7 Valuation Introduction to Finance Chapter Lawrence J. Gitman Jeff Madura Introduction to Finance Valuation

Learning Goals Describe the key inputs and basic model used in the valuation process. Review the basic bond valuation model. Discuss bond value behavior, particularly the impact that required return and time to maturity have on bond value. Explain yield to maturity and the procedure used to value bonds that pay interest annually.

Learning Goals Perform basic common stock valuation using each of three models: zero-growth, constant-growth, and variable-growth. Understand the relationships among financial decisions, return, risk, and stock value.

Valuation Fundamentals The (market) value of any investment asset is simply the present value of expected cash flows. The interest rate that these cash flows are discounted at is called the asset’s required return. The required return is a function of the expected rate of inflation and the perceived risk of the asset. Higher perceived risk results in a higher required return and lower asset market values.

Basic Valuation Model CF1 (1 + k)1 CF2 (1 + k)2 CFn (1 + k)n V0 = + + . . . + Where: V0 = value of the asset at time zero CFt = cash flow expected at the end of year t k = appropriate required return (discount rate) n = relevant time period

Basic Valuation Model Using present value interest factor notation, PVIFk,n from Chapter 5, the previous equation can be rewritten as: V0 = [(CF1 x PVIFk,1)] + [CF2 x (PVIFk,2)] + … + [CFn x (PVIFk,n)] Example Nina Diaz, a financial analyst for King industries, a diversified holding company, wishes to estimate the value of three of its assets—common stock in Unitech, an interest in an oil well, and an original painting by a well-known artist. Forecasted cash flows, required returns, and the resulting present values are shown in Table 7.1 on the following two slides.

Basic Valuation Model Table 7.1 (Panel 1)

Basic Valuation Model Table 7.1 (Panel 2)

Bond Fundamentals A bond is a long-term debt instrument that pays the bondholder a specified amount of periodic interest over a specified period of time. Note: a bond is equal to debt.

Bond Fundamentals The bond’s principal is the amount borrowed by the company and the amount owed to the bondholder on the maturity date. The bond’s maturity date is the time at which a bond becomes due and the principal must be repaid. The bond’s coupon rate is the specified interest rate (or dollar amount) that must be periodically paid. The bond’s current yield is the annual interest (income) divided by the current price of the security.

Bond Fundamentals The bond’s yield to maturity is the yield (expressed as a compound rate of return) earned on a bond from the time it is acquired until the maturity date of the bond. A yield curve graphically shows the relationship between the time to maturity and yields for debt in a given risk class.

Bonds with Maturity Dates Annual Compounding I1 (1 + i)1 I2 (1 + i)2 (In + Pn) (1 + i)n B0 = + + . . . + For example, find the price of a 10% coupon bond with three years to maturity if market interest rates are currently 10%. 100 (1 + .10)1 (1 + i)2 (100 + 1,000) (1 + .10)3 B0 = +

Bonds with Maturity Dates Annual Compounding Using Microsoft® Excel For example, find the price of a 10% coupon bond with three years to maturity if market interest rates are currently 10%. Note: the equation for calculating price is =PV(rate,nper,pmt,fv)

Bonds with Maturity Dates Annual Compounding Using Microsoft® Excel For example, find the price of a 10% coupon bond with three years to maturity if market interest rates are currently 10%. When the coupon rate matches the discount rate, the bond always sells for its par value.

Bonds with Maturity Dates Annual Compounding Using Microsoft® Excel What would happen to the bond’s price if interest rates increased from 10% to 15%? When the interest rate goes up, the bond price will always go down.

Bonds with Maturity Dates Annual Compounding Using Microsoft® Excel What would happen to the bond’s price it had a 15-year maturity rather than a 3-year maturity? And the longer the maturity, the greater the price decline.

Bonds with Maturity Dates Annual Compounding Using Microsoft® Excel What would happen to the original 3-year bond’s price if interest rates dropped from 10% to 5%? When interest rates go down, bond prices will always go up.

Bonds with Maturity Dates Annual Compounding Using Microsoft® Excel What if we considered a similar bond, but with a 15-year maturity rather than a 3-year maturity? And the longer the maturity, the greater the price increase will be.

Graphically Bond prices go down As interest rates go up

Bonds with Maturity Dates Semi-Annual Compounding Using Microsoft® Excel If we had the same bond, but with semi-annual coupon payments, we would have to divide the 10% coupon rate by two, divided the discount rate by two, and multiply n by two. For the original example, divide the 10% coupon by 2, divide the 15% discount rate by 2, and multiply 3 years by 2.

Bonds with Maturity Dates Semi-Annual Compounding Using Microsoft® Excel If we had the same bond, but with semi-annual coupon payments, we would have to divide the 10% coupon rate by two, divided the discount rate by two, and multiply n by two. Thus, the value is slightly larger than the price of the annual coupon bond (1,136.16) because the investor receives payments sooner.

Coupon Effects on Price Volatility The amount of bond price volatility depends on three basic factors: Length of time to maturity Risk Amount of coupon interest paid by the bond First, we already have seen that the longer the term to maturity, the greater is a bond’s volatility. Second, the riskier a bond, the more variable the required return will be, resulting in greater price volatility. Finally, the amount of coupon interest also impacts a bond’s price volatility. Specifically, the lower the coupon rate, the greater will be the bond’s volatility, because it will be longer before the investor receives a significant portion (the par value) of the cash flow from his or her investment.

Coupon Effects on Price Volatility

Price Converges on Par at Maturity It is also important to note that a bond’s price will approach par value as it approaches the maturity date, regardless of the interest rate and regardless of the coupon rate.

Price Converges on Par at Maturity It is also important to note that a bond’s price will approach par value as it approaches the maturity date, regardless of the interest rate and regardless of the coupon rate.

Annual coupon interest Yields The current yield measures the annual return to an investor based on the current price. Current yield = Annual coupon interest Current market price For example, a 10% coupon bond which is currently selling at $1,150 would have a current yield of: Current yield = $100 $1,150 = 8.7%

Yields The yield to maturity measures the compound annual return to an investor and considers all bond cash flows. It is essentially the bond’s IRR based on the current price. I1 (1 + i)1 I2 (1 + i)2 (In + Pn) (1 + i)n PV = + + . . . + Notice that this is the same equation we saw earlier when we solved for price. The only difference then was that we were solving for a different unknown. In this case, we know the market price but are solving for return.

Yields The yield to maturity measures the compound annual return to an investor and considers all bond cash flows. It is essentially the bond’s IRR based on the current price. Using Microsoft® Excel For example, suppose we wished to determine the YTM on the following bond.

Yields The yield to maturity measures the compound annual return to an investor and considers all bond cash flows. It is essentially the bond’s IRR based on the current price. Using Microsoft® Excel For example, suppose we wished to determine the YTM on the following bond. To compute the yield on this bond we simply listed all of the bond cash flows in a column and computed the IRR. =IRR(d10:d20)

Yields The yield to maturity measures the compound annual return to an investor and considers all bond cash flows. It is essentially the bond’s IRR based on the current price. Note that the yield to maturity will only be equal to the current yield if the bond is selling for its face value ($1,000). And that rate will also be the same as the bond’s coupon rate. For premium bonds, the current yield > YTM. For discount bonds, the current yield < YTM.

Common Stock Valuation Stock returns are derived from both dividends and capital gains, where the capital gain results from the appreciation of the stock’s market price due to the growth in the firm’s earnings. Mathematically, the expected return may be expressed as follows: E(r) = D/P + g For example, if the firm’s $1 dividend on a $25 stock is expected to grow at 7%, the expected return is: E(r) = 1/25 + .07 = 11%

Stock Valuation Models The Basic Stock Valuation Equation D1 (1 + k)1 D2 (1 + k)2 Dn (1 + k)n P0 = + + . . . +

Stock Valuation Models The Zero Growth Model The zero dividend growth model assumes that the stock will pay the same dividend each year, year after year. For assistance and illustration purposes, I have developed a spreadsheet tutorial using Microsoft® Excel. A non-functional excerpt from the spreadsheet appears on the following slide.

Stock Valuation Models The Zero Growth Model Using Microsoft® Excel

Stock Valuation Models The Zero Growth Model Using Microsoft® Excel

Stock Valuation Models The Constant Growth Model The constant dividend growth model assumes that the stock will pay dividends that grow at a constant rate each year, year after year. For assistance and illustration purposes, I have developed a spreadsheet tutorial using Microsoft® Excel. A non-functional excerpt from the spreadsheet appears on the following slide.

Stock Valuation Models The Constant Growth Model Using Microsoft® Excel

Stock Valuation Models The Constant Growth Model Using Microsoft® Excel

Stock Valuation Models Variable Growth Model The non-constant (variable) dividend growth model assumes that the stock will pay dividends that grow at one rate during one period, and at another rate in another year or thereafter. A non-functional excerpt from the spreadsheet appears on the following slide.

Stock Valuation Models The Variable Growth Model Using Microsoft® Excel

Stock Valuation Models The Variable Growth Model Using Microsoft® Excel

Stock Valuation Models The Variable Growth Model Using Microsoft® Excel

Stock Valuation Models The Variable Growth Model Using Microsoft® Excel

Decision Making and Common Stock Value Changes in Dividends or Dividend Growth Valuation equations measure the stock value at a point in time based on expected return and risk. Changes in expected dividends or dividend growth can have a profound impact on the value of a stock.

Decision Making and Common Stock Value Changes in Dividends or Dividend Growth Changes in risk and required return can also have significant effects on price.

Decision Making and Common Stock Value Changes in Dividends or Dividend Growth Changes in expected dividends or dividend growth can have a profound impact on the value of a stock.

Using Microsoft® Excel The Microsoft® Excel Spreadsheets used in the this presentation can be downloaded from the Introduction to Finance companion web site: http://www.awl.com/gitman_madura

7 End of Chapter Introduction to Finance Chapter Lawrence J. Gitman Jeff Madura Introduction to Finance End of Chapter