# Fair value model

### EXECUTIVE SUMMARY

This report outlines a solution and information regarding the fair value model for instalment and revolving products in the retail environment. The values were calculated as accurate as possible on account level for the Vehicle and Asset Finance and Home loans product areas, specifically for the Provisions department of Nedbank. It is of utmost importance that these calculated values comply with the relevant accounting standards as these values will be disclosed in the annual financial statements.

In today's active and unstable markets, people are interested in what an asset is worth at present. For this reason the student project team need to determine the fair value for the Vehicle and Asset Finance and Home loans products in Nedbank Retail by using credit assumptions at inception and balance sheet date. Credit assumptions are the probability of default, loss given defaults, interest rate et cetera.

A SAS / Excel based model was developed for calculating the fair values where the code was written in SAS and the output given in Excel. It is important to note that the calculation of the fair values for the revolving products in Nedbank Retail is the first attempt and the extent for improvement is enormous. The fair value model used the current IAS 39 (International Accounting Standards) Provision model for calculating discounted cash flows per account. The purpose of the fair value model is to use these cash flows to calculate the fair value adjustment per account. The net book value of each account is then adjusted by this calculated value to obtain the fair value for each account.

For the majority of the development of the fair value model data issues were experienced and this was the vast reason for using the Basel credit assumptions instead of the IAS (International Accounting Standards) assumptions for the calculations. The credit assumptions together with the Internal Rate of Return obtained by using the discounted cash flows were used in the fair value model. This document's function is to propose the formation for the fair value model and to help the user to understand the underlying calculations.

### INTRODUCTION

In today's active and unstable markets, people are interested in what an asset is worth at present. For this reason various considerations were taken into account and it was concluded that fair value is the most appropriate measure for financial instruments. The fair value of financial instruments is the amount at which these instruments could be exchanged in a transaction between two willing parties not being forced, neither in the case of a liquidation sale. The term fair value can formally be defined as:

• "The price at which an asset or liability could be exchanged in a current transaction between knowledgeable, unrelated willing parties (FASB, 2004).
• "The price that would be received to sell an asset or paid to transfer a liability in an orderly transaction between market participants at the measurement data (IFRS, 2009).

The actual estimate of the fair value of a loan or a group of loans will be based on the discounted value of future cash flows, expected to be received from a single or group of loans. Cash flows are calculated by using the current IAS 39 Provisions model; this model uses the credit assumptions, interest rates, discounted rates and loan information for the calculation. The selection of the discount rate reflecting the relative risk requires judgement and understanding of the problem.

According to Tschirhart (2007), the estimated default or survival probabilities are used for loan facilities in estimating the fair value because default on a loan obligation is treated as an obligor event. "If an individual loan obligor's default probabilities change it will be reflected in the obligor's loan facility fair value estimate, thus if this probability would change because of certain factors the loan facility fair value estimate will also change in the appropriate direction "(Tschirhart, 2007).

The primary aim of this project was to develop a model to assist Nedbank in the estimation of the fair value in order for disclosure in the annual financial statements. This value is required by the accounting standards and the reason why a successful model is of immense importance. The guidelines on how and why to disclose a fair value on the annual financial statements are contained in the various Reporting Standards and will be discussed in the report.

It was recommended that the International Accounting Standards Board take action to improve and simplify the accounting requirements for financial instruments. To do this, the IASB (International Accounting Standards Board) and the FASB (Financial Accounting Standards Board) are working together to develop a complete standard to improve the measurement and reporting of financial instruments. The objective to do this is to replace the existing IAS 39 (International Accounting standard) and to create an IFRS that is simplified.

One of the objectives of IFRS (International Financial Reporting Standards) is to ensure that the financial statements sufficiently reflect the fair value of all assets of a financial institution.

Another standard is the FAS 107 (Financial Accounting standard) that requires all financial institutions to disclose the fair value of loans and other financial instruments, in the footnotes to annual financial statements. These requirements highlight the importance of a fair value that can be disclosed in financial statements.

This report will introduce the reader to all the relevant concepts of the fair value model, and will provide the results obtained from this newly developed model. The methodology for these calculations will be explained for a better understanding of the technicalities of the model.

### PROBLEM DESCRIPTION

The project concept statement is outlined as follow:

To develop a Fair Value Model for Nedbank Retail in order to determine the fair value of Retail's loans and advances as required by IFRS (International Financial Reporting Standards).

In essence, the problem faced by Nedbank Retail was that there were no current measure of fair value on account level for Home Loans, Personal Loans, Card Products, Vehicle and Asset Finance and Transactional and Investment Products which are referred to as the five product areas. Certain financial standards require that the fair value for all the products held by Nedbank Retail must be disclosed in financial statements. In the light of this, a fair value model needs to be developed, to provide Nedbank with fair values for these products.

The fair value measurement will enable Nedbank to compare the fair values with the net book values. Furthermore, it will enable Nedbank to use the fair values obtained for disclosure in financial statements according to the International Financial Reporting Standard 7, which describes the disclosure of financial instruments.

### PROJECT SCOPE

The scope of this project was set around the development of a fair value model that would be built according to certain assumptions; these assumptions formed the basis of the project.

The current IAS Provisions model was used to discount the cash flows of the loans and to get a better understanding of the assumptions and inputs used for the model. A thorough literature study was undertaken to include all the necessary requirements to the model.

In the retail environment there are a distinction between transactional and instalment products. In the initial project scope we would have used a product in each of the two groups; the data for VAF (Vehicle and Asset Finance) which is an instalment product and TIP (Transactional and Investment Products) which is a transactional product. These products would have been used in the fair value calculation. However the student project team and the client decided to conduct the calculations on Home Loans instead of the Transactional and Investment Products (TIP). This change meant that both of the products fall within the instalment group and that the model will only produce fair values for the VAF and Home Loans products.

The calculation for the other products will be excluded from the scope of this project; the reason for the exclusion of these products is insufficient data and limited time. The report will explain the methodologies used for the calculation of a fair value of the two retail products.

### PROJECT OBJECTIVES

In order for the project to add value, the following objectives conducted from the project scope had to be reached to ensure that sufficient value is added to Nedbank Retail:

1. Thorough research on the implementation and effectiveness of a fair value model. This meant to get a good understanding of the term fair value and the implementation of this term.
2. Development of a useful fair value model that can be implemented to provide valuable information to users. This objective was the most critical objective of the entire project and the largest amount of time was devoted for successful completion. The model should also be user-friendly because it must be understandable and easy interpretable.
3. Implement the fair value model in order to determine the fair value on account level for the different product areas according to accounting standards for disclosure in annual financial statements.
4. Compare fair values with net book values. There exists a difference between the fair values and the net book values. The last objective was to use the fair values obtained to get a better understanding of the differences between the fair value and the net book values and then to draw a successful conclusion regarding this difference.

All of the objectives set out by the student project team were reached. The methodology that was followed to achieve these objectives will be explained in the next section.

### PROJECT METHODOLOGY

The fair value model was developed in SAS and Excel, where the code was written in SAS and the output given in Excel. The fair value calculation was conducted on account level for the VAF (Vehicle and Asset Finance) and Home Loan products of Nedbank Retail. The whole fair value calculation was based on a five step procedure, the completion of these steps were in sequence. The five step strategy followed was:

1. Determine credit assumptions at inception.
2. Determine credit assumptions at balance sheet date.
3. Determine credit spread at inception (Internal Rate of Return).
4. Discount Cash Flows at calculation date using (2) and (3).
5. Compare Fair Value with net book value.

Because the IAS credit assumptions at inception were not complete we used the Basel PD's (Probability of Default) and LGD1's (Loss Given Default) at inception.

• Probability of Default: The likelihood that a loan will not be repaid and will fall into default.
• Loss Given Default: The actual total loss that is experienced by a bank when a debtor defaults on an loan.

The credit assumptions at the balance sheet date, in other words, the current PD's and LGD1's were obtained to complete step two of the strategy. The credit assumptions at inception were used as input into the current IAS Provisions Model to obtain the discounted cash flows for each account. After determination of these cash flows, the IRR function within SAS was used to calculate the IRR per account.

The Internal Rate of Return is the effective interest rate such that a series of payments have a zero net present value. By taking the initial outlay of a loan and using the expected cash flows for that same loan the IRR function in SAS calculates the interest rate where the cash flows net present value equals zero.

This function takes all the calculated cash flows and the initial loan amount, thus the amount of capital at inception as input to calculate the IRR per account. This step in other words is the credit spread at inception and is step three of the strategy for the fair value calculation.

The current PD's and LGD1's, which in essence is the credit assumptions at balance sheet date are then used in conjunction with the IRR calculated in step three. These assumptions are used as input in the IAS Provisions model, where the current interest rate and discount rate is replaced with the newly calculated IRR. The cash flows are then discounted back by making use of the IAS Provisions model and the current assumptions. These discounted cash flows are then subtracted from the balance of the loan in order to obtain the provisions amount for each account.

The calculated "provision amount is compared to the IAS 39 provisions amount which is calculated on a monthly basis by using the IAS assumptions. The fair value adjustment is considered to be the difference between these two Provision amounts. The net book values for each account are the IAS 39 provision amount subtracted from the balance. Fair value is the calculated "provision amount, using the credit assumptions at inception the calculated IRR, subtracted from the balance.

Finally the calculated fair values for VAF (Vehicle and Asset Finance) and Home Loans are compared with the net book values of each of the products. This final evaluation is also the last step in the strategy for calculating the fair values for the financial instruments within Nedbank Retail.

### Introduction

Given the Financial Accounting Standards Board (FASB) stated long-term goal of having all financial assets and liabilities recognized in statements of financial position at fair value. In this literature study, some aspects of the fair value approach will be discussed regarding accounting standards for this calculation.

The first discussion involves some accounting standards regarding fair value and the disclosure of the calculated values. The term fair value accounting will be discussed followed by the difference between fair value and the impairment approach currently used by Nedbank to provide protection against probable credit losses.

The valuation technique for determining the fair value are discussed thoroughly, after which some factors within the approach followed in the project will be explained. A conclusion at the end will give a summary of the study on fair value.

### Accounting standards regarding fair value

The fair value measurement of financial instruments is dependent on financial accounting standards, for this reason it is necessary to discuss some important points on these standards. Inside the financial world there will be distinguished between three different standards for fair value measurements. It is the International, United States or Canadian accounting standards. However in this report we only focus on the International and the US accounting standards. The IAS 39 (International Accounting Standards) is an internationally recognised standard which focuses on the recognition and measurement of financial instruments. The issuer of this standard is the International Accounting Standards Board (IASB). The FAS 157 (Financial Accounting Standards), which is a United States, recognized accounting standard focus on the measurement of a fair value. This accounting standard is issued by the Financial Accounting Standards Board (FASB). Table 6.1 show some main differences between the IAS 39 and FAS 157 regarding fair value.

• This statement states that the fair value of an asset is the amount for which this asset could be exchanged, between knowledgeable, willing parties in an arm's length transaction.
• IAS 39 provides a hierarchy to be used in determining the fair value for a financial instrument:
1. Quoted market prices in an active market
2. Valuation technique using market inputs
3. Cost less impairment.
• Fair value is the price at which an asset could be exchanged in a current transaction between knowledgeable, unrelated willing parties.
• FAS 157 emphasizes that fair value is a market-based measurement, establishing a fair value hierarchy for measurement:
• Level 1: Quoted market prices in active markets.
• Level 2: Prices other than quoted prices (valuation technique with observable market data).
• Level 3: Unobservable inputs using estimates and assumptions.

The problem faced by the student project team is such that the IAS 39 standard is applicable due to the fact that in South Africa we are only interested in the International Accounting Standards. Nedbank also uses the IAS 39 for calculating the provision amounts on account level for all of the product areas within Nedbank Retail.

The "IAS 39 Financial Instruments: Recognition and Measurement implementation is quite difficult according to many auditors and accountants due to the complicated requirements needed to deal with the large range of different financial instruments. For this reason the necessity for reviewing the accounting of financial instruments grew tremendously.

It was recommended that the International Accounting Standards Board take action to improve and simplify the accounting requirements for financial instruments. To do this, the International Accounting Standards Board (IASB) and the Financial Accounting Standards Board (FASB) are working together to develop a complete standard to improve the measurement and reporting of financial instruments. The objective to do this is to replace the existing IAS 39 and to create an International Financial Reporting Standards that is simplified.

One of the objectives of IFRS (International Financial Reporting Standards) is to ensure that the financial statements sufficiently reflect the fair value of all assets of a financial institution. The IASB will try and explore all possible approaches to measurement in order to reduce the complexity of IAS 39 and at the same time remaining consistent with their objectives. This preparation will take a few years because the implementation of a full fair value accounting approach will entail decisions of a variety of complex issues.

### Disclosure of Fair Value

The disclosure of a calculated fair value is very important and that is why the calculation needs to comply with the Accounting Standards. The disclosure of the fair value is described in the International Financial Reporting 7 which is the standard for disclosing financial instruments. The following section of the standard for "Financial Instrument: Disclosures, according to the International Accounting Standards Board, were obtained from the International Financial Reporting Standards 2008/2009 as issued at 30 November 2008.

### Fair Value

25 Except as set out in paragraph 29, for each class of financial assets and financial liabilities, an entity shall disclose the fair value of that class of assets and liabilities in a way that permits it to be compared with its carrying amount.

26 In disclosing fair values, an entity shall group financial assets and financial liabilities into classes, but shall offset them only to the extent that their carrying amount are offset in the statement of financial position.

27 An entity shall disclose:

1. the methods and, when a valuation technique is used, the assumptions applied in determining fair values of each class of financial assets or financial liabilities. For example, if applicable, an entity discloses information about the assumptions relating to prepayment rates, rates of estimated credit losses, and interest rates or discount rates.
2. whether fair values are determined, in whole or in part, directly by reference to published price quotations in an active market or are estimated using a valuation technique (see paragraphs AG74 AG79 of IAS 39).

### No active market: valuation technique

AG74 If the market for a financial instrument is not active, an entity establishes fair value by using a valuation technique. Valuation techniques include using recent arm's length market transactions between knowledgeable, willing parties, if available, reference to the current fair value of another instrument that is substantially the same, discounted cash flow analysis and option pricing models. If there is a valuation technique commonly used by market participants to price the instrument and that technique has been demonstrated to provide reliable estimate of prices obtained in actual market transactions, the entity uses that technique.

AG75 The objective of using a valuation technique is to establish what the transaction price would have been on the measurement date in an arm's length exchange motivated by normal business considerations. Fair value is estimated on the basis of the results of a valuation technique that makes maximum use of market inputs, and relies as little as possible on entity-specific inputs. A valuation technique would be expected to arrive at a realistic estimate of the fair value if (a) it reasonably reflects how the market could be expected to price the instrument and (b) the inputs to the valuation technique reasonably represent market expectations and measures of the risk-return factors inherent in the financial instrument.

AG76 Therefore, a valuation technique (a) incorporates all factors that market participants would consider in setting a price and (b) is consistent with accepted economic methodologies for pricing financial instruments. Periodically, an entity calibrates the valuation technique and tests it for validity using prices from any observable current market transactions in the same instrument (ie without modification or repackaging) or based on any available observable market data. An entity obtains market data consistently in the same market where the instrument was originated or purchased. The best evidence of the fair value of a financial instrument at initial recognition is the transaction price (ie the fair value of the consideration given or received) unless the fair value of that instrument is evidenced by comparison with other observable current market transactions in the same instrument (ie without modification or repackaging) or based on a valuation technique whose variables include only data from observable markets.

AG76A The subsequent measurement of the financial asset or financial liability and the subsequent recognition of gains and losses shall be consistent with the requirements of this Standard. The application of AG76 may result in no gain or loss being recognized on the initial recognition of a financial asset or financial liability. In such a case, IAS 39 requires that a gain or loss shall be recognised after initial recognition only to the extent that it arises from a change in a factor (including time) that market participants would consider in setting a price.

AG77 The initial acquisition or origination of a financial asset or incurrence of a financial liability is a market transaction that provides a foundation for estimating the fair value of the financial instrument. In particular if the financial instrument is a debt instrument (such as a loan), its fair value can be determined by reference to the market conditions that existed at its acquisition or origination date and current market conditions or interest rates currently charged by the entity or by others for similar debt instruments. Alternatively, provided there is no change in the credit risk of the debtor and applicable credit spreads after the origination of the debt instrument, an estimate of the current market interest rate may be derived by using a benchmark interest rate reflecting a better credit quality than the underlying debt instrument, holding the credit spread constant, and adjusting for the change in the benchmark interest rate from the origination date.

AG78 The same information may not be available at each measurement date. For example, at the date that an entity makes a loan or acquires a debt instrument that is not actively traded, the entity has a transaction price that is also a market price. However, no new transaction information may be available at the next measurement date and, although the entity can determine the general level of market interest rates, it may not know that level of credit or other risk market participants would consider in pricing the instrument on that date. An entity may not have information from recent transactions to determine the appropriate credit spread over the basic interest rate to use in determining a discount rate for a present value computation. It would be reasonable to assume, in the absence of evidence to the contrary, that no changes have taken place in the spread that existed at the date the loan was made. However, the entity would be expected to make reasonable efforts to determine whether there is evidence that there has been a change in such factors. When evidence of a change exists, the entity would consider the effects of the change in determining the fair value of the financial instrument.

AG79 In applying discounted cash flow analysis, an entity uses one or more discount rates equal to the prevailing rates of return for financial instruments having substantially the same terms and characteristics, including the credit quality of the instrument, the remaining term over which the contractual interest rate is fixed, the remaining term to repayment of the principal and the currency in which payments are to be made. Short-term receivables and payables with no stated interest rate may be measured at the original invoice amount if the effect of discounting is immaterial.

1. whether the fair values recognized or disclosed in the financial statements are determined in whole or in part using a valuation technique based on assumptions that are not supported by prices from observable current market transactions in the same instrument (ie without modification or repackaging) and not based on available observable market data. For fair values that are recognised in the financial statements, if changing one or more of those assumptions to reasonably possible alternative assumptions would change fair value significantly, the entity shall state this fact and disclose the effect of those changes. For this purpose, significance shall be judged with respect to profit or loss, and total assets or total liabilities, or, when changes in fair value are recognized in other comprehensive income, total equity.
2. if (c) applies, the total amount of the change in fair value estimated using such a valuation technique that was recognized in profit or loss during the period.

28 If the market for a financial instrument is not active, an entity establishes its fair value using a valuation technique. Nevertheless, the best evidence of fair value at initial recognition is the transaction price (ie the fair value of the consideration given or received), unless conditions described in paragraph AG76 of IAS 39 are met. It follows that there could be a difference between the fair value at initial recognition and the amount that would be determined at that date using the valuation technique. If such a difference exists, an entity shall disclose, by class of financial instrument:

1. its accounting policy for recognizing that difference in profit or loss to reflect a change in factors (including time) that market participants would consider in setting a price; and
2. the aggregate difference yet to be recognised in profit or loss at the beginning and end of the period and a reconciliation of changes in the balance of this difference.

29 Disclosures of fair value are not required:

1. when the carrying amount is a reasonable approximation of fair value, for example, for financial instruments such as short-term trade receivables and payables;
2. for an investment in equity instruments that do not have a quoted market price in an active market, or derivatives linked to such equity instruments, that is measured at cost in accordance with IAS 39 because its fair value cannot be measured reliably; or
3. for a contract containing a discretionary participation feature (as described in IFRS 4) if the fair value of that feature cannot be measured reliably.

30 In the case described in paragraph 29(b) and (c), an entity shall disclose information to help users of the financial statements make their own judgments about the extent of possible differences between the carrying amount of those financial assets or financial liabilities and their fair value, including:

1. the fact that fair value information has not been disclosed for these instruments because their fair value cannot be measured reliably;
2. a description of the financial instruments, their carrying amount, and an explanation of why fair value cannot be measured reliably;
3. information about the market for the instruments;
4. information about whether and how the entity intends to dispose of the financial instruments; and
5. if financial instruments whose fair value previously could not be reliably measured are recognised, the fact, their carrying amount at the time of derecognition, and the amount of gain or loss recognised.

### Fair value accounting

Various considerations were taken into account and we came to the conclusion that the most appropriate measure for financial instruments is the fair value. Critics believe that if companies in Asia and the United States of America had measured all of their financial instruments at fair value, downturns in the economy would not have caused losses that investors and taxpayers had to pay during the economic crisis. The reason is that depositors, regulators and investors could have achieved greater regulatory and market discipline by having the fair value of all financial instruments.

If available, a quoted market price in an active market is the best indication of a fair value and should be used as the basis for the measurement. However, if a quoted market price is not available, the estimation of a fair value must be done by using the best information available in the circumstances. The biggest difference between prices observed in active markets and prices observed in inactive markets is that for inactive markets an entity needs to put a lot more work into the valuation process to calculate a fair value for a financial instrument. Therefore, when there are no quoted market prices as in the case of loans, the estimation of a fair value is quite complicated. This is the reason why IAS 39 provides the user with some guidance of how to compute the fair value estimates.

When financial instruments are not traded in active markets, such as loans, fair value accounting involves biased estimations based on valuation models. The measurements must carefully be chosen as there are several considerations that need to be taken into account for these estimations to be subjective.

"The increasing use of fair value accounting is because accounting standard setters came to the conclusion that the fair value calculation appears to meet the conceptual framework criteria better than other measurement bases (Yong, 2008). The other measurement bases mentioned in the statement is historical cost and amortized cost.

After the recent financial crisis, fair value accounting has been taking a lot of criticism for being the cause of various financial institutions to collapse. As growth continued before the crisis on its given upward tendency, the balance sheets of financial institutions grew with the same trend. The consequence of the crisis was that we saw massive fair value write-downs; this was mainly on financial assets carried by various entities. "In one fell swoop, fair value accounting had most certainly lost its appeal as entities saw their assets whither into obscurity and their liabilities ascend to record levels (Truscott, 2009).

According to Jackson (2000), full fair value accounting raised many concerns. The main concerns are:

By estimating and verifying fair values, some costs would be imposed on banks. The only instruments with ready fair values are the ones with a market price. Loans however, are not actively traded and accounts for the largest part of the Banks on-balance sheet assets. By estimating the fair values for loans would force a large amount of administrative costs onto the bank.

1. Volatility in net worth

The biggest concerns about the fair value approach are the possible volatility of fair values. Under fair value accounting, assets are updated at each financial reporting period for some changes in the fair value. As these adjustments in fair value are often posted through profit or loss it has the ability to cause huge amount of instability in a banks income statement in times of economic volatility. Fair value accounts could be excessively influenced by current market conditions which might only be temporarily. The volatility in fair values can also be adverse in cases where the fair value measurements are estimates causing uncertainty, especially if the market is behaving as a herd.

1. Earnings

Many investors use the earnings realised in the previous financial year as a guide to what future earnings of an entity might look like. These investors may not be comfortable with earnings shown only in terms of the alteration in fair value.

1. Consistency with banking industry practices

A key consideration is whether the fair value approach would bring the accounts found in banks closer to the perception which banks themselves have of the value of these accounts.

Although there are a few concerns surrounding the fair value approach, many critics feel this approach have the ability to indicate the current market state. According to Truscott (2009), smooth earnings may be much easier to accept, while there are disputes that volatile fair values are just mirroring the realities of the economic markets in which banks operate and as a result are a better indication of a bank's true position.

The objective of the fair value approach is to measure all financial instruments at fair value and to recognise all gains and losses from changes in fair value immediately. The estimation of fair value for loans must be done in such a way that it takes into account both the interest rate on the loan and the current evaluation of the credit risk. The goal of fair value is to show the actual financial situation of the bank in the future value-based financial statements, so that "hidden reserves are avoided.

After these considerations, fair value accounting is seen to be a step up on historical cost accounting because the valuation of assets is incessantly affected by the current market conditions. The main reason is that current information is much more valuable than historical information, as it provides a better chance to project future cash flows. From a theoretical point of view, the fair value approach can help to improve market control and in that way encourage management to make decisions which can reinforce financial stability.

### Difference between Impairment and Fair Value within IAS 39

The current approach used by Nedbank Retail to provide protection against probable credit losses is the Impairment approach. The bank expects with this approach that on the balance sheet date there will be accounts not paying their loan obligations. If these bad debt accounts are identified during the current financial year they may be written off in the income statement. However, most of the time this is not the case and they need to be carried forward where a provision is created for these doubtful accounts. According to IAS 39, the only time provision can be provided with this approach is when there is objective evidence of impairment. Impairment is defined as the probability than an enterprise will not be able to collect all amounts outstanding according to the contractual terms. The one drawback of this approach is that it often leads to provisions for loan losses being created after the market fluctuations have affected the credit quality of the individual borrower. The provisions made in this approach are thus referred to as backward-looking.

For Fair value, the loan portfolio's value is written up or down as soon as market fluctuations take place. This ensures that the current values of the loans are presented in the annual financial statements. Therefore, with the fair value the alteration in credit risk is recognised at an earlier stage and is more forward looking than the impairment approach.

With the IAS 39 Impairment approach, Loans are recognised at nominal value in the financial statements and any losses incurred by the financial institution that granted the loan are written off directly to the nominal value. If the debtors ability to pay off the loan show that the loan or even a fraction of it is not likely to be repaid, therefore a impairment event, a loan loss provision is made and the nominal value in the financial statements of the loan is written down by the provision amount.

Using the fair value approach, provisions will be substituted by direct write-ups and write-downs of the nominal value of the loan as soon as there is evidence of a change in the credit risk. It is important to note that in theory, both the fair value approach and IAS 39 Impairment approach can over a period lead to the same accounting result.

According to Anderson (2001), these arguments can be explained by making use of the following example:

### Example: Describing the difference between the Impairment and Fair value principles

• The figure below explains the theoretical development in the valuation of a loan at a buoyant effective interest rate. This is done by taking into consideration the change in the credit risk according to the Impairment and fair value principles.
• To begin with, a loan amount of R 100 000 is granted. At the starting point, the valuation is believed to be identical according to both of the valuation principles. In the first period the likelihood of loss augmented by 3 percentage points, this increase caused the fair value of the loan to fall below the original nominal value, since it implied higher credit risk. According to the impaired principle the loan is entered at the nominal value of R100 000 despite the fact that the likelihood of loss has increased. In the second period the higher credit risk influenced the debtor which caused a risk of loss. The influence on the debtor is seen as an impairment event and a provision is required. According to the fair value principle, the augmented likelihood of loss had been taken into account at an earlier stage.

The sooner the problems of the change in the current market are detected, the sooner the bank can become fully aware of them and take the necessary actions. With fair value, higher "provision will be provided in times when expected loan losses are high and it will protect the bank. Income statements will be loss distorted in periods when actual loan losses are significantly higher or lower than the expected level. When using the Impairment approach, large profits can be expected in times when the market is in an upward trend and large losses in times when the market is not performing.

### Valuation technique for fair value

When the bank measures fair value by using a valuation technique, the bank will select the most applicable valuation models to use in the measurement. The bank will consequently make any assumptions necessary and consider the confidence that can be placed on any available pricing information in order to estimate the fair value. Despite the valuation technique used by the bank, it must include the appropriate risk adjustments.

According to the IASB Expert Advisory Panel, judgement is applied when making the decisions on the valuation technique; two entities might arrive at different estimates of the fair value of the same instrument even though both still meet the objective of fair value measurement. The difference is caused by the altered inputs used in the model, even though the two entities used the same model.

Some experts feel that when two entities are valuing the same instrument, they should always arrive at the same answer when measuring fair value. If they arrive at different answers, then one or both entities are wrong. However, according to the IASB it is definitely possible that entities will arrive at different estimates of the fair value of the same instrument at the same measurement date, and the valuation techniques and inputs used by both entities can still meet the objective of fair value measurement and be in compliance with the accounting regulation. There exist different estimates of fair value and this is reflected by the judgement and assumptions used in the valuation techniques and the uncertainty of estimating the fair value of instruments that has no quoted market price.

The difference in the fair values emphasizes the importance of the appropriate disclosure of the techniques used and judgements made. The disclosure of these techniques and judgements are essential because they are of great meaning for the users of financial statements.

### Approach followed in Project

As explained earlier, the whole fair value calculation was based on a five step procedure, the completion of these steps were in sequence. The five step approach followed was:

1. Determine credit assumptions at inception.
2. Determine credit assumptions at balance sheet date.
3. Determine credit spread at inception (Internal Rate of Return).
4. Discount Cash Flows at calculation date using (2) and (3).
5. Compare Fair Value with net book value.

Some factors within this approach will now be discussed to give more insight within the technicalities behind the calculation.

### Credit assumptions at inception and balance sheet date

The credit assumptions at inception are determined by making use of an application scorecard. A scorecard is a statistical model that assigns a score to a customer which corresponds to a probability that the customer will behave in a certain manner in the future. To reduce the level of biased evaluation in the credibility of the debtor the risk level of each debtor is calculated. An application scorecard is defined by Creditinfo Solutions as a scoring model based on the information obtained within the acquisition of new clients, predominantly from the information stated in the client's application. This model will be applied during the time a bank will decide if the loan for which a client has applied for is granted or refused. The application scorecard will also predict the probability of a person defaulting on a loan. The interest rate of a loan will be determined by the bank by taking the probability of default, loss given default and other variables into consideration.

To determine the credit assumptions at balance sheet date a client will again be scored by using the behavioural information of that client. The scorecard in this instance is called a behavioural scorecard and is simply a scoring model based on the behavioural information. Therefore, making use of this scorecard the probability of an existing account turning bad can be predicted.

In the project the student project team was required to obtain the application credit assumptions for each account. Within the first six months after the account was opened the account is allocated application credit assumptions. After this six month period, the account will be run through a behavioural scorecard and obtain behavioural credit assumptions.

### Probability of Default

Probability of Default (PD) is the likelihood that the borrower of a loan will not be able to make the required repayments on the loan. For each client who applies for a loan at the bank, a PD will be calculated. Therefore, the higher the probability of default a bank estimates a client to have, the higher the interest rate the bank will charge the client. The credit history of this client together with the nature of the loan will be taken into account when this calculation is done.

Most of the banks make use of external ratings agencies to help with the probability of defaults, although banks are encourage making use of their own internal rating methods. A possible method for estimating a PD will be making use of historical data. Calculating a historical PD is not a very complex calculation. According to Dorfmann (2004), the calculation by making use of historical data does not include a loss component but only the number of defaults within the given period. An example of a formula for this calculation is given below:

1 year-PD for rating grade Y = Number of obligors with rating Y(at beginning of the given time period)that defaulted during the given time periodNumber of all olbligors with rating Y atthe beginning of the given time period

There are however many other methods for calculating these PD's. For this project we are not interested in the exact calculations of the PD's but only used them in the Internal Rate of Return and discounted cash flow calculations.

### Loss Given Default

Loss Given Default (LGD) is defined as the amount of money the bank will lose when a borrower defaults on a loan. LGD is the amount of likely loss on the exposure and is articulated as a percentage of that exposure. There are quite a few methods to calculate the LGD, but the most used method is where the actual total losses are compared with the possible exposure at the time of default. This calculation is not calculated for each loan but is rather calculated over the entire portfolio of loans. The bank determines the appropriate LGD to be applied to each exposure. As with PD estimation, the LGD's are expected to correspond to a conventional view of long-run averages.

### Internal Rate of Return (IRR)

In the project we need to determine the credit spread at inception to discount the cash flows at balance sheet date, in other words the Internal Rate of Return. Consequently it was necessary to determine the Internal Rate of Return at inception to be used in the calculation of discounting cash flows at calculation date. In this calculation the discounted cash flows that were calculated by making use of the credit assumptions at inception and the IAS Provisions model as well as the initial loan amount. The IRR function within SAS was used to calculate this Internal Rate of Returns for each account.

Internal Rate of Return can be seen as the discount rate that causes the NPV of all cash flows to equal zero. This term is formally defined by SAS as: The interest rate such that the sequence of payments has a zero net present value. Net Present Value on the other hand will show the value of a stream of cash flows which is discounted back by some percentage that represents the minimum desired rate of return.

The IRR function in SAS returns the internal rate of return over a specific base period of time for a set of cash payments:

C0, C1, C2,......, Cn-1, Cn.

The time intervals between any two successive payments are said to be equal. The IRR is given by:

where x is the real root, nearest to 1, of the polynomial

i=0ncixi=0

The routine uses Newton's method to look for the internal rate of return nearest to 0. It's important to note that a root does not always exist for the equation and it depends on the value of payment. In this case a missing value will be returned.

The initial outlay of a loan is used together with the expected cash flows for the same loan to determine the rate where the cash flows net present value equals zero. It can be formulated as follows:

n= Positive integer.

N= The total number of periods.

Cn= Cash Flows.

NPV= Net Present Value.

The Internal Rate of Return is given by r in:

NPV= n=0NCn(1+r)n=0

There are however many mathematical methods that can be used to approximate r. According to Investopedia, by using the secant method, r is given by

rn+1= rn- NPVn(rn-rn-1NPVn-NPVn-1)

where rn is considered the nth approximation of the IRR.

To begin with, the formula requires two unique pairs of estimation of the IRR and NPV (r0,NPV0) and (r1,NPV1), and produces a sequence of

(r0, NPV0), (r1, NPV1), ..., (rn-2, NPVn-2), (rn-1, NPVn-1), (rn, NPVn), (rn+1, NPVn+1)

that may converge to (r,0) as n ?8. If the sequence converges, then iterations of the formula can continue indefinitely so that r can be found to an arbitrary degree of accuracy.

Other uses for IRR can be found when a firm wants to determine if a project will be worthwhile to take on, thus to establish the rate of the returns that will be generated to see if they are more than the initial investment. According to Investopedia, IRR can also be compared against existing rates of return in the securities market. If a firm can't find any projects with an IRR that is larger than the returns that can be generated in the financial market it will simply choose to invest in the financial market.

### Discounted Cash Flow (DCF)

Discounted cash flow (DCF) is the amount of money someone is prepared to pay today in order to obtain the expected cash flow in the future. The discounted cash flow is a valuation method used to determine if an investment is worthwhile to make. The DCF use future cash flows and discount them to arrive at a present value used to establish the value of a company or project under consideration or to evaluate the potential of different investments. Almost in the same way as the IRR, if the value obtained from the discounted cash flow analysis is higher than the present cost of an investment, one will not take the investment option.

The DCF is calculated by estimating the money to be paid and the cash thought to be received in the future. The valuation approach for DCF is taking projected future cash flows and discounting them at a rate of return, which is reflecting the supposed riskiness of the cash flows. According to the Value Based Management.net, the discount rate reflects two things:

1. The time value of money ( a person would rather want cash instantaneously than having to wait and must as a result be remunerated by paying for the delay)
2. A risk premium that reflects the extra return investors demand because they want to be remunerated for the risk that the cash flow might not materialise after all.

The formula for the DCF is given by Investopedia as follows:

DCF= CFn(1+r)n

= CF1(1+r)1+ CF2(1+r)2+...+ CFn(1+r)n

where CF= Cash Flow

r = Discount rate

n = period.

In the calculation of the DCF, each consecutive year's cash flow is discounted to a greater extent than the previous year, due to the fact that it is received further out in time.

The whole purpose of the DCF calculation is to estimate the money you would receive from an investment, therefore to convert future income to today's money. The reason why a person would want to know the present value of money you would receive in the future is to determine if that same amount of money is more than the money at present. The money you own now could be invested and can gain return or interest, between now and the future. Money you will not have until sometime in the future cannot be used now. For this reason the future money's value is discounted to show if it's worth less at present.

According to investopedia, it's important to note that DCF is simply a perfunctory valuation tool, which makes it subject to the axiom "garbage in, garbage out. All of the discounted cash flows in the project were calculated by the IAS 39 Provisions model.

### Conclusion on Literature study for Fair Value

The fair value approach has taken a lot of criticism around the measurement error in fair value estimates of a bank's assets. But according to Landsman (2005), although fair value estimates of bank assets likely contain measurement error relative to true economic values, so do book value estimates.

It appears that the movement towards fair value accounting is irreversible. However, various measurement issues in valuing financial assets should be taken into consideration, especially when subjective fair values estimates are involved. According to Yong (2008), managers are ought to consider some important considerations when implementing fair value accounting:

• The availability of observable inputs, and how that would influence the estimation of fair values;
• The validity of valuation models used to estimate biased fair values, given that valuation models might overlook certain key assumptions;
• The possible impact of increased volatility in their firms' earnings, and valuations as a result of fair value accounting, and how best to mitigate the increased volatility;
• The possibility of systemic risk during periods of rapidly falling markets.

Although fair value accounting has been criticised for inducing volatility in reported earnings, it must be remembered that smoothing reported earnings are not the objective of accounting policies. "Accounting rules should aim to achieve the core objective of financial reporting, that is, to present a true and fair view of the operating results for the period and of the financial position at the balance sheet date (Bhattacharyya,2008). All financial statements should report economic reality.

### RESULTS OF FAIR VALUE MODEL

In this section we will discuss the results obtained by using the project methodology. Al the methods and assumptions used in calculating the fair value per account will be explained. Output of the fair value calculations were grouped according to each client group and risk class used in the project. The generalised process followed will be described and the exact detail of the fair value calculation for each of the two products will be given.

### Generalised Process

The development of the fair value model can be divided into a five step strategy that was used for the successful calculation of a fair value for each account. Each of the steps contributed significantly towards the completion of the project. The steps were completed in sequence because they were dependent on the predecessor step and calculation.

The process consists of the following steps

1. Determination of the credit assumptions at inception by looking at the application information for each account
2. Determination of the credit assumptions at balance sheet date by looking at the credit information that is found on the current book of each product.
3. Determination of the credit spread at inception which consists of calculating the Internal Rate of Return. This Internal Rate of Return calculation made use of the discounted cash flows calculated using the credit assumptions determined in step one.
4. Discounting the cash flows at calculation date by using the credit assumptions at balance sheet date and using the calculated Internal Rate of Return. The fair value and net book value is determined by using the provision amounts and the balance amount for each account.
5. Summarise the calculated fair values for output in Excel and compare the fair value and net book value to draw a conclusion.

The following sections describe the specific methodologies used in each of the two products within the project. Vehicle and Asset Finance (VAF) will be described first followed by the Home Loans product.

### Home Loans

The Home loans product segregates into further product segments. These product segments are formed by the different market splits targeting different client groups. The different client groups for Home loans that featured in the project were:

• Private banking (CG1)
• Personal banking (CG2)
• Retail banking (CG3)
• Nedbank staff (CG5)
• NedEnterprise (NED)
• People mortgage lending (PML)

### Obtaining required information

The first step in determining the credit assumptions at inception was to obtain the necessary data which contained the information required. As explained earlier in the report, the IAS assumptions and information regarding the application information for each account was not sufficient enough to use in any of the fair value calculations. For this reason the student project team had to make use of the Basel application information for all of the calculations using assumptions at inception.

The Basel information is found on the "Theuns_final dataset which contains all the loan information for each account necessary for the required calculations. These "Theuns_final datasets is found on the "Baseldbr data base. Since we are only interested in the Home loans product, we only obtained the performing accounts that fall within this product.

This was possible by making use of the following piece of SAS code:

It is clear that if the "ProductTypeEnum field equals 'HL' that account falls within the Home loan product. To determine and obtain all the active accounts within the Home loan product the "nonperformingflag field must equal zero and the "inalgo field must equal one.

Unfortunately the "Theuns_final datasets could only be obtained from August 2007 to August 2009. We considered August 2009 as the calculation date in the project for calculating the fair values on account level for the different product areas in Nedbank Retail. The accounts opened before August 2007 was grouped together. The information for these accounts on August 2007 is regarded as the "application assumptions. Table 7.1 is an illustration of a part of the dataset "Theuns_final.

### Current Book

To obtain the current book for 2009/08 we used the "Mortconsolidated30_data0908 dataset which can be found on the "Bank SAS library. This library is created by the IAS 39 Provisions model where the "Mortconsolidated30_data0908 dataset consists of all the Provision calculations and information created by this model. The "Mortconsolidated30_data0908 dataset was then merged with the "Theuns_final0908 dataset for Home loans to obtain the different variables needed to determine the current book used in the calculations. The reason for the merging of these two datasets is because the Home loans system contains both the Home loan products and the Personal loan products. In both the Home loan product and VAF product we used the account's account number to merge the different datasets. After the current book for August 2009 was determined we segregated the Home loans current book into months by using the "DateOpened field to create the "Prob3.Inf datasets. Table 7.2 below shows a part of the dataset "Prob3.Inf_200908.

### Home Loan product system

The Home loans product system contains both the Home loans products and the Personal loan products. The datasets used in the project for Home loans ranged from August 2007 to August 2009, earlier datasets are also available if applicable. The "MortMain datasets obtained from the "Crestmis data base consists of all the information of loans on the book up until the date the dataset was created for. The "MortMain datasets were formatted to obtain certain data fields for calculation purposes. The following fields were obtained:

• Acct Each account number.
• TOB_app Time on book at inception.
• Periodrem_app The period remaining on the loan at inception.
• Balance_app The balance of the loan at inception.
• Interest_rate_app Interest rate on the loan at inception.
• Discount_rate_app Discount rate used to discount the cash flows at inception.
• Agegr_app The age group of the loan at inception.
• CG_Class_app Client group at inception.

### Merging current book with Home loan product system

The datasets "Prob3.Inf_date created by segregating the current book for Home loans were merged with the corresponding "MortMain datasets for each month. Due to the fact that we only have "Theuns_final datasets from August 2007 we grouped all the accounts on the current book, as explained earlier, that was opened before this date. In this case we merged the "Mort_main_200708 dataset with the group of accounts opened before August 2007. The datasets that was created by merging these two datasets are called "Mort_date, Table 7.4 below shows a part of the "Mort_200908 dataset.

### Obtaining Application assumptions

Within the first six months from the time an account is opened that account will be allocated some credit assumptions that was given at application. After the six months from inception the account is allocated behavioural assumptions, where the bank looked at the client's behaviour. This behaviour includes the history of repayments of the loan and any changes in the client's ability to repay the loan. Consequently the student project team merged the "Mort_date dataset where the accounts were opened on a certain date with the current book of six months after the date opened. By doing this comparison one can obtain the credit assumptions at application, in other words, the credit assumptions at inception. The dataset "Test_2 was created and the following fields were used for further calculations, a part of this dataset is also given by Table 7.5:

• Acct The account's account number.
• PD_B The probability of default at inception.
• LGD1_B Loss given default at inception.
• CG_Class_app The client group the account was at inception.
• DateOpened The date the loan was opened.
• TOB_app The time on book at inception.
• Periodrem_app The period that remained on loan at inception.
• Balance_app The balance of the loan at inception.
• Interest_rate_app The interest rate that was charged at inception.
• Discount_rate_appThe discount rate used to discount the cash flows at inception.
• Agegr_app The age group the account was at inception.

### Monthly probability of default

The Basel approach only provided the student project team with one yearly PD but the IAS 39 Provisions model requires monthly PD's to calculate the discounted cash flows. To generate the monthly PD's we used PD curves received from the Home loans team in Nedbank Retail. All the yearly Basel PD's were transformed by making use of the following curves in each of the client groups:

### Cumulative PD curves

• Figure 7.1: The cumulative PD1 to PD12 for the CG1, CG2 and BOE client groups
• Figure 7.2: The cumulative PD1 to PD12 for the CG3 and CG5 client groups
• Figure 7.3: The cumulative PD1 to PD12 for the CG4 and NED client groups
• Figure 7.4: The cumulative PD1 to PD12 for the PML client group
• Figure 7.5: Summary of the cumulative PD's for all the client groups

### Marginal PD curves

• Figure 7.6: The marginal PD1 to PD12 for the CG1, CG2 and BOE client groups
• Figure 7.7: The marginal PD1 to PD12 for the CG3 and CG5 client groups
• Figure 7.8: The marginal PD1 to PD12 for the CG4 and NED client groups
• Figure 7.9: The marginal PD1 to PD12 for the PML client group
• Figure 7.10: Summary of the marginal PD's for all the client groups

To calculate the monthly PD's based on the different PD curves we used the ratios from each PD. The PD1 to PD11 are divided by PD12, these calculated ratios were then applied to the one Basel PD which is seen as the PD12. Table 7.6 below shows the calculation for determining the ratios to calculate the monthly PD's.

For the calculation of the discounted cash flows the IAS 39 Provision model uses the monthly marginal PD's. This was achieved by using the newly calculated monthly PD's to calculate the marginal PD's. The SAS code that was used to do this transformation by using the PD ratios as well as the calculations for marginal PD's is given below, this piece of code was used for the CG1 and BOE client groups:

For purposes of the Home loan product the student project team was required to determine the PD13 to PD360 for calculation purposes. The same approach was used as for determining the monthly PD's. The ratio by which the PD13 to PD360 was multiplied was calculated in exactly the same way as with the monthly PD's.

### Obtaining current assumptions

To obtain current assumptions for each account we simply look at the information that is found on the current book for Home loans. The current assumptions are used in exactly the same way as with the assumptions at inception.

### Creating a dataset to calculate cash flows

The "Mortall200908 dataset that is used by the IAS 39 Provision model to calculate the discounted cash flows were merged with the "Test_2 dataset which contains all the application assumptions. To use this newly merged "Mortall200908 dataset we had to format it in order to obtain all the necessary fields to run through the slightly changed IAS 39 Provisions model. For calculation purposes the student project team needed to change certain fields in the "Mortall200908 dataset. The following piece of code was used to make the required changes:

The changed "Mortall200908 dataset was run through the IAS 39 Provisions model to calculate the cash flows needed for the IRR calculation.

### Internal Rate of Return

This calculation required the student project team to make use of the IRR function within SAS. The exact calculations used in this function were explained in the Literature study section. This function requires the projected cash flows calculated by the IAS 39 Provisions model and the Balance at the time of inception. The cash flows were obtained from the "Specificdata dataset created by the IAS 39 Provisions model. For calculation purposes we created a dataset "App_IRR_app which only consists of the account and IRR field, a part of the "App_IRR_app dataset is illustrated by Table 7.7 below:

### Discounting cash flows using internal rate of return

To determine the discounted cash flows at calculation date, the student project team made use of the credit assumptions at balance sheet date and the newly calculated IRR. The credit assumptions at balance sheet date which is found on the current book formed the "Mortall200908_MC2 dataset. The "App_IRR_app dataset was merged with the "Mortall200908_MC2 dataset to replace the current interest rate with the newly calculated IRR. This newly merged dataset containing the current assumptions and IRR were run through the IAS 39 Provisions model for the second time.

### Fair Value calculation

To determine the fair value per account, the "Provision amounts that were calculated by the IAS 39 Provisions model using the Basel credit assumptions at balance sheet date and IRR are subtracted from the current Balance of each account. The net book value on the other hand is determined by subtracting the IAS 39 Provisions amount from the current balance. The IAS 39 Provisions amount is calculated on a monthly basis by making use of IAS assumptions at balance sheet date and the effective interest rate. A fair value adjustment was also calculated by simply taking the difference between the net book value and fair value. The following SAS code was used to calculate the values:

For comparison purposes the student project team grouped the calculations into the different client groups and risk classes. The total values of the whole Home loans book were also given to give an overview of all the results.

After all the calculations were summarised in reports created in SAS, the output was exported to Excel file called "Results. The following output summarises the fair value calculations for the Home loans product:

The fair value is the amount a willing buyer would pay for the whole Home loans book. In this case we see that the fair value for the Home loans book is R 99 442 783 833. By looking at the Home loans results we can see that the net book value of the Home loans book is currently R 361 434 198 more than the amount a willing buyer would pay. The main reason for this difference is that the fair value calculation takes expected and unexpected future losses into account whilst IAS 39 does not. This difference is also explained in more detail in the literature study

If we look at the "Risk_class table, one can see that the IAS 39 has provided less provision than the fair value approach for both the "IBNR00 and "IBNR30 risk buckets. The main reason for this difference is that IAS 39 will provide provision when an impairment event has taken place. Looking at the "CG_class table, one can see that the bulk of the Home loans book lies within the CG3 (Ratail banking) client group and is also the reason for the large fair value adjustment.

### Vehicle and Asset Finance

The VAF product segregates into further product segments. During this project we only used the following client groups:

• Private banking (CG1)
• Personal banking (CG2)
• Retail banking (CG3)
• Nedbank staff (CG5)
• NedEnterprise (NED)
• People mortgage lending (PML)

### Obtaining required information

As with the Home loans product, the VAF product's Basel information is found on the "Theuns_final dataset which contains all the finance information for all the accounts that will be used for further calculations. In this case we are only interested in the performing accounts that fall within the VAF product. The "Theuns_final data set is obtained from the "Baseldbr data base, the SAS code used for obtaining only the VAF products from the "Theuns_final dataset are given below:

The "ProductSubTypeName field had to equal 'NVF' to obtain all the VAF products from the dataset. To have only active and performing accounts, the "inalgo field must equal one and the "nonperformingflag field must be equal to zero.

Since both the VAF and Home loan products make use of the "Theuns_final dataset and the problem of not having these datasets earlier than August 2007. The student project team applied the same strategy of using the information at August 2007 for all the accounts that was opened before August 2007 and regarded this information as the "application assumptions. The reason for applying this strategy is to obtain the earliest information of these accounts possible. Table 7.9 shows a part of the "Theuns_final dataset which only contains accounts that fall within the VAF product.

### Current Book

For the VAF product we used the "Theuns_final0908 dataset as the current book because in the project this was the only product within the VAF product system. After the "Theuns_final0908 dataset was set as the current book we segregated the VAF current book in months by making use of the "DateOpened field. Table 7.10 below illustrates a part of the "Prob1.Inf_200801 dataset which is one of the tables obtained after dividing the VAF current book.

### VAF product system

For the VAF product the student project team used a dataset which contains all the information found on the VAF product system. This "Abf_final dataset is a merged dataset of all the "abfmain datasets on the "Crestmis data base. All the "abfmain datasets from January 2001 to August 2009 is found on this dataset. To obtain the application information for all the accounts on this dataset, the "Age field needs to equal zero. The "Abf_final dataset was formatted in the same way as the "MortMain datasets to get the following fields that will be used for further calculations:

• Acct Each account's account number.
• Cap_app The capital amount at inception.
• TOB_app Time on book at inception.
• Periodrem_app The period remaining on the loan at inception.
• Interest_rate_app Interest rate on the loan at inception.
• Discount_rate_app Discount rate used to discount the cash flows at inception.
• Agegr_app The age group of the loan at inception.
• CG_Class_app Client group at inception.

### Obtaining Application assumptions

With the VAF product the student project team used the "Prob1.Inf_date datasets which is the VAF current book segregated into months by making use of the date opened. The "Prob1.inf_date datasets were merged with the current book of six months after the account was opened. Consequently the "Prob1.inf_date dataset is merged with the "Theuns_final dataset of six months after the date opened. As explained earlier the accounts are allocated application credit assumptions within the first six months after date opened. After the six month period the account is allocated behavioural credit assumptions. By merging these two datasets one can obtain credit assumptions at inception. The dataset "Test_2 was created by combining all the merged datasets the following field are used for further calculations:

• Acct The account's account number.
• PD_B The probability of default at inception.
• LGD1_B Loss given default at inception.
• CG The client group the account was at inception.
• NGR The net group rate at inception.
• DateOpened The date the loan was opened.

### Monthly probability of default

The monthly PD's was generated in the same way as with the Home loan product. As the Basel approach only provided one yearly PD, the student project team received PD curves from the VAF team which they used in transforming the one PD into twelve monthly PD's. The following curves were used in the transformation:

### Cumulative PD curves

• Figure 7.11: The cumulative PD1 to PD12 for the CG1 and BOE client groups
• Figure 7.12: The cumulative PD1 to PD12 for the CG2 client group
• Figure 7.13: The cumulative PD1 to PD12 for the CG3 client group
• Figure 7.14: The cumulative PD1 to PD12 for the CG4 and NED client groups
• Figure 7.15: The cumulative PD1 to PD12 for the CG5 client group
• Figure 7.16: Summary of the cumulative PD's for all the client groups

### Marginal PD curves

• Figure 7.17: The marginal PD1 to PD12 for the CG1 and BOE client groups
• Figure 7.18: The marginal PD1 to PD12 for the CG2 client group
• Figure 7.19: The marginal PD1 to PD12 for the CG3 client group
• Figure 7.20: The marginal PD1 to PD12 for the CG4 and NED client groups
• Figure 7.21: The marginal PD1 to PD12 for the CG5 client group
• Figure 7.22: Summary of the marginal PD's for all the client groups

To calculate the monthly PD's based on the different PD curves we used the ratios from each PD. The PD1 to PD11 are divided by PD12, these calculated ratios were then applied to the one Basel PD which is seen as the PD12. Table 7.13 below shows the calculation for determining the ratios to calculate the monthly PD's.

In order for the IAS 39 Provisions model to calculate the much needed discounted cash flows the student project team was ought to transform the yearly PD to twelve monthly PD's. The SAS code that was used to do this transformation by using the PD ratios as well as the calculations for marginal PD's are given below, this piece of code was used for the CG1 and BOE client groups:

### Obtaining current assumptions

Obtaining current assumptions for each account we simply used the information found on the "Theuns_final0908 dataset, which is regarded as the VAF current book.

### Creating a dataset to calculate cash flows

The "Vafall200908 dataset that is used by the IAS 39 Provision model to calculate the discounted cash flows, were merged with the "Test_2 dataset which contains all the application assumptions. The "Vafall200908_4 dataset that was formed by merging the "Vafall200908 and "Test_2 datasets was formatted in order to obtain all the necessary fields to run through the slightly changed IAS 39 Provisions model. For calculation purposes the student project team needed to change certain fields in the "Vafall200908_4 dataset. The following piece of code was used to make the required changes:

After the "Vafall200908 dataset was changed we merged this dataset with the formatted "Abf_final dataset that was explained in section 7.3.3. The "Test dataset that was formed by merging the "Vafall200908_4 and "Abf_final_3 datasets was set to "Vafall200908 to run through the IAS 39 Provisions model to obtain the necessary cash flows to calculate the IRR.

### Internal Rate of Return

This calculation made use of the IRR function in SAS as with the Home loans product. The required cash flows used by the function were calculated by the IAS 39 Provisions model. These calculated cash flows were obtained from the "Specificdata dataset created by the IAS 39 Provisions model. For calculation purposes the "App_IRR_app dataset was created which only consist of the account's account number and IRR field, a part of this dataset is illustrated by Table 7.14 below:

### Discount cash flows using internal rate of return

To determine the discounted cash flows at calculation date, the student project team made use of the credit assumptions at balance sheet date and the newly calculated IRR. The credit assumptions at balance sheet date which is found on the current book formed the "Vafall200908_C2 dataset. The "App_IRR_app dataset was used to merge with the "Vafall200908_C2 to replace the current interest rate with the newly calculated IRR. This newly merged dataset containing the current assumptions and IRR were run through the IAS 39 Provisions model for the second time.

### Fair Value Calculation

To determine the fair value per account, the Provision amounts calculated by the IAS 39 Provisions model using the credit assumptions at balance sheet date and IRR are subtracted from the current Balance of each account. The net book value on the other hand is determined by subtracting the original Provisions amount from the current balance. The original Provisions amount is calculated on a monthly basis by making use of IAS assumptions. In this calculation the current IAS assumptions were used including the original interest rate. A fair value adjustment was also calculated by simply taking the difference between the net book value and fair value. The following SAS code was used to calculate the values:

For comparison purposes the student project team grouped the calculations into the different client groups and risk classes. The total values of the whole VAF book were also given to provide an overview of all the results.

After all the calculations were summarised in reports created in SAS, the output was exported to Excel file called "Results. The following output summarises the fair value calculations for the VAF product:

The fair value for the VAF book is R 9 026 475 685. By looking at the VAF results one can see that the net book value of the VAF book is currently R133 944 324 more than the amount a willing buyer would pay. As explained earlier, the main reason for this difference is that the fair value calculation takes expected and unexpected future losses into account whilst IAS 39 does not.

If we look at the "Risk_class table, one can see that the IAS 39 has provided less provision than the fair value approach for all of the accounts not impaired. As with the Home loans product the reason for this difference is that the IAS 39 will only provide provision when an impairment event has taken place. Again as with Home loans the bulk of the VAF book lies within the CG 3 client group and is the reason for the large fair value adjustment. For the CG 4 (Small business services) and NED (NedEnterprise) client groups we can see that the net book value for VAF is under priced

### CONCLUSION

This report introduced the reader to fair value and all the relevant aspects and background, surrounding this term. In today's active and unstable markets, people are interested in what an asset is worth at present. For this reason the student project team needed to determine the fair value for some of the products in Nedbank Retail by using credit assumptions at inception and balance sheet date.

An SAS / Excel based model was developed successfully for the Vehicle and Asset Finance (VAF) and Home loans products to calculate the fair value on account level. The literature study introduced the basic concepts of the fair value calculation and also provided the reader with insight into some of the accounting standards regarding the term fair value and the calculations for this value.

Because Nedbank Retail had no measure of fair value on account level for all the product areas, this report dealt with providing a methodology that can be used to calculate fair values for these products. The results section gave the relevant results but also described the exact methodology that was followed to calculate this fair value on account level for the VAF and Home loans products.

However, it is important to note that the calculation of the fair values for the revolving products in Nedbank Retail is the first attempt and the extent of improvement is enormous.

### REFERENCES

• ANDERSEN, J., BAERTELSEN, P. 2001. Application of the Fair Value Principle to the Banks' Financial Statements. [Web:] http://www.nationalbanken.dk/C1256BE9004F6416/side/Monetary Review [Date of access: 29 July 2009].
• BARTH, M.E., LANDSMAN, W.R., WAHLEN, J.M. 1995. Fair value accounting: Effects on banks' earnings volatility, regulatory capital, and value of contractual cash flows. Journal of Banking & Finance, 19 (1995), 577-605.
• BESSIS, J. 2002. Risk Management in Banking. 2nd Edition, John Wiley & Sons Ltd. England.
• BHATTACHARYYA, A.K. 2008. Fair-value reporting of financial instruments: Good or bad?. [Web:]
• http://www.business-standard.com/india/storypage.php?autono=322663 [Date of access: 4 August 2009].
• DORFMANN, A. 2004. Sound Calculation for Probability of Default (PD). [Web:] http://www.financetrainer.com/Portals/2/PDFs/445.pdf [Date of access: 26 October 2009].
• ENRIA, A., CAPPIELLO, L. 2004. Fair Value Accounting and Financial Stability. Occasional paper series. 13:7-33.
• GWILLIAM, D., JACKSON, R.H.G. 2008. Fair value in financial reporting: Problems and pitfalls in practice. Journal of Accounting Forum, 32(2008), 240-259.
• HARNANDEZ, F. G. 2003. Another step towards full fair value accounting for financial instruments. Journal of Accounting Forum, 28(2004), 167-179.
• JACKSON, P., LODGE, D. 2000. Fair value accounting, capital standards, expected loss provisioning, and financial stability. [Web:] http://www.bankofengland.co.uk/publications/fsr/2000/fsr08art5.pdf [Date of access: 26 November 2009].
• KHURANA, I.K., KIM, M. 2003. Relative value relevance of historical cost vs. Fair value: Evidence from bank holding companies. Journal of Accounting and Public Policy, 22(2003), 19-42.
• LANDSMAN, W. 2005. Fair Value Accounting for Financial Instruments: Some Implications for Bank Regulation. [Web:] http://www.bis.org/events/armpr05/landsman1.pdf [Date of access: 28 July 2009]
• MAGNAN, M. 2009. Fair Value Accounting and the Financial Crisis: Messenger or Contributor. Scientific Series. 27:1-3.
• MANN, F., MICHAEL, I. 2002. Dynamic provisioning: issues and applications. [Web:] http://www.bankofengland.co.uk/publications/fsr/2002/fsr13art6.pdf [Date of access: 26 November 2009].
• Mc CLURE, B. 2005. Discounted Cash Flow Analysis. [Web:] http://www.investopedia.com/university/dcf/ [Date of access: 1 August 2009].
• Statement of Financial Accounting Standards No.107. [Web:] http://www.fasb.org/pdf/aop FAS107.pdf [Date of access: 29 July 2009].
• TRUSCOTT, J. 2009. Fair value accounting: The saviour or villain of accounting in the future?. [Web:] http://www.saica.co.za/Portals/0/news/Fair%20value%20accountingFinal.pdf [Date of access: 28 July 2009].
• TSCHIRHART, J. 2007. Bank Commercial Loan Fair Value Practices. [Web:] http://www.federalreserve.gov/pubs/feds/2007/200729/200729pap.pdf [Date of access: 29 July 2009].
• YONG, K. 2008. Fair Value Accounting: SFAS 157 and IAS 39. [Web:] http://www.qfinance.com/balance-sheets-best-practise/fair-value-accounting [Date of access: 1 August 2009].

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