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This book focuses on the valuation needed to apply IFRS (International Financial Reporting Standards), and provides coverage of financial instruments – indeed this is the starting point of the exposition. The book adopts a logical sequence where models of financial instruments are explained first and models of other assets (such as property, an enterprise, or multiple intangibles) are presented as extensions.

The book uses mathematical notation in presenting many of the models, but the focus is on application rather than proof. The mathematics is presented at a level that assumes sufficient background in high school algebra and coordinate geometry, prior knowledge of elementary probability, and a knowledge of basic statistics. Readers should also be aware of what linear regression does and should be able to run a regression and interpret the output. Calculus is not assumed.

The models discussed almost always require a computer to apply. However, the emphasis is on understanding the models rather than learning computer skills, especially in the case of financial instruments.

### 1. Overview

Abstract
In this chapter, we introduce the concept of valuation. We discuss different measures of current value required in accounting. These are—fair value, value in use and recoverable amount. We briefly survey the different situations where IFRS requires or allows measuring a current value. These include: PPE under the revaluation model, investment properties under the fair value model, many categories of financial instruments, purchase price allocation in a takeover, and recording asset impairments.
Stephen Lynn

### 2. Forwards and Options

Abstract
In this chapter, we cover forward and option contracts. We introduce generic forward contracts. We move to vanilla options, focusing on options to buy or sell one share, without much loss of generality. We start by briefly defining standard option types—calls vs puts, European vs American vs Bermuda exercise styles, and Asian options. We move to models to value European options when no dividends are due during the option life. Using a simple one-step model of price movements, we explain two approaches to solving option models—the dynamic hedging approach and the risk-neutral probabilities approach. We then introduce the put-call parity relationship. This relationship helps find the price of a European put given that of a similar European call and vice versa. We cover some standard lattice models including the Cox-Ross-Rubinstein binomial model, the equal-probabilities binomial model, and a version of the trinomial model. We introduce the Black-Scholes model as the limit of a binomial model as the number of steps increase. We proceed to adapt the models where possible to the valuation of American options when no dividends are due during the option life. Then we extend the models further where possible to handle fixed dividends that fall due during the option life. We briefly discuss valuation of Bermuda options. We proceed to look at the valuation of employee stock options (ESOs) following the requirements of IFRS 2 Share-based compensation. We briefly discuss the modified Black-Scholes approach allowed under U.S. GAAP, as well as the Hull-White model of ESO valuation, adapted to comply with IFRS 2. We turn to Asian options, showing how they can be valued by Monte Carlo simulation. We close with how to estimate the volatility parameter for option models using approaches based on historical prices as well as one based on the implied volatility from a traded option.
Stephen Lynn

### 3. Government Bonds

Abstract
Valuing government-issued debt gives us the risk-free rate, a key parameter in valuation models. We focus on government bonds for this chapter. We start by discussing yields on zero-coupon debt. This leads to concepts of spot and forward interest rates and discount factors for various maturities (risk-free rates and discount factors). We discuss different yield conventions and how to convert between them. We turn next to coupon bonds—bonds with periodic fixed interest payments. We explain how to value them in terms of a portfolio of zero coupon bonds. In practice, for longer maturities, only coupon bonds exist. We discuss how to use the relationship between coupon bonds and zero-coupon bonds to estimate zero-coupon prices and yields for these maturities—a procedure known as bootstrapping. We further discuss how to use the Svensson model to fit a non-linear curve that matches actual government bond prices. The Svensson model is used by the European Central Bank and the German Bundesbank to report their interest rates. Then we discuss two lattice models of risk-free rates—the Black-Derman-Toy model and the Ho-Lee model. These models can be used to value interest-rate derivatives. Finally we discuss how we can use estimated risk-free rates for different currencies to estimate the forward exchange rate between them, using a model known as covered interest rate parity (CIRP).
Stephen Lynn

### 4. Risky Bonds, Floaters and Swaps

Abstract
We turn from risk-free government debt to the more general case of risky bonds. These are usually valued using discount rates that are based on the risk-free rate plus some spread to reflect the higher risk. We start by discussing the concept of duration, a necessary input to our analysis. We discuss two types of spread: First, the Z-spread—a fixed spread above the zero curve or the term structure of spot interest rates; Second, the nominal spread—a fixed premium above the yield to maturity of a government coupon bond that is approximately similar to the bond being valued. We then turn to estimating the spread for a particular bond using a market approach—finding the spread for quoted bonds with a similar credit rating. This leads us to estimating a credit rating when not available—a synthetic credit rating, by comparing standard financial ratios for an issuer, with published averages for issuers with various ratings. We discuss how to use the Jarrow-Lando-Turnbull model to handle future changes in credit rating based on a transition matrix. We turn next to the valuation of floating-rate notes or floaters. We show that a floater with discount rates matching its coupon rates has a value at par. We use this fact to derive floater values under more general conditions. We turn next to a vanilla interest rate swap—an instrument where a fixed rate is exchanged for a floating rate, or vice-versa. We show how a vanilla interest rate swap can be valued using a replicating portfolio that includes a long position in a fixed-rate instrument paired with a short position in a floating-rate instrument, or vice-versa. Finally, we discuss complex instruments that have embedded options—convertible bonds, callable bonds, and puttable bonds. We discuss the Goldman-Sachs lattice model to value convertible bonds. We discuss how to use the Black-Derman-Toy lattice to value callable and puttable bonds.
Stephen Lynn

Abstract
We start by listing situations when business valuation models are needed in accounting: when valuing shares of a private company in an equity portfolio, in accounting for a takeover, and in performing an impairment test of goodwill. We proceed to discuss the two main approaches to business valuation—the ratio-based approach, and the discounted cash flow (DCF) approach. We discuss a few variations of these approaches, distinguishing between models that value the entire enterprise (enterprise valuation), and those that value just the equity (equity valuation). For DCF models, we distinguish between one-stage, two-stage, three-stage and general multi-stage models. General multi-stage models are based on cashflows projected for a fixed number of years—the planning period—followed by a terminal value, representing the projected value at the end of the planning period. We discuss different approaches to estimating the terminal value. For DCF models of enterprise valuation, we discuss three approaches—WACC, adjusted present value (APV), and residual income valuation. The WACC model discounts projected free cash flows available to both debtholders and shareholders. These cash flows are discounted using a weighted average of the required return demanded by debtholders and shareholders, weighted by their respective proportions in the enterprise’s capital structure.
Stephen Lynn

### 6. Inputs to Business Valuation

Abstract
We discuss the inputs for enterprise valuation, particularly in a DCF model—the cost of capital, the projected cash flows, and the selection of comparable companies or guideline companies. We first discuss the projection of cashflows. We start by explaining the mid-year convention and the partial-year adjustment, that help align projected cash flow dates to the valuation date. We turn to the construction of proforma income statements and balance sheets, using an example. We discuss how Monte Carlo simulation can be used to model uncertainty in cash flows and parameters. We discuss how to handle multiple-currency cashflows using CIRP. We turn next to the cost of capital. The weighted average cost of capital is built up from the cost of equity and the cost of debt. The cost of equity is usually measured using CAPM (the capital asset pricing model). We discuss how to apply the CAPM to find the cost of equity for a private company by aggregating betas for a set of similar listed guideline companies. We turn to the cost of debt and how to estimate it, for example by constructing a synthetic credit rating. Finally, we discuss how to combine the cost of equity and the cost of debt to arrive at the WACC. For small and/or very specialized enterprises, it may be difficult to find listed similar companies. For such companies, an alternative to using CAPM is to use a build-up model to derive the cost of equity. We briefly discuss this model. We turn next to the choice of guideline companies—listed companies that are similar to the entity being valued. We consider how location, size, industry and strategic positioning are factors in choosing guideline companies.
Stephen Lynn

### 7. Intangibles Valuation, Purchase Price Allocation (PPA) and Goodwill Impairment

Abstract
We start by outlining the key requirements of IAS 38 Intangible Assets in conjunction with relevant aspects of IFRS 3 Business Combinations. We proceed to briefly outline the three broad approaches to intangibles valuation—market, income, and cost approaches. We then proceed to examine selected standard intangible valuation techniques in more detail, with examples—the relief from royalty model, the replacement cost model, the with and without model and the multi-period excess earnings model. We then take up lifing—models to estimate the life of intangibles. We show with an example how intangibles life can be determined by fitting a survival curve based on a Weibull distribution. We also briefly discuss Iowa type curves as alternatives to the Weibull survival curve. We turn next to purchase price allocation (PPA) in a takeover. This is the task of apportioning the purchase price of the acquired company among its various assets and goodwill, with the assets including newly-identified intangibles. We turn next to the task of fair-valuing NCI. We consider two approaches to fair-valuing NCI. Firstly, we consider a top-down model that starts with a model of equity based on a control perspective, and then successively applies discounts for lack of control and for lack of marketability. Secondly, we explain a bottom-up model that attempts to directly project the cashflows due to NCI and to discount them at a rate that is specific to NCI. Finally, we discuss the impairment of goodwill with an example. We focus on the calculation of value in use.
Stephen Lynn

### 8. Property

Abstract
We start by reviewing when valuation is needed—when property is measured using the revaluation model under IAS 16 or under the fair value model for investment properties under IAS 40, and for impairment testing. We proceed to discuss the concept of “highest and best use” in the particular context of valuing land. We outline three approaches to property valuation—the market, income and cost approaches. Under the market approach, we discuss the comparable transaction approach and the multiple regression approach. The comparable transactions approach values a property using the adjusted recent sales price of a similar property. In this context, we discuss two rules for measuring similarity between properties—the Euclidean norm, and the Minkowski p-norm. Multiple regression analysis values a property using data on the prices and other attributes of a number of other properties in the neighborhood. It seeks the pricing model that best fits actual data on pricing and these attributes from recently sold properties. We study two regression approaches—the standard ordinary least squares (OLS) approach and a spatial regression approach, geographically weighted regression. We turn next to income-based approaches, which derive the fair value of a property by capitalizing rental income from the property. We discuss two broad approaches—direct capitalization, which applies a standard multiple or rate based on the rental income, and yield capitalization, which applies a discounted cash flow methodology. Finally, we discuss the cost approach, which values a property at the replacement cost. This approach starts by estimating the required outlay for a brand-new replacement property (“duplication cost new”) and then applying a series of adjustments for the loss of value due to factors such as age.
Stephen Lynn