Principles OF Finance - Lecture notes 1-10 PDF

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BS2100 with Richard Payne...

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Principles of Finance 1 Present Value 2 How to Calculate Present Values 3 Value of Bonds and Common Stocks 4 Valuing Government Bonds 5 Risk, Return and the Cost of Capital 6 Portfolio Theory and Asset Pricing 7 Market Efficiency 8 Forwards and Futures 9 Put and Call Options 10 Option Pricing Theory

Corporate Finance Organisations invest in real assets, which generate income. Some of these assets, such as plant and machinery, are tangible; others, such as brand and patents are intangible. The investment decisions involve spending money, the financing decision involves raising it. The secret of a success in financial management is to increase the value, ideally maximise it. Investment decision = purchase of real assets Financing decisions = sales of financial assets

Consideration To carry on a business, a corporation needs an almost endless variety of real assets. The corporation pays for the assets by selling claims on them and on the cashflows they will generate. These claims are called financial assets or securities. Securities include bonds (fixed incomes), shares of stocks, etc. Investment decision = purchase of real assets Financing decisions = sales of financial assets A Corporation is a legal entity. In the view of law, it is a legal person that is owned by its shareholders. As a legal person, the corporation can make contracts, carry on a business,

borrow, or lend money, and sue or be sued. A corporation’s shareholders have limited liabilities (Ltd.) which means that: shareholders liabilities are limited by the amount of capital they invest. Corporations face two main financial decisions. First, what investments should the corporation make? Second, how should it pay for the investments? (investment and financing decision). The stockholders who own the corporation want their managers to maximize their overall value and the current price of its shares. The stockholders can all agree on the goal of value maximization, this, as long as financial markets give them the flexibility to manage their own savings and investment plans. Investment decisions involve a trade-off. The firm can either invest cash or return to shareholders, for example, as an extra dividend. When the firm invests cash rather than paying it out, shareholders give up the opportunity to invest it for themselves in financial markets. If the firm’s investment can earn a return higher than the opportunity cost of capital, stock prices increases. If the firm invests at a return lower than the opportunity cost of capital, stock price falls. Managers will consider their own personal interest (this conflict is called a ‘principal-agent problem’.     

Corporate finance is all about maximizing value The opportunity cost of capital sets the standard for investments A safe dollar is worth more than a risky dollar Smart investment decisions create more value than smart financing decisions Good governance matters

Lecture 1 Present Value computations

A discount rate is the reward that investors demand for accepting delayed rather than immediate gratification. Simple interest  the interest earned or paid is just the original balance of the deposit/loan times the interest rate. So over T periods, the total balance of your deposit/debt will grow to be X + r × X × T = X(1 + rT) Compound interest  interest must be paid on previously charged/earned interest. So over T periods, the total balance of your deposit/debt will grow to be X(1 + r)^T . Future values of cashflows  we are given a cashflow of X today. What value will this cashflow grow to if invested at interest rate r for T periods? FV (r,T) = X(1 + r)^T This amount is called the future value of X, assuming an interest rate of r and an investment period of T. Present values 

Discount factor  When computing present values, we often make use of it. it is just the PV of £1. Discount factor vary with the interest rate and investment horizon.

Net Present Value Most investments involve multiple cashflows received and paid at different points in time. Positives cashflows are receipts Negative cashflows are payments

Consider two investors; George (G) wants to consume now (he is impatient). Anne (A) wants to wait (she is patient). Both have current income of $185,000 and expect zero income in a year. Each can invest in an opportunity costing $185,000 now and returning a guaranteed $210,000 at the end of the year. They also have access to a risk-free bank where the borrowing and lending rate is 5% per annum. Both should choose to undertake the investment. The OPPORTUNITY COST of a project is the rate of return the other project (the one NOT chosen) would provide you. To calculate the Rate of Return: Return = Profit / Investment = 800,000 – 700,000 / 700,000 = .143, or 14.3%

Lecture 2 Perpetuities Investment that makes a level stream of cash flows forever (perpetuity) Investment that produces a level stream of cash flows for a limited period (annuity) Consider an asset that promises a fixed nominal cashflow at the end of every period from now until the end of time.

Perpetuities with growth At the end of one period one is promised a cashflow of C and at the end of each subsequent period, the cashflow promised growth at rate g. Thus, the second cashflow C(1+g), and the third is C(1+g)^2 …..

Annuities Normal cashflow streams, consisting of the payment of a fixed nominal cashflow, once per period but only for a known, finite number of periods.

Annuities with growth Consider a cashflow stream such that at the end of one period one is promised a cashflow of C and at the end of each subsequent period, the

cashflow promised grows at rate g. However, the cashflow stream terminates after T payments. This is an annuity with growth

Quoted interest rates and effective interest rates Convention Whenever we talk about interest rates we tend to scale them up or down so that they cover a period of exactly ONE YEAR.

Quoted Interest Rates Rate r is always annualised. The actual rate that you will pay/receive on a K month loan/deposit is K/12 r

Effective Interest Rates The effective (annual) interest rate is the actual interest you would receive on a deposit on an annual basis, expressed as a percentage.

Example: PVs when frequencies compounding differ

Computing payment and frequencies

If a U.S. Government bond promises to pay a semi-annual interest of 10% a year, the investor in practice receives interest of 5% every six months. Suppose a bank offers you an automobile loan at an annual percentage rate (APR) of 12% with interest to be paid monthly. This means that each month you need to pay one-twelfth of the annual rate, that is, 12/12 = 1% a month. Thus the bank is QUOTING a rate of 12%, but the effective annual interest on your loan is 1.01^12 – 1 = 0.1268 or 12.68%. This, demonstrates that we need to distinguish between the QUOTED annual interest rate and the EFFECTIVE annual rate. When interest rate is paid annually, the effective and quoted interest rate the same. When the interest is paid more frequently, the effective interest rate is higher than the quoted rate. If you invest 1$ at a rate of r per year compounded m times a year, your investment at the end of the year will be worth [1 + (r/m)]^m and the effective interest rate is [1 + (r/m)]^m – 1. In our automobile example r = .12 and m = 12. So the effective interest rate was [1 + .12/12]^12 – 1 = .1268 or 12.68%

Continuous Compounding

A deposit of X; an annual quoted interest rate of r (called continuously compounded interest rate); m periods per year where m tends to infinity. FV = Future value of an investment for T years at continuously compounded rate r Discounting in continuous time You will receive a cashflow of X in T years. You want to calculate the Present Value

Inflation rate: the (usually annual) rate at which the level of prices in the economy grows. Denote it by π Nominal interest rate: the rate at which the balance of a deposit grows in cash terms. Denote it by r Real interest rate: the rate at which the balance of a deposit grows in purchasing power terms. Denote it by i

Lecture 3 Bonds Bonds are called FIXED-INCOME SECURITIES They are so named as the cashflow they deliver to an investor, as well as the dates that these cashflows will arrive, tend to be known (fixed) in advance Bonds are borrowing/lending arrangements formalised in contractual form.  

The bond issuer is raising money (borrowing) The investor has delivered some money to the issuer (a loan) and expects to see his money repaid with interest over time

Zero-coupon bond A K-year zero-coupon bond promises the purchaser a single payment (face value), K years from the current date. The date of the payment is called the maturity date and K is the time to maturity. K-year coupon bond It promises the investor periodic cashflows:    

At regular intervals until maturity, the bondholder receives a coupon payment (payments can be made annually, semi-annually, or quarterly) Coupon payments are usually the same at every payment date The ratio of the total annual coupon payment to the face value is called Coupon Rate On the maturity date, the bondholder receives both a coupon payment and the face value

Bonds: Yield to Maturity After calculating the present value of the bond through the interest rate, we now turn the valuation around. If the price of the bond is known, what is the interest rate? What return do investors get if they buy the bond and hold it to maturity? To find this value, we solve for y (Example below) The YTM is the constant, hypothetical discount rate of return that, when used to compute the PV of a bond’s cashflows, gives you the bond’s market price as the answer. It is a transform of the price. We talk about YTMs rather than prices as prices can be very different across bonds due to different coupon rates; but yields are annual discount rates and thus much more easily compared A higher bond price must mean a lower YTM and vice versa

A bond, that is priced above its face value is said to sell at a PREMIUM (investors who buy a bond at a premium face a capital loss over the life of the bond, so the YTM on these bonds is always less than the current yield). A bond that is priced below its face value sells at a DISCOUNT (Investors in discount bonds look forward to a capital gain over the life of the bond, so the YTM on a discount bond is greater than the current yield).

Coupon rates are FIXED at the issue date, while prices and thus YTMs can VARY through the bond’s lifetime. Bond prices and interest rates (YTM) move in opposite directions.

Stock and stock markets Stockholders are the owners of the firm. They have the right to vote on company policy and strategy.

Definitions:

There are different ways to measure aggregate value of the company Market value – the total stock market value of the firm’s stock (price multiplied by number of shares outstanding)

Book value – accounting value of the firm’s equity as reflected on company’s balance sheet Liquidation value – the amount that would be available to shareholders if the firm was liquidated and all creditors paid off. Constant dividends and stock prices Assume that we expect all future dividends to be constant at D. The calculation to find the price is the same to find a perpetuity D = constant future dividend r˜ = Expected return required by investors

If we expect dividends to grow at constant rate in the future (g). We adopt the Gordon Growth Formula (for stock pricing). It implies that stock prices are higher when dividends or their growth rates are higher and stock prices fall when return rise.

Stock prices, earnings, and dividends Dividends must be paid out of a firm’s net earnings If a firm chooses to invest more today and pays a lower dividend, that might increase stock prices as it allows the firm to make greater payments in future

ROE, retained earnings and dividend growth  The rate at which a firm’s earnings can grow is governed by its ROE and its Plowback ratio..

Lecture 4 Nominal Interest Rate: The rate you pay when you borrow cash Real Interest Rate: The nominal rate adjusted for Inflation rate. Nominal Rate = Real rate + Inflation In certain views of the world (e.g. the Fisher hypothesis), the expected real rate of interest is constant. Term structure of Interest Rate  Relationship between short- and long-term interest rate. Relationship between spot rates and the time to maturity.

Cashflow to be received at different future dates should be discounted using different discount rates. If you are pricing cashflows, each cashflow has its own relevant interest rate depending on when it arrives. The PV of the entire stream is sum of each cashflow discounted at the appropriate interest rate.

FACTS When YTM Rise, bond prices fall. (vice versa) Long dated bonds are more sensitive than short bonds to YTM changes (as yields rise, the price of the longer dated bond declines more quickly than that of the short-dated bond)

Duration

Duration is a measure of the sensitivity of the price -- the value of principal -- of a fixedincome investment to a change in interest rates. Duration is expressed as a number of years. Duration is a direct relationship between the duration of a bond and the exposure of its price to changes in interest rates.

Bond prices are said to have an inverse relationship with interest rates. Therefore, rising interest rates indicate bond prices are likely to fall, while declining interest rates indicate bond prices are likely to rise. The bigger the duration, the greater the interest-rate risk or reward for bond prices

Modified Duration (also called Volatility) It is often reported for fixed income instruments. Useful as it can be employed to give approximate percentage changes in the price of a bond for a know change in yields. If yields change by Delta(y) then the percentage in price is:

Macaulay Duration It is the weighted average term to maturity of the cash flows from a bond. Weight of each cash flow: determined by dividing the PV of the cash flow by the price Frequently used by portfolio managers who use an immunization strategy Difference  Macaulay duration and modified duration are mainly used to calculate the durations of bonds. The Macaulay duration calculates the weighted average time before a bondholder would receive the bond's cash flows. Conversely, modified duration measures the price sensitivity of a bond when there is a change in the yield to maturity.

Forward rates Forwards rates are calculated to determine future values. For instance, an investor can purchase a one-year Treasury bill or buy a six-month bill and roll it into another six-month bill once it matures. The investor will be indifferent if both investments produce the same total return. The investor will know the spot rate for the six-month bill and will also know the rate of one-year bond at the initiation of the investment, but he/she will not know the value of a six-month bill that is to be purchased six months from now. To mitigate reinvestment risk, the investor could enter into a contractual agreement that wold allow him/her to invest funds six months from now at the current forward rate.

The term structure of interest rates It is the relationship between interest rates or bond yields and different terms or maturities. The term structure of interest rates is also known as a yield curve. It reflects expectations of market participants about future changes in interest rates and their assessment of monetary policy conditions. A term structure is mapping between maturities and spot rates at those maturities. Graphically, it is a plot of spot rates (YTM) on the y-axis against maturities on the xaxis. Common method of valuing bond Term structure shape  upward sloping (i.e. spot rates for longer maturities are greater than those for smaller maturities) (Not always true, sometimes they are downwards, sometimes they are flat) Long-term spot rates are higher than shortterm rates. This does not mean that investing long is more profitable than investing short. The Expectations Theory of the term structure tells us that bonds are priced so that an investor who holds a succession of short bonds can expect the same return as another who holds a long bond. The Expectations Theory predicts an upward-sloping term structure only when future short-term interests are expected to rise.

Shape is determined by: Expectations theory  Spot rates are just combination of forward rates (since the agents construct forward rates as rational forecasts of future one-period interest rate) Today’s upward sloping term structure might be suggesting that markets think that interest rates are going to rise

Liquidity Premium Theory  Based on the expectation theory (term structure slope reflects expected future interest rate changes) Add the notion that savers prefer short-term securities over long-term. Therefore, longterm securities must offer a larger average return Market segmentation theory  Different clienteles of investor operate in long and shortterm markets (not trading across them). Outcome is that the term structure can look whichever way you want it to.

Lecture 5 Equity markets and the study relationship between the returns offered by equity portfolios and the risk carried by those investments. Defining Risk Considering an investor and its total portfolio asset, we measure the RISK of the portfolio with its VARIENCE or alternatively with its square root, the STANDARD DEVIATION.

Variance definition: consider a portfolio that will deliver one of N possible returns, R1, R2, R3, ..., RN, tomorrow and each outcome has an associated probability P1, P2, P3, ..., PN. The variance (σ^2) is: EQ1

Example: The mean return is clearly 10% = ((40% + 10% + 10% − 20%)/4). Thus, the variance is σ^ = 0.25 × [(0.40 − 0.10) ^+ (0.10 − 0.10) ^ + (0.10 − 0.10) ^ +(−0.20 − 0.10) ^ ] = 0.045 So the standard deviation = √ 0.045 = 0.212 = 21.2%

Often, we are not given probabilistic information on an investment and its outcome, but we are given HISTORICAL DATA on its performance. Therefore, we use the SAMPLE VARIANCE to measure risk. Sample variance definition: you are given historical, annual (for example) returns on an investment over K years. Call the return in the first year R1, in the second year R2, .... and the return in the Kth year is Rk. The sample variance is; EQ2 Example: Suppose that you’re told that in the most recent 5 years, the nominal annual returns on the US stock market have been -35.6%, 32.4%, 16.5%, 3.8% and 13.8%. What is the sample variance? Well the sample mean return over this period is 6.2% so; S^ = 1/4 ((−0.356 − 0.062)^ + (0.324 − 0.062)^ + (0.165 − 0.062)^ +(0.038 − 0.062)^ + (0.138 − 0.062)^ ) = 0.065 So, the standard deviation = √ 0.065 = 0.255 = 25.5%.

Portfolio risk and return Portfolio weights: Xi is the proportion of your invested wealth that you have allocated to asset i. 

These can be positive or negative but must sum across stock to give ONE

Expected returns: µi is the mean/expected return on asset i. Variance: σ^ Correlations: Define ρi,j to be the correlation between the returns on stocks i and j. The correlation must be between -1 and +1 and ρ1,2 = ρ2,1

Expected portfolio returns: EQ3

Portfolio return variance: EQ4

Note: Holding all else constant, and with positive weights, increasing the correlation between the stocks will tend to make the portfolio return more volatile. Decreasing the correlation will make the portfolio less volatile.

Diversification Facts: Stocks tend to be positively correlated, but their correlation is usually much less than +1 Implication: Building a portfolio containing many stocks is smart thing to do beca...