Understanding the Time Value of Money

Explain (a) time value of money (TVM). (b) How the structure of interest rates guides individuals to make investment decisions that are most desired by society as a whole.

Time value of Money

The time value of money (TVM) is the idea, which indicates that the money availably currently worth more than the same amount of money in the future. This is due to the earning potential of the money. This is one of the major principles in finance, which says that, because money has potential to earn interest, therefore, sooner the money is received, more valuable it would be. The time value of money is also sometimes called as discounted value of money (Chen, 2020). However, there are some other reasons are also behind this concept. Apart from earning interest, money can also be invested in order to earn profit. Hence, the profit potential of money is foregone for the period when it is received late (Rahman, 2018). There is inflation that can decrease the purchasing potential of the money. This is because due to inflation, the money would be able to buy fewer commodities in future than it is today. Thus, the real value of money will decline in future (Rahman, 2018). Then, there is an element of risk when the money is lending to someone that the money may not be paid back. In order to compensate for that risk, interest is charged as the risk reduces the value of the money (Rahman, 2018).

Terms related to TVM

The present value of money is the future value of money discounted to the current day or the present value of a series of payments which is total of every future payment discounted at the current date. An appropriate interest rate is used to discount the amounts. This interest rate corresponds to the actual earning potential of the money.

The future value of money is the amount expected to receive in future, after adding the cumulative earnings of a payment or a series of payments till that specific future date in to that payment or series of payment. The interest is compounded like it is reinvested and earns further interest.

Time value of money principle: It is a principle that is used to compare two different cash flows pertaining to two different projects of companies for investment purpose. The objective behind this principle is to state the return that each investment option can provide.

Number of periods: It is the time periods to which a payment or series of payments is discounted or inflated in order to calculate the appropriate return.

Time Value of Money Formula

Generally, the time value of money formula depends on a particular situation and may change slightly in response to the particular situation in question. For example, the formula used to calculate perpetuity or annuity payments may use less or additional factors. However, generally, a TVM formula takes into account the following variables.

FV = Future value of money

PV = Present value of money

i = interest rate

n = number of compounding periods per year

t = number of years

Based on these variables, the formula for time value of money is;

FV = PV x [ 1 + (i / n) ] (n x t) (Chen, 2020)

Importance of Time Value of Money Concept

Time value of money is a very useful concept. It is widely used in finance to make important decisions. It is particularly used in making investment decisions. Investment decisions are the decision to invest funds in the long run. Time Value of money technique help investors to compare the cash flows from two or more different projects whether they occur uniformly or at different points in time in future by discounting at the present date. In this way, the investor can choose the best project among the available projects. Time value of money also helps in making financial decisions. These decisions are taken in order to optimise the capital structure of firm, like raising funds through debt, equity or any other source. Through TVM, a firm can compare the cost of different resources by using effective interest rate. The present cost of different resources can be compared to make the best decision. Operational decisions are also optimized with the help of TVM. For example, the optimum debtor or creditor cycle can be decided using TVM (Rahman, 2018),

Application of TVM in Real Life

There are numerous applications of TVM in real life. Some most prominent of these applications are as follows,

Asset Replacement and valuation Problem

TVM helps to find out the amount of money a company would require replacing an asset in future and so the company can set aside a certain amount of money for that purpose. For example, if a company needs to replace a machine in 3 years’ time, it can calculate the amount of money that would be required today or in future and then can budget accordingly. In the same way, TVM helps in valuing investment in equity, debt, fixed deposits etc. (Rahman, 2018).

Investment Problem

Time value of money helps to find out the implicit rate of return of an investment. For example, “Company offering to pay Rs. 201,475 at the end of 10 years with deposit of Rs. 15,000 p.a. How much implicate rate of return ABC ltd is offering to its customers? Outcome: Company is offering 5.3% of annual return”(Rahman, 2018).

Loan Repayment

TVM helps to find out the true cost of a loan and how much money the company would be paying over the life of the loan and in each periods, so that the company can arrange the money accordingly or add it into its budget. For example, if a company takes a loan of $10 million and wants to pay it over 5 years in five equal instalments, through TVM formula, the company can find out the amount of instalment it would be paying in each period (Rahman, 2018).

Profit Problem

TVM also helps to identify the cumulative growth rate and how much growth the company requires in sales and income in order to achieve a certain profit target. For example, if a company targets to earn a profit of 10 million in 3 years’ time, TVM can help in calculating the growth rate it requires for this purpose (Rahman, 2018).

(b) How the structure of interest rates guides individuals to make investment decisions that are most desired by society as a whole.

Interest rates are very important aspect of modern economic system. The interest rates impact the returns on investments and savings and the cost of borrowings. Interest rates are also indicators of economic and financial market activities in future. Interest rates play several functions in economy and provide trade-off between present and future consumption. For example, on the basis of the interest rates, households decide whether it is worthwhile to save or invest in business or consume (Taylor, Greenlaw, 2020). Interest rates are also used as a term at which the goods or money can be traded off at a future date. They are in fact the price of money. For example, if one decides to save his or her money in a bank account, the alternative earnings potential of the money forgone in this case is the price of the money (Bergo, 2003). The interest rate is also utilised as an instrument in the economic policy. The interest rates are set in a way in order to achieve financial policy objective, like low inflation or price stability or increasing inflation in case of stagflation. In the same way, it regulates the behaviour of the households regarding savings, consumption and investment. When the interest rate is low, it is less beneficial for the households to save money and thus they either consume it or invest it in businesses where they can earn higher return. In the same way, when interest rate is lower, it is more beneficial for the firms to take debt in order to growth their business. This is also useful for the firms because low interest rate boost consumption that boosts the demand. “In the longer term, the interest rate level influences capital accumulation in the economy and the potential for economic growth. The equilibrium interest rate is the rate, which ensures that capital accumulation corresponds to saving in the economy. This results in an output potential that over time satisfies demand without generating pressures in the economy” (Bergo, 2003). Thus the interest rate regulates the behaviour of the households and investors and they make the investment decisions that are most beneficial for the economy. The government can use the interest rate as a tool to influence the behaviour of the households in the design manner (Bergo, 2003).

Explain how state preference theory is a useful way of looking at firm investment decisions under uncertainty.

A major part of Finance is about the matters of investment decisions of organisations and firms through connecting with the source of demand and supply for securities in the capital market. Organisations receive capital on credit for investment purposes in real assets through the sale of securities; a person receives claims against the organisation’s assets through investment in securities. So, securities provide opportunities for an individual’s choice of investment in consumption against time through financing fruitful activities (Adair, Berry, and McGreal, 1994). These are the Organisation’s decisions that decide about aggregate security supply and an individual’s consumption and/ investment decisions, which decide aggregate security demand both are interconnected with security prices. Through the connection between demand and security supply, security prices produce consistent sets of individual and company’s investment decisions (Adair, Berry, and McGreal, 1994). Personal decision making under the factor of uncertainty is achieved through the increasing utility of end of period payoffs which were expected like selecting the high rate of utility, the productive investment is finalised. A person can analyse the probability of security distribution of end-of-period payouts. Hence, the utility criterion which was expected is the way of selecting in between exclusive investments with the different probability distribution of end of period payouts (Adair, Berry, and McGreal, 1994). Investment decisions for Securities by and individual are selected through a person’s choice to get a consumption pattern for a particular period. Normally, this period contains the uncertainty factor. So, when investor selects an investment then he has selected some distributions for future returns. Particularly the worth of security or amount of consumption depends upon the state of the economy. Uncertain values of securities can be shown as a vector of probable payouts on somewhere of future dates. A person’s portfolio will become a matrix of possible payouts for different securities which made his portfolio. In-state preference model, uncertainty is an inability to decide about which state will remain in at some future time or date. For an investor, security is a set accompanying different payouts and each payout contains different state of nature mutually (Tirimba, 2014) Hence, security represents a claim to a vector or bundle of state-contingent payouts. When the uncertainty factor of the world is revealed at once, then payoff on securities can be exactly determined. The probability of associated period security payouts is equivalent to the probability of the state of nature which is occurring. Thus once again, the nature of the state is assumed to determine fundamental reasons for economic uncertainty in the economy (Tirimba, 2014).

When the state of nature is once determined end-of-period security payouts on every risky security will also be determined. So by finalising individuals' securities holding and then against individuals, it will follow that if the state of nature is determined at once then aggregate end-of-period value and individuals will also be determined at the same time (Tirimba, 2014). In-between infinite numbers of states of nature and also an infinite number of end of period payouts for assets having risky nature, set of states should be mutually different and also exhaustive as well like, only one state of nature will be occurring and that would be ∑ρs=1. (Lewin, 2006) In the equilibrium of the capital market, prices of the market are set in that way that supply and demand become equal. In-state preference framework, a condition that is compulsory for market equilibrium needs any two portfolios with the same state-contingent payout vector should be priced differently. This is condition is also known as single price law of the market. (Tirimba, 2014) If this law is not applied then every individual would like to purchase a security at a lower rate and would like to sell them at higher price and if both securities are lying under positive supply, then prices will never represent equilibrium of the market. If short selling is has permitted in the capital market, then we can achieve the second necessary condition which is related to market equilibrium – there will be a deficiency of riskless arbitrage opportunity. In the condition of short sales, if security prices decrease during the period of the short sale, then an individual can earn profit and if security prices rise during this period then he has to bear the loss. But in both cases, the owner’s profit or loss is opposite to the profit and loss of short-sellers. Let take an example, let suppose that two portfolios having identical payouts in all types of states were sold on different prices where pA>pB. Then, there will be a possibility to sell short A and purchase B. Resultantly, there will be riskless gain in the current period pA – pB. Since it is assumed that, all investors prefer more gain to less, and then this arbitrage opportunity is very inconsistent with the market equilibrium. In the situation where the capital market is complete and, then any market security payout vector can be accurately replicated through a portfolio of pure securities and thus, it follows that, if short selling is permitted, the no-arbitrage gain situation needed that price of market security should be equal to the price of linear combinations of pure securities which will replicate market security’s payouts vector. In order to determine that, what finalises the price of market security, we should have the knowledge about, what how the price of pure security is determined as market security can always be determined through the set of pure securities available in the complete market (Tirimba, 2014).

Prices of pure securities will be exhibited to depend upon:

Time preferences productivity and also the consumption of capital

Expectation about the probability that a specific state will occur

A person’s attitude regarding risk provided and towards variability across all states of aggregate end of period profit or gain.

Through relating a riskless asset, the relation among time preference and prices of pure security can be easily seen.

A riskless asset can be defined as an asset that provides the same return in every state. Let take an example, that the asset provides one dollar in each of three given states. The price of the said riskless asset would be as p1+p2+p3=0.8 or the sum of prices of all pure securities. Price of riskless claim against a dollar at the end of a period is a present value of a dollar at a risk-free rate which is written as rf i.e. [1/(1+ rf)]=∑ρs. The actual size of the interest rate will show individual time reference for the consumptions and the productivity of the capital. The second determinant of security prices is the people who believe about the linked likelihood of every given state π. This is a feature that causes differences in security prices. Said believes are known as state probabilities πs (Bowman, 1975). In principle, subjective belief concerning the probability of every state given can vary among all individuals. But, we normally presume that individuals always willing on relative probability or containing same or homogeneous expectations (Bowman, 1975). When homogeneous expectations were given, prices of pure securities can be decayed into the probability of state (πs) and price for expected dollar in states will remain as θs i.e. Ps = πs × θs. The price of the anticipated dollar is the same among all states. The price of pure securities may be different because of the difference in the probability of state. Let’s see all this in some easy ways: The price of pure security is equivalent to the anticipated end of period payouts which is discounted on its anticipated rate of return. So if θs were indifferent among all states, then the expected rate of return will be the same for all sets of securities (Bowman, 1975). Probabilities among all states are different, and then expected payouts among securities must be different as well. If anticipated payouts change, then anticipates return may be the same only if the price of pure security changes proportionality with a probability of state. The third determinant of prices for security and also the other reason for the variance in those prices are based on a person’s attitude for a risk. If an individual is a risk-taker, then they will diversify their concerning holdings to decrease variability of usage in the next period (Bowman,1975) When the price of a dollar depending on the state (θs) are the same or equal in every state, then risk lover investors will invest with equal capital in every pure security. This will remove the uncertainty factor regarding future wealth. But, on the other hand, if every individual can perform the same and aggregate of wealth is different in each state, there is multi-dimensional risk present in the economy (Bowman,1975). For an example, if the future economy contains three possible states and the first state was with a probability of less gain which provides $ 1 billion. The second state was considered as average yielding with a probable gain of $ 2 billion and the third state was assumed with a booming economy which will yield around $ 3 billion.

On average, investors present in the economy have to give portfolios of (X 2X 3X). Thus, even if an individual is risk-takers, wealth in every state should not be the same. For undertaking given differences, θs change in between all three states. Particularly, θs will be very high in the first given state where wealth is more unusual. Now when aggregate wealth is not different in some states then risk-takers investors would like to hold the same number of pure securities for all given states and then prices of anticipated dollar payouts will be the same in all states as there will be no reason for indifference. Investors will not prefer to hold an unbalanced number of claims to the provided states having the same aggregate wealth reason is this will result in bearing the risk that may be having diversifies nature and now there will be no reason for anticipating return against diversified risk (Bowman,1975). Provided with the state preference theory there is a possibility for formulating portfolio choice issue in an anticipated utility fashion with a reason that market security may be explained as combination of Arrow-Debreu securities or also as pure securities assume that portfolio selection issue is a simple problem of selecting Arrow-Debreu securities that enhances utility provided wealth constraint.

Question: Compare and Contrast the capital asset pricing model (CAPM) with the arbitrage pricing theory (APT).

Capital Asset Pricing Model (CAPM)

The CAPM (Capital Asset Pricing Model) is a valuation model for financial assets. It is a theoretical model based on market equilibrium. That is, it is assumed that the supply of financial assets equals the demand. The market situation is one of perfect competition and, therefore, the interaction of supply and demand will determine the price of the assets. Furthermore, there is a direct relationship between the return on the asset and the risk assumed. The higher the risk, the higher the profitability so that if we could measure and grant values ​​at the assumed risk level, we could know the exact percentage of potential profitability of the different assets (Mcclure, 2019). It should be noted that the CAPM model only takes into account systematic risk. However, the total risk of a financial asset also includes unsystematic or diversifiable risk, that is, the intrinsic risk of the security in question.(Rossi 2016)

CAPM model formula

The CAPM model tries to formulate this reasoning and considers that the profitability of an asset can be estimated as follows:

E (ri)= rf + β [E (rm) – rf]

E (ri): Expected rate of return of a specific asset, for example, of an Ibex 35 share.

rf: Return of the asset without risk. Actually, all financial assets carry risk. So we look for lower risk assets, which in normal scenarios are public debt assets. Beta of a financial asset: A measure of the sensitivity of the asset with respect to its Benchmark. The interpretation of this parameter allows us to know the relative variation of the asset's profitability with respect to the market in which it is listed. For example, if an IBEX 35 share has a Beta of 1.1, this means that when the IBEX rises 10%, the share will rise 11%. E (rm): Expected rate of return of the market in which the asset is listed. For example, from the IBEX 35, Decomposing the formula, we can differentiate two factors: rm - rf: Risk associated with the market in which the asset is listed. ri - rf: Risk associated with the specific asset. Therefore, we can see that the expected return on the asset will be determined by the value of Beta as a measure of systematic risk (Rossi 2016).

CAPM Model assumptions

The model assumes several assumptions about the behaviour of the markets and their investors:

Static model, not dynamic. Investors only consider one period. For example, one year.

Investors are risk averse, not risk prone. For investments with a higher level of risk, they will require higher returns.

Investors only attend to systematic risk. The market does not generate higher or lower returns for assets due to unsystematic risk.

The return on assets corresponds to a normal distribution. Mathematical hope is associated with profitability. The standard deviation is associated with the level of risk. Therefore, investors are concerned about the deviation of the asset from the market in which it is listed. Therefore, Beta is used as a measure of risk.

The market is perfectly competitive. Each investor has a utility function and an initial wealth endowment. Investors will optimize their profit based on the deviations of the asset from its market.

Arbitrage Pricing Theory (APT)

Also known by its English acronym APT (Arbitrage Pricing Theory), it is an asset valuation equilibrium model. Its central idea is that the expected profitability of an asset must be a linear function of its systematic risk, measured by a series of beta coefficients associated with many other common explanatory factors. In this sense, like the Capital Asset Pricing Model (CAPM), the APT considers that, the only risk, which the market is willing to pay, is systematic, since the rest of the risk can be eliminated via diversification (Nickolas, 2019).

Historical Perspective

The capital asset valuation model (CAPM) has emerged, with its different versions, as the benchmark asset valuation model in the world of finance in general. However, this model is not without criticism, among which is that of simplifying the systematic risk of the securities, measured by the beta, in a single source. In order to overcome the previous criticism, as well as other limitations of CAPM, the APT was born. This theory was formulated by Stephen A. Ross (1976) and is based on the principle of absence of arbitration using a factorial model to obtain it. Although Stephen A. Ross has not received any Nobel Prize in Economics for his contribution in the field of financial economics, there were two other academics Myron Scholes and Robert Merton who received it in 1997 for their work on derivative asset valuation, in which they already used the principle of absence of arbitration in their reasoning (for more information, consult the website of the Nobel Foundation) (Nickolas, 2019).

Mathematical Foundation

The derivation of the APT only requires the fulfilment of three starting assumptions:

- There are no arbitration opportunities.

- The returns of the securities can be described using a factor model.

- The existence of numerous securities traded in the market allows the diversification of the idiosyncratic risk of investments.

As has been included in the definition of the APT, the essential idea of ​​this model is that the expected profitability of an asset is a function of its systematic risk, measured by a series of betas associated with many other common explanatory factors. Mathematically, we can express the previous idea in the following way:

E (ri) = rf + λ1 · βi1 + λ2 · βi2 + ... + λk · βik

Where E (ri) is the expected return on asset i; rf the return on the risk-free asset; λL the risk premium with respect to factor L, and βiL the beta coefficient of asset i with respect to factor L. The previous lambdas or factor risk premiums indicate how much extra return is obtained for each unit of risk that asset i present. The interpretation of the previous mathematical formula is direct: in a market in equilibrium, the return that an investor expects to obtain from an asset is equal to that which would be obtained from a risk-free investment plus compensation for the systematic risk that it has to bear. This compensation, in turn, is given by the different risk premiums with respect to the k common explanatory factors of profitability, multiplied by the corresponding beta coefficients with respect to each of the k factors considered (Nickolas, 2019).

Comparative Analysis with CAPM

APT and CAPM are different approaches to asset valuation, but they are not necessarily contradictory. In fact, the CAPM could be considered a particular case of the APT, when a single explanatory factor is considered for the profitability of the investments and this factor is given by the market portfolio. In the academic field, there is a general consensus when APT is considered a more robust model than CAPM for the following reasons: - It does not make any assumption regarding the empirical distribution to be followed by the yields of the securities. - It does not establish strong assumptions about the utility functions of individuals; at least nothing stronger than rationality and risk aversion. - It allows the profitability of the securities to depend on many factors and not just one. - It further establishes a relationship on the relative price of any set of assets. Thus, it is not necessary to measure the total universe of assets to test the theory. - It does not assign any essential role to the market portfolio. - It can be easily extended to a multi-period framework. Notwithstanding the foregoing, the theoretical apparatus on which the APT is based is more complex than that corresponding to the CAPM, which together with the fact that its empirical contrast is more complex and its practical use much less accessible, make the APT a “promise” model, which still resists being a reality. In this sense, it is necessary to show that the APT does not establish anything about what should be the common explanatory factors of the profitability of the securities, offering investment managers and intermediaries the opportunity to decide which are the most important, but leaving open a problem for academic research and its application in the professional field. Finally, APT can be used for similar applications to CAPM, both in the investment field and in business decision-making (Nickolas, 2019)

Explain the five axioms of choice under uncertainty. Show and explain: (a) How these axioms lead to the development of utility functions. (b) The definition of risk premia and the development of Pratt-Arrow risk aversion. And (d) the development of mean-variance as choice criteria

The choice or a decision a consumer makes when the outcomes are uncertain is known as choice under uncertainty, where it becomes difficult for the customers to make effective choice of the bundles of goods and services. Decision making behaviour is analysed through two parts, one is abstracting a real situation to math and another is cranking through the math to the answer. In order to make effective choice under the uncertain situations, there are five axioms, where the behaviour of the customers is to follow the axioms and make the ultimate purchase decision. The five aims are such as probability, order, equivalence, substitution and choice. Through these phase, the customers can fulfil its utility in long run. The first axiom is probability, which is to quantify any uncertainty to the choice where probability will be measured in such uncertain situation. The second axiom is order, where the individual is willing to order to bundle of goods and services which is known as transitivity of preferences. Equivalence is another axiom, where the customers try to find equal opportunity in the market where for example, the individual prefer basket A to basket B. substitution is the next axiom of choice under uncertainty, where the individuals are willing to substitute an uncertain deal for a certain deal where the customers search alternative baskets to make the deal under certain circumstances. The fifth axiom is choice, in which the individual has the scope to choose the best deal where it would be effective to maximise the utility of the consumers. Utility function is the concept of measuring the references of the customers over a set of goods and services. Utility represents the satisfaction that the consumers receive for choosing and consuming a particular basket of goods and serve ices. The utility function is the measurement of welfare or satisfaction of the consumer as functions of consumption of real goods such as food, clothing etc. Utility function is helpful to measure the choice and references of the customers. Here, the above mentioned five axioms of choice are effective to develop the utility functions where it is possible to analyse the particular basket of the products and services that make the consumers satisfied. Hence, the five axioms help the customers to make effective purchase decision for the particular basket of goods and services as well as improve utility. The first axiom is fruitful, where the customers can measure probability of the risk or uncertainty in choosing the basket of goods, and second axiom or order is also effective to develop the utility function. The utility functions include the consumption of the referred good and services and the added up volume is considered as total utility. Hence, the axioms of choice are effective to develop the utility functions. Apart from the two axioms, the third axiom is Equivalence, where the consumers can identify the similar products and analyse the satisfaction for consuming the products. The fourth one is substitution where before making effective purchase decision, the consumers try to identify the substitute products in the market with similar values of the products and services and here, it is also effective to develop the utility function of the consumers. The fifth axiom is choice, where the customers try to make effective decision for the particular basket of goods and services in a certain situation to maximise the satisfaction level and it further determines the utility of the consumers. Risk premia is the minimum amount of money by which the expected return on the risky asset must exceed the known return on the risk free asset. In such situation, the consumers are influenced by holding the risky asset rather than risk free asset and it is positive if the person is risk averse. Risk premia strategies target the absolute return through long and short term investment across various factors an asset classes and the risk premia products are tend to be much cheaper and more transparent than the hedge funds. The people are beneficial of holding such equity or shares where the asset outperforms in the market. The risk averse person likes to have lower return with known risk rather than higher return with unknown risk. Pratt-Arrow risk aversion is calculated by absolute risk aversion where the value of the absolute risk aversion greater than zero indicates the risk averse investors. If the absolute value of risk aversion decreases, wealth will increase. Hence, through the analysis of Pratt-Arrow risk aversion, it is possible to make effective choice for the asset which has effective return on investment with low risk. Mean variance is the analysis of the portfolio of asset such that the expected return is maximised for a given level of risk. It is the process of weighting risk for expressing the variance against the expected return and the investors uses the mean variance technique to make the decisions about which financial instruments are effective to invest in, based on the how much risk the person is willing to take on in the exchange for different level of rewards. It is calculated by extracting the average value of the sample where the investors can make rational decision by having all the sufficient information. The efficient portfolio is the one offering the highest expected return for a given level of risk as measured by men variance. Hence, mean variance is effective to select the best portfolio as well as it helps the consumers to diversify the risk and choose the low risk portfolio for higher value optimisation.

The term of real options was established by Stewar Myers in 1977, to refer to the application of option theory in the valuation of non-financial assets, specifically to investment in real assets that have a flexibility component, such as investment in research and development and in the expansion of manufacturing plants (Yeo, &Qiu, 2003). Real options are a method of valuing investment projects based on the premise that real investment projects can resemble financial options (call and put) and not a portfolio of risk-free bonds like the NPV, which leaves It is useful when situations arise in which the project does not necessarily have to be carried out immediately, that is, be carried out later or in parts (contingent growth) In other words, the focus of real options is the extension of Financial Option Theory to options in real (non-financial) assets that allow modifying a project with the intention of increasing its value (Yeo, &Qiu, 2003). Real options allow you to add value to the business, by increasing profits or reducing losses. The term option is often not used to describe these opportunities, rather they are referred to as intangibles rather than call or put options, but when evaluating major investment proposals, these intangible options are often the key to the decisions. The analysis of real options is essential in the following situations according to Schulmerich, (2005),

When there are contingent investment decisions. Another class of approaches cannot correctly value this type of opportunity.

When the uncertainty is extensive enough and it becomes sensible to wait for more information, avoiding regretting irreversible investments.

When the uncertainty is large enough to take flexibility into account. Only the real options approach can correct the value of flexibility investments.

Generally, the opportunity to invest depends on more variables than the NPV or IRR of the project. Kester (1984) considered that, the four most relevant factors that influence the opportunity to invest are:

The time during which you can decide to carry out an investment project.

The risk of the project.

The degree of exclusivity of the company's right to accept an investment project. The exclusive options are logically more valuable and result from patents, from the exclusive knowledge of the market by the company, or from a technology that the competition cannot imitate. Shared opportunities generally have a lower value.

In the traditional view, a high level of uncertainty leads to a reduction in the value of assets. The real options approach shows that, increased uncertainty can lead to high asset values, if managers identify and use their options to respond flexibly to unfolding events. One of the most important changes in the approach of real options: the uncertainty creates opportunities. Rethinking strategic investments, managers should try to see the markets in terms of the origin, direction and evolution of uncertainty, thus determining the degree of exposure of their investments and, then, respond to position them and thus obtain a better benefit from them.

Financial options as the basis of real options

Options and futures are the main modalities of financial derivative instruments used to minimize risks in financial business operations, isolate the company's economic activity from fluctuations in financial markets and increase the effectiveness of business forecasts, facilitating the trust in management, providing greater security for the company's transactions abroad (Schulmerich, 2005). An option grants the right, but not the obligation, to buy or sell a specified amount of an underlying asset (a share, a commodity, a currency, a financial instrument, etc.) at a pre-established price (the strike price) within a certain period (Schulmerich, 2005). There are two types of options: call options and put options. The call option or call option grants the right, but not the obligation, to buy a certain quantity of a good at a certain price, to be exercised during a certain period. On the contrary, the put option or put option grants the right, but not the obligation, but to sell a quantity of a good. In both cases, to acquire this right, a premium must be paid (Schulmerich, 2005). The options can be American or European, the only difference is that the American option can be exercised at any time during the life of the contract, while the European option can only be exercised upon expiration. The possibility of exercising the right to the option at any time makes American options more valuable than European ones. However, this makes American options more difficult to value. Option pricing models are based on the consideration of the following variables: price of the underlying asset, exercise price, time to expiration, interest rate and market volatility (Schulmerich, 2005).

3. TYPES OF REAL OPTIONS

3.1. Option to alter scale of operation

This option is divided in turn into following types,

Expand. The option to expand production or the operational scale of a project if conditions are favourable, or decrease it if it is unfavourable, is a real option equivalent to an American purchase option. The expansion options include the possibility of choosing the size or dimension and the possibility of making continuous investments (investment in stages) ("Real Options - Learn the Different Types & Pricing of Real Options", 2020).

Contract. If the conditions turn out to be negative, the company can make the decision to operate with a smaller size than the existing one, that is, with less productive capacity. This decision would allow the company to reduce or save part of its costs. This option can be compared to a put option on part of an initially planned project, the strike price of which is the potential costs saved ("Real Options - Learn the Different Types & Pricing of Real Options", 2020).

Stop and restart or temporary closure of operations. Sometimes, companies have the possibility to temporarily stop their productive activities when the income obtained is not enough to cover variable operating costs and then start again when the situation is more favourable. Closing or stopping activities also involve costs, as well as restarting them ("Real Options - Learn the Different Types & Pricing of Real Options", 2020).

Option to permanently abandon or close operations

It must be disinvested when the project is not economically justified. Once the project is no longer profitable, the company will cut its losses and exercise this option to abandon the project. This actual settlement option provides partial failure insurance and is formally equivalent to an American put option with a strike price equal to the sale value of the project (Yeo, &Qiu, 2003). The total value of a project must consider its abandonment value, which, generally, is not known at the time of its initial evaluation, but depends on its evolution in the future. There are two important questions to consider in the analysis of the abandonment value (Yeo, &Qiu, 2003).

The need to take it into account, in some way, in the investment decision.

The determination of the moment or time interval in which said abandonment value reaches its maximum value.

The total value of the project would be its own cash flows plus the value of the put option. A project that can be liquidated is worth more than the same project without the possibility of abandonment. The reality of globalisation and internationalisation of markets, including financial markets, has altered the perspective from which finance and the world are viewed. The markets have become more sophisticated, new instruments and approaches have been created that, with the evolution of knowledge and the appearance of new theories, have brought with them numerous and substantial advances in the world of finance. All of these require efficient financial managers to modify their way of acting and operating to ensure that they make sound financial decisions and that they respond to the requirements of the firms. However, until now the real options are a subject little studied in academic institutions and much less used in companies, a particularly tangible situation in the construction sector (Yeo, &Qiu, 2003).

Disadvantages of Using Real Options for Financial Investment Decisions

The use of real options for financial decision making is most suitable when the environment and market conditions relevant to the particular project are very flexible and volatile. It may not benefit the rigid or stable environments much and it is more appropriate to use traditional corporate finance techniques for such projects. In the same way, Real Option Valuation is applicable in the case where the corporate strategy of a company offers flexibility, has enough information flow, and has appropriate amount of funds to cover the potential downside risks that are associated with the use of real option valuation technique (Kenton, 2019).

Conclusion

Real options currently become a good tool for evaluating investment projects in conditions of risk and uncertainty, which are not taken into account by traditional investment valuation methods, such as the net present value (NPV), the internal rate of return, among others. There are many options, which can be effective throughout the life of a project (not everything has to be carried out as initially planned) and therefore, a project that values ​​and considers these options would be worth more than one that does not. Likewise, the influence of intangibles in decision-making is growing considerably, but in many situations they are not quantitatively valued. The real options thus become a necessary path to explore in the valuation of investment projects, so that operational flexibility is taken into account, allowing decisions to be made more in line with an increasingly changing reality. Like all the methods that are just beginning to be studied and applied, the real options cause some resistance, when used as an efficient method for decision making. It is still being evaluated with traditional methods and these evaluations with alternative methods such as real options are utilised more as supplementary information. On the other hand, the information used in sectors such as construction is quite informal, so making certain assumptions has some degree of difficulty. However, it is necessary to continue developing applications in this and other sectors in which uncertainty is quite high, so that this, in addition to intangibles, can be included for more efficient decision-making.

Question: Explain the importance of corporate governance in valuation.

Introduction

The objective of this paper is to explore the impact of the corporate governance practice on the company valuation. A popular answer to the question regarding the importance of corporate governance in the company valuation is that corporate governance does not matter much when it is working well. However, when it fails, it impacts the companies severely. As a matter of fact, beyond extreme cases of governance failures, it is quite difficult to answer this question. However, the paper will strive to identify the answer to this question by qualitatively reviewing authentic literature.

Corporate Government

Corporate governance is the set of rules, principles, and procedures governing the structure and functioning of the governing bodies of a company. Specifically, it establishes relations between the board of directors, the board of directors, shareholders and other interested parties, and stipulates the rules that govern the decision-making process on the company for the generation of value (Corporate Governance Principles and Recommendations, 2017).

Importance of Corporate Governance

In recent years, and more specifically as a result of the onset of the financial crisis, the international community has understood the importance of listed companies being properly and transparently managed. Good corporate governance is the basis for the functioning of markets, as it increases credibility, stability and helps to boost growth and wealth generation (Corporate Governance Principles and Recommendations, 2017) The weakness shown by the corporate governments of large organisations in the past has multiplied the demands for transparency, truthfulness, good practices and responsible business behaviour by investors, consumers, and society in general, which not only pay attention to the financial indicators, but they also want to know how those results have been achieved (Corporate Governance Principles and Recommendations)

Corporate Governance and Company Valuation

Wernick (2018) said that, “firms’ governance significantly affects their share prices and firm value. Second, given that the two studies came to the same conclusion despite using differently sized indexes suggests that not all governance provisions and rules always matter equally.” Companies, and especially listed companies, have begun to realise that transparency is an asset that they cannot do without. And not only because the Transparency Law, which came into force last July and was developed through a ministerial order earlier this year, requires compliance with certain requirements. Furthermore, having good governance principles, complying with and explaining them can be a profitable investment. Corporate governance is a strategy for creating value in companies. The growing activism of institutional investors, the existence of increasingly eloquent empirical evidence that corporate governance is indeed a strategy of creation of value and the suffering in the very skin of loss of advantages on the part of the companies more reluctant to adapt to the new standards have determined a strategic change, which is already being seen on the horizon of our market (Wernick, 2018). Some studies indicate that, on average, good corporate management implies a premium to the share price. It is not that good government to avoid the accounting fraud, but that its main objective is to ensure what profit growth occurs. Transparency ensures the responsibility of directors and managers creates value for the company and favours responsible business practices. Good governance rules can be the main part of increasing companies' market value (Costa, 2017). However, a recent survey carried out by PricewaterhouseCoopers indicated that, 70% of those interviewed considered that measures such as introducing independents to councils were cosmetic and opportunistic. According to the survey, it was expressed by the participants that an upcoming stock market rise would forget the companies' concern for good governance (Dart, 2007). Despite these opinions, the occupation by the good government is evident. Today companies think of good government because analysts, institutional investors, and society ask for it. The companies know that if they do not implement good corporate governance practices, their valuation will be negatively impacted. On the other hand, good corporate governance will increase the confidence of analysts and investors (Skaife, Collins and Lafond 2004). The econometric studies available currently confirm that good corporate governance practices determine an increase in the value of the company or the share price. And thus, it results in a reduction in their cost of capital. The conjecture that corporate governance pays is thus corroborated. It is easier for such companies to get additional debt capital as compared to had they not implemented good corporate governance practices (Skaife, CollinsandLafond 2004). Companies are increasingly aware of its importance of corporate governance and give it more and more value. Analysts also take better account of corporate governance criteria. Market values ​​also reflect the information about whether or not good governance is being done well (Garayand Gonzalez 2008). The application of good corporate governance has a very positive influence on the valuation of a company and therefore on the listing of its shares. Today, most institutional investors, in addition to analysing their financial information, demand to know the degree of application of the principles of good governance to assess the interest of investing or disinvesting in listed companies. This trend also reaches small investors. Hence, good governance and transparency undoubtedly add value to the share price. The triangle made up of truthful financial information (Garay and Gonzalez 2008).

The value of intangibles

A recent study by Accenture also affects the reward that exchanges offer to companies that invest in these types of assets. While previously companies generated their future growth through tangible assets, such as buildings, factories, and equipment, in today's economy, based on services, every time more companies generate value from intangible assets, such as intellectual property, business integrity, brand reputation, customer loyalty, the talent of their professional team and leadership skills ("The Circular Economy Could Unlock $4.5 trillion of Economic Growth, Finds New Book by Accenture", 2020). According to data from the Accenture report, 94% of top company managers around the world say that managing intangible assets and those related to intellectual capital is a very important issue. 37% believe that, it is one of the three most important aspects and another 13% recognise that, it is the primary aspect. Likewise, 49% consider that intangible assets are the main source of long-term value creation for the shareholder. And within these intangibles, corporate governance is increasingly recognised as one of the most important contributions to the operation of companies ("The Circular Economy Could Unlock $4.5 trillion of Economic Growth, Finds New Book by Accenture", 2020). In a report, OECD noted that three-quarters of institutional investors consider that the variables related to good governance are already as important as those related to financial aspects when evaluating a company to make investment decisions. Companies are increasingly convinced that, good governance has an impact on their results. The problem is in quantifying it. What seems clear is that, good governance ensures managerial accountability, value creation, and responsible business practices. The most sophisticated investors have become fully aware of its fundamental importance and indeed appear to be willing to pay a substantial premium for the securities of a well-run company. This is because such companies are expected to perform better and provide good returns to their investment. Hence, it can be said that, the investors are aware about the fact that good corporate governance is associated with better performance for an organisation (Garay and Gonzalez 2008).

Conclusion

Thus it is evident from the above discussion that corporate governance has an important role in the company valuation. If a company has good corporate governance practice, it would be more valued by the analyst and investors, because it is expected to perform well. Such companies also have higher capital value as compared to the companies that do not have high capital value and thus able to secure more debt, which further helps in increasing the shareholders’ value. Different researchers also reached this conclusion that, corporate governance has a very important role in the value of the corporation. Thus the companies should focus on improving the corporate governance of the firm.

Explain (a) the value of cash and methods for valuing a firm's cash holdings. (b) Which would you expect to hold more cash: a good firm or a bad firm? Explain why

Cash Holdings and Firm Valuation

The cash held by the firms will be valued dollar against dollar by investors if capital markets are conditionally perfect. Thus, it is irrelevant if the firm pays out money as dividends or the firms hold it without paying. When firms pay out the in dollars to investors, it will always increase cash whenever it’s required for positive NPV projects. On the other hands, if there is imperfect situation in the market or agency costs occurs in between managers and concerning stock holders, or it conflicts among stock and bondholders, then the held dollars by the firms will not be valued dollar against dollar by investors.

2.1. Costs and benefits to cash holdings

Holding cash will not be a simply zero NPV investment, if there is imperfect situation prevailing in market. There are various motives for the organisations’ cash holdings and also he explained about protective motives and related transactions. Motive of transaction for cash holding is totally based on Orr (1966) and Miller (Ma, 2012) who argued that, cash is only held by the organisations for meeting daily transactions or daily needs. In 1997, Mulligan supported the transaction motive, where organisation’s cash holding is purely based on their activities, innovative modernity and also their cost of opportunities, both papers emphasis that economies of scale are present over there in cash holdings. Firms may also old cash for protective measures. In said case, organisation may also hold money for the purpose of investment in Positive NPV Projects during the periods when there is high financial cost externally. (Ma, 2012) This situation has great importance for the firms having Positive NPV investment opportunities but it’s really hard for them to generate required internal cash to take full advantage of it. It would suggest positive NPV to cash holdings by organisations that have higher probability of being more restricted out of market credits during tough time of credits. According to da Cruz et al., (2019), in 1999 Opler et al., found backing up support for protective objective of cash holdings. We will not debate on transactions motive for cash holdings in this paper because in said models, there is a focus on cash in hand instead of marketable securities. As we check marketable securities and cash at the same time, so we cannot and we will not conclude about transaction motive. So, the in this paper, our focus is on protective measures to hold cash so that during tough time when external financing will be hard to get, investment will be possible to continue (da Cruz et al., 2019). Tenkir & Haifeng (2020) say that, in 1984 it was it was discussed in Myers and Majluf about the firms who were maintaining financial flexibility that external financing become more costly due to unbalanced information between management and investors. Study of above mentioned personnel suggest a positive value for the firms having strong financial position and better growth opportunities. Lack of slack position, firms may choose positive NPV projects which will result underinvestment. It will be more prominent in the organisations having uncertainty upcoming investment opportunities, capital markets are too much slow in giving required capital, which cause the firms stop for further investment. As a result, now many firms may maximize shareholder value by keeping maximum cash in hand balance to avoid from above mentioned situation (Tenkir&Haifeng 2020). One dollar of cash has greater value then the dollar to investor, if cash held by the firm make the firm enable to work in project which enhances its value. Cash holding are more valuable for some shareholders when we look up at their operating performances. Study shows that performance of last five years of firms having rich cash was not very different as compare the firms which were not cash rich (Tenkir&Haifeng 2020). A large amount of cash held by the firms my get wasted by firms managers in NPV projects having negative value. So, he suggested that it would be much better for the management of firms that they should pay the cash in shape of dividends instead of cash and also future investment should be financed through debts. In 1984, Easterbrook claimed that if management is going to capital market on regular basis, then it will make their management more disciplined and it will also control their uneconomical behaviours towards the firm’s objectives. Above mentioned studies also claimed that firms can use capital markets to get more control on managerial resourcefulness. In 1999, Harford also supported argument of Jenses that, cash rich firms may result in decreasing value of procurements. Harford also revealed that cash sorting may result negative reaction by investor. And also in 1994, Lopez-de-salinas and shleifer explained that organisations spend cash indifferently having cash payouts. In the end in 1976, Jensen and Meckling explained about the conflict which was raised in between bondholder and stockholders on the induction of risky bonds in the firms. As on the value of organization, equity is call option, shareholder gives priority to a risky investment programmer (Tenkir&Haifeng 2020). Shareholders prefer liquidity on discount as cash holding is a risk free factor. It will be more prominent in the organisation where risk of financial activities is high as benefits of cash may grow to bondholders. In previous years, we have seen the battles between Kirk Kerkorian and Chrysler in which shareholders has force the management to pay out of excessive cash held over there with the firm. Depending upon the relation between marginal shareholder, marginal tax rates and the corporation, taxes may also play a vital role in deciding the worth of cash holdings.(Ma, 2012)

Estimated Marginal tax rates have a little bit impact on cash value. On request results can be seen from the authors. If shareholders show concern that management will not spend cash with responsibility or bondholder can take a benefit of liquidity of cash, markets may value the cash of the firms on less value on dollars against dollar. Previous study argues on both debates of need of cash of firms. Theory and the evidences shows that organisations should hold maximum cash as they can, but it can cost to the shareholders if it is held in large quantity. But question is how investors value the cash holdings and how value is determined by the investors? It is discussed below given sections. In the balance sheet, high level of cash may signal a danger in near future. If cash level is high or low in company’s balance sheet as a permanent feature, then investors may raise a question that why this money is being held and not being used. Cash may be shown in balance sheet either management is not sure where to invest this money or they are not about that if it will meet coming investment opportunities (Ma, 2012). Cash held has an opportunity cost, keeping this for long time may result expensive luxury because difference may occur in between the interest received on holdings and total price was supposed to be paid for having it as calculated company’s cost of capital (Ma, 2012). If the company can earn return of 20% on its equity by investing in a project or by expanding its business, it will be huge costly blunder to have cash in the bank accounts. If project’s profit is less than the cost of capital of the company, then cash must be handed over to its shareholders. Often, a cash rich firm bears a risk for being more careless. The firm may practice some sloppy habits, including less control on cash spending and also unwilling to control growing expenditures. Cash holding of large amount will reduce pressure on management to function (da Cruz et al., 2019).

How Companies Disguise Excess

Companies must not get into this fool statement that by holding large cash will reduce their pressure and they have more flexibility and also they can make procurements on speed whenever they feel it is required. Firms that have excessive cash carry agency cost where firms have tried to pursue territory building. In this frame mind, companies must take an eye on their balance sheet items particularly “strategic reserves” and also “restructuring reserves” as they can be used for storing of cash (da Cruz et al., 2019). It has been briefed about firms that investment funds should be increased in capital markets. Capital markets bring higher discipline and higher transparency for making investment decisions, and it will also decrease agency costs. Cash load will make companies skirt in open process and also to avoid scrutiny that moves with this, but normally it will cost to the investor’s returns (da Cruz et al., 2019). Thus, a good firm is not expected to hold large amount of cash and instead, it is a bad firm that would hold a large amount of cash.

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