter. X takes a housing loan of Rs. If the rate of depreciation is 10 per cent.
If the same trend continues. X pays Rs. The rate of compound interest is 5 per cent per annum. Find their shares in the sum of Rs. If it depreciates at 10 per cent per annum. If Mr. What annual deposit is required per cottager if there are 30 cottages on the road?
Show the complete schedule. Make out the rest three and last three lines of the schedule. How much is in the fund at the end of 3 years? Find the quarterly deposits necessary to accumulate Rs. A couple is saving a down payment for a home. They want to have Rs. Find the amount in the fund at the end of 9 years and complete the rest of the schedule.
Prepare a schedule for this problem. How much must be deposited in the fund at the end of each year? Make out a schedule showing the growth of the fund. Make out schedule for this problem. What quarterly deposit is required in a bank account to accumulate Rs. A company wants to save Rs. He should accept b Rs. What quarterly deposits for the next 5 years will cause the fund to grow to Rs. A cottagers' association decides to set up a sinking fund to save money to have their cottage road widened and paved.
A city needs to have Rs. Verify that the sum-of-the-interest column plus the sumof-the-deposit column equals the sum of the increase-in-the-fund column. What is the total annual expense of the debt?
A homeowners' association decided to set up a sinking fund to accumulate Rs. 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. A couple wants to save Rs. How much is in the sinking fund at the end of 4 years? At the same time. What monthly deposit is required to accumulate Rs. A borrower of Rs. In its manufacturing process.
The company sets up a sinking fund to finance the replacement of the machine. Find a the semi-annual expense of the debt. If the fund contains Rs. PartC 1. How many years to the nearest quarter will it take them. A company issues 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. They can save Rs. A city borrows Rs. On a debt of Rs. PartD 1. Do a complete schedule for this sinking fund. Find the value of the sinking fund at the end of the 1 Oth year.
A sinking fund accumulating at. Recommendations on Capital Charge 2. Cooke Basel I was originally designed to apply only to internationally active banks in the G countries. 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. On 26th June. After much discussion. Against this background. By end. Basel II norms are centred on sustained economic development over the long haul and include www.
Bankhaus Herstatt. The distinctive feature of the Herstatt failure was the way it disrupted the clearing mechanism for spot foreign exchange transactions. The G supervisors joined in.
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'. The Basel committee on banking supervision had come out with a new consultative paper on 'New Capital Adequacy Framework' in June. It came into effect by end It was. 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.
The new standards are mandatory for Internationally active banks. Influence of level ofNPAs. What is Capital Adequacy? It is a cushion against unexpected losses Under the new accord. The new risk sensitive approach seeks to strengthen the safety and soundness of the industry by focusing on: Risk-based capital Pillar 1. The new framework maintains the minimum capital requirement of 8 per cent of risk assets. The Second Pillar.
It proposes. Each of these three pillars has risk mitigation as its central plank. 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 revised credit risk measurement methods are more elaborate than the current accord. 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.
Minimum Capital Requirement The first pillar sets out the minimum capital requirement. Basel II focuses on improvement in measurement of risks. In this. It sets the minimum ratio of capital to risk weighted assets and in doing so.
Supervisory Review Process Supervisory review process has been introduced to ensure. The requirements under this pillar are common to all regulated firms. Credit Risk Alternative methods for computing capital requirement for credit risk are depicted below. The process has four key principles: The IRB method proposes two approaches: Qualitative disclosures such as risk management objectives and policies.
For the measurement of credit risk. It is proposed to be effected through a series of disclosure requirements on the capital. These disclosures should be made at least semi-annually and more frequently if appropriate. To ensure that risks e. The Third Pillar. Basel II proposes three principle options: Credit Loss within the entire banking group are considered. Market Discipline Market discipline imposes strong incentives to banks to conduct their business in a safe.
General Market Risk: Capital charge for general market risk is designed to capture the risk of loss arising from changes in market interest rates. Trading book includes: The guidelines address the issues involved in computing capital charge for interest rate related instruments in the trading book.
As banks in India are still in a nascent stage of developing internal risk management models. As per the guidelines. This is similar to credit risk.. The specific risk charges are divided into various categories such as investments in Govt securities.
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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. The Basel committee suggested two broad methodologies for computation of capital charge for market risk. Three approaches have been proposed for the measurement of operational risks: There are also the Regional Rural Banks with links to their parent commercial banks.
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. RBI prefers that banks measure all of their general market risk by calculating the price sensitivity modified duration of each position separately. As the duration method is a more accurate method of measuring interest rate risk.
This has also been the guiding principle in the approach to the new Basel Accord. The process of providing financial services is changing rapidly from traditional banking to a one-stop shop of varied financial services. On the other hand. Foreign bank branches operate profitably in India and. For this purpose. We have the dominance of Government ownership coupled with significant private shareholding in the public sector banks. The aim has been to reach global best standards in a deliberately phased manner.
We also have cooperative banks in large numbers. RBI has stipulated and achieved a minimum capital adequacy of 9 per cent. The framework adopted by banks would need to be adaptable to changes in the business. Enhancing the area of disclosures Pillar III.
Issues Proposed Measures www. Improving the level of corporate governance standards in banks. In terms of AS The non-fund based exposures to entities. These are largely in alignment with the international best practices. Unsecured advances.
JAIIB-MACMILLAN eBook-Accounting and Finance for Bankers
Secured advances 10 per cent of total outstanding. The proposed schedule for provisioning should be as under: Category Category Age of delinquency Provisioning per cent Substandard 90 days to 15 months. The age of delinquency may also be reviewed to ensure that all working capital exposures beyond a delinquency of 36 months are fully provided.
As a result. The provisioning requirements on substandard assets may be increased to 20 per cent for secured advances and 30 per cent for unsecured advances.
Banks are maintaining capital for both credit risk and market risk exposures. The 'complex' banks as defined in Paragraph 7. The capital adequacy framework. The system should move forward to a differential capital regime. Migration to a fuller CAC is likely to throw up numerous challenges to the banks' risk management systems. The working capital exposures in the NPA accounts will attract a per cent provisioning requirement on both the secured and unsecured portions.
Migration to Basel II at the minimum approaches would be making the banks' capital adequacy framework more risk sensitive than under the Basel I. As of March It may be raised to at least 66 per cent. Banks will be maintaining capital for operational risks under the Basel II in addition to the credit risks and market risks. Considering the fact that retail exposures include a much wider weaker segment.
Reserve Bank has advised banks in India to implement the revised capital adequacy framework popularly known as Basel II with effect from 31st March. The Indian banking system will be adopting the standardised approach for credit risk. On a quick broad assessment. In view of this and since the system may not be able to rank risk objectively. The risk.
They should be required to set off losses against capital funds. RBI should decide on the methodology for setting off the losses against capital funds. 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.
Market Risk Risk associated with interest and other returns. Operational Risk Risk associated with unexpected disasters and events. 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. Definition and Meaning 3.
The mode and time of repayment are clearly expressed in the documents. In a less technical sense. The former means. In cases of insolvent estates. The holder of debt capital does not receive a share of ownership of the company when they provide funds to the firm. In a still more enlarged sense. Loans are granted by the banks or institutions based on the records and documentary evidences and. By a liquid debt. In the payment of debts. Debts are also divided into active and passive.
In India. When the debtor fails to meet the conditions of repayment as per the contract of loan. Debts are discharged in various ways. In return for loaning this money. A bond is issued for a specified period. A bond is generally issued at a discount less than par value and redeemed at par. This advantage relates to the differential tax treatment of interest payments on debt and dividend payments on equity. It is to be repaid on maturity. The interest payments on debt are said to be tax-deductible.
The mix of debt and equity is known as the capital structure of the firm. The fact that debt capital has a lower cost than equity capital. In contrast. At the end of tenth year. The expected cash flows consist of annual interest payments plus repayment of principal. In case of a bond.
Irrespective of the level of profits or losses. With the dividends now being taxed on the companies. Redemption Value: The value.
If the company fails to pay the coupon interest or the redemption value. 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. Coupon rate: A bond carries a specific rate of interest. It represents the amount borrowed by the firm.
Private sector companies can issue secured or unsecured bonds. Market value may be different from the par value or the redemption value. This tax deducibility of debt payments means that the debt capital provides a 'tax-shield' which is not provided by the equity capital and. Face Value: Also known as the par value and stated on the face of the bond. A bond is redeemable after a specific period. Bonds are negotiable promissory notes that can be used by individuals. This entitles the bondholder to receive Rs.
Bonds issued by the government or the public sector companies are generally secured. In addition to the fact that debt is cheaper than equity capital because there is less risk. What is the value of this bond? The required rate of return on bond is 10 per cent. 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. 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 purchases the bond and holds until maturity? Solution If kd is the yield to maturity then. Illustration Consider a Rs. The YTM is the discount rate. Using it. It is because. A bond price is inversely proportional to its yield to maturity. Given the maturity. The required rate of return is 13 per cent. When the required rate of return kd is greater than the coupon rate.
When the required rate of return is less than the coupon rate. For any given change in YTM. For a given difference between YTM and coupon rate of the bonds. When the required rate of return is equal to the coupon rate. When the required rate of return kd is less than the coupon rate. In tabulated form it can be represented as follows: Years to Maturity Bond Value 7 Market price of the bond will be equal to Rs.
Let the YTM be 10 per cent. 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. Bond ABC: For this holding period.
When the interest rates rise. The expected market rate is 15 per cent. For any bond. Consider a The duration of this bond can be computed as follows: There is a simple way of computing the desired holding period duration. Multiply each of the present values by respective numbers of years left before the present value is received.
Consider another identical bond Y but with differing YTM of 20 per cent. Determine the cash flows from holding the bond.
It is the weighted average of www. The holding period for which the interest rate risk disappears. If the YTM increase by 20 per cent. What is lost on reinvestment. Sum these products up and divide by the present value to get the duration of the bond. The concept was first introduced by F Macaulay and thus. The market value of the bond will be Rs. It is also possible to compute the duration of an entire portfolio of bonds. Over 70 pages and hundreds of questions with answers. Over pages of important lessons on Excel Shortcuts, Formulas and Functions.
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