chapter 7 valuation lawrence j. gitman jeff madura introduction to finance

Chapter

7

Valuation

Lawrence J. GitmanJeff Madura

Introduction to Finance

7-2Copyright © 2001 Addison-Wesley

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.

Learning Goals


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.


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

CF1

(1 + k)1

CF2

(1 + k)2

CFn

(1 + k)nV0 = + + . . . +

Basic Valuation Model


V0 = [(CF1 x PVIFk,1)] + [CF2 x (PVIFk,2)] + … + [CFn x (PVIFk,n)]


Using present value interest factor notation, PVIFk,n from Chapter 5, the previous equation can be rewritten as:

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.



Table 7.1 (Panel 1)



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.


100

(1 + .10)1

100

(1 + i)2

(100 + 1,000)

(1 + .10)3B0 = + +

I1

(1 + i)1

I2

(1 + i)2

(In + Pn)

(1 + i)nB0 = + + . . . +

Bonds with Maturity Dates

Annual Compounding

For example, find the price of a 10% coupon bond with three years to maturity if market interest rates are currently 10%.



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 equationfor calculating price is =PV(rate,nper,pmt,fv)


When the coupon rate matches the discount rate, the bond always sells for its par value.



• For example, find the price of a 10% coupon bond with three years to maturity if market interest rates are currently 10%.


When the interest rate goes up, the bond price will always go down.



• What would happen to the bond’s price if interest rates increased from 10% to 15%?


And the longer the maturity, the greater the price decline.



• What would happen to the bond’s price it had a 15-year maturity rather than a 3-year maturity?


When interest rates go down, bond prices will always go up.



• What would happen to the original 3-year bond’s price if interest rates dropped from 10% to 5%?


And the longer the maturity, the greater the price increase will be.



• What if we considered a similar bond, but with a 15-year maturity rather than a 3-year maturity?


Graphically

As interest rates go up

Bon

d prices go do

wn


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.



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.


The current yield measures the annual return to an investor based on the current price.

Yields

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.

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.

I1

(1 + i)1

I2

(1 + i)2

(In + Pn)

(1 + i)nPV = + + . . . +



Using Microsoft® Excel For example, suppose we wished to determine the YTM on the following bond.

Yields



Using Microsoft® Excel For example, suppose we wished to determine the YTM on the following bond.

Yields

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.


For example, if the firm’s $1 dividend on a $25 stock is expected to grow at 7%, the expected return is:

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

E(r) = 1/25 + .07 = 11%

Common Stock Valuation


Stock Valuation Models

The Basic Stock Valuation Equation

D1

(1 + k)1

D2

(1 + k)2

Dn

(1 + k)nP0 = + + . . . +



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.



The Zero Growth Model Using Microsoft® Excel



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.




The Constant Growth Model Using Microsoft® Excel



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.




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.



Changes in Dividends or Dividend Growth Changes in risk and required return can also have significant

effects on price.



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

Chapter

7

End of Chapter

Lawrence J. GitmanJeff Madura

Introduction to Finance

chapter 7 valuation lawrence j. gitman jeff madura introduction to finance

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