Principles of Managerial Finance 9th Edition Chapter 7 Bond & Stock Valuation

Learning Objectives Describe the key inputs and basic model used in the valuation process. Apply the basic bond valuation model to bonds and describe the impact of required return and time to maturity on bond values. Explain yield to maturity (YTM), its calculation, and the procedure used to value bonds that pay interest semiannually.

Learning Objectives Understand the concept of market efficiency and basic common stock valuation under each of three cases: zero growth, constant growth, and variable growth. Discuss the use of book value, liquidation value, and price/earnings (PE) multiples to estimate common stock values. Understand the relationships among financial decisions, return, risk, and the firm’s 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 V 0 = CF 1 + CF 2 + … + CF n (1 + k) 1 (1 + k) 2 (1 + k) n Where: V 0 = value of the asset at time zero CF t = cash flow expected at the end of year t k = appropriate required return (discount rate) n = relevant time period

Ex1. 假設永續經營 A 公司之資產帶來每年 300 元之現金流入，要求報酬 率為 12% ，則該資產之價值為： V 0 = $300*(PVIFA 12, ∞ )= $300/0.12=$2,500 EX2. 假設某油畫在五年後出售可得 $85,000 ，要求報酬率為 15% ，則 現在價值為： V 0 =$85,000*PVIF 15%, 5 =$42,245 EX 3. 假設某油井在未來四年會帶來下列的現金流入： $2,000 、 $4,000 、 $0 、 $10,000 ，要求報酬率為 20% ，則現在價值為： V 0 =$2,000*PVIF 20%, 1 +$4,000*PVIF 20%, 2 +$10,000*PVIF 20%, 4 =$9,262

What is a Bond? 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 that a bond = debt)

General Features of Debt Instruments The bond’s principal is the amount borrowed by the company and the amount owed to the bond holder 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 $ amount) that must be periodically paid. The bond’s current yield is the annual interest (income) divided by the current price of the security. Maturity value, face value, par value, future value

General Features of Debt Instruments 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 yield to maturity for debt in a given risk class. 和 holding period return 不同

Bonds with Maturity Dates Annual Compounding B 0 = I 1 + I 2 + … + (I n + P n ) (1+i) 1 (1+i) 2 (1+i) n For example, find the price of a 10% coupon bond with three years to maturity if market interest rates are currently 10%. B 0 = (100+1,000) (1+.10) 1 (1+.10) 2 (1+.10)

Using 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

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

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 Excel Why different? (1) economic condition changed (2) firm’s risk changed Sell at a discount

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 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 Excel Sell at a premium

Annual Compounding Using 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. Bonds with Maturity Dates

Graphically As interest rates go up Bond prices go down 10% coupon bond, 本金 =1,000 斜率一定為負，愈長期的債券，斜率愈負 15-year bond

Bonds with Maturity Dates Semi-Annual Compounding Using Excel For the original example, divide the 10% coupon by 2, divide the 5% discount rate by 2, and multiply 3 years by 2. 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. 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. Bonds with Maturity Dates Semi-Annual Compounding Using Excel 若半年付息一次 Note ： EAR=(1+i/2) 2 -1 若 4 個月付息一次 則 EAR=(1+i/3) 3 -1

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 higher the market interest rate, the lower the price volatility. 其他變數不變的情況下 % changes in the bond price for a given % change in required return Required return, discount rate, expected return, yield to maturity, market interest rate

Finally, the amount of coupon interest also impacts a bond’s price volatility. Specifically, the lower the coupon, the greater will be the bond’s volatility, because it will be longer before the investor receives a significant portion of the cash flow from his or her investment. 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

Coupon Effects on Price Volatility (1) (2) (1) 價格降 53.8% (2) 價格降 47.7% 所以 5%coupon bond 的價格風險 較大 票面利息越高的債券，其斜率的絕對值越小 15% coupon bond 5% 5% coupon bond 注意： YTM( 市場利率 ) 越大時斜率絕對值越 小

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.

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

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 is that we are solving for a different unknown. In this case, we know the market price but are solving for return. PV = I 1 + I 2 + … + (I n + P n ) (1+i) 1 (1+i) 2 (1+i) n Yields 已知 bond price ，倒回去求 YTM

Using 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.

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. Using Excel

Note that the yield to maturity will only be equal if the bond is selling for its face value ($1,000). And that rate will be the same as the bond’s coupon rate. For premium bonds, the coupon interest rate > YTM. For discount bonds, the coupon interest rate < YTM. 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. Bond price > face value Bond price < face value

The yield to call is the yield earned on a callable bond. To calculate the yield to call, simply substitute the call date for the maturity date plus the call premium if there is one. For Example, suppose we wished to determine the yield to call (YTC) on the following bond where the call premium is equal to one year extra coupon interest. Yields 假設此 callable bond 在第 10 年時可以 call

Yields The yield to call is the yield earned on a callable bond. To calculate the yield to call, simply substitute the call date for the maturity date plus the call premium if there is one. Yield to call

Risk and Yield Fluctuations

The Reinvestment Rate Assumption It is important to note that the computation of the YTM implicitly assumes that interest rates are reinvested at the YTM. In other words, if the bond pays a $100 coupon and the YTM is 8%, the calculation assumes that all of the $100 coupons are invested at that rate. If market interest rates fall, however, the investor may be forced to reinvest at something less than 8%, resulting a a realized YTM which is less than promised. Of course, if rates rise, coupons may be reinvested at a higher rate resulting in a higher realized YTM. Interest rate risk price risk reinvestment risk

持有期間報酬率 (holding period return) 假設持有票面利率 10% ，面值 $1000 ，三年到期的債券，假設 現在市場利率為 10% ，也就是 YTM=10% ，現在價格為 $1000 。若持有一年後出售時市場利率上升為 11% ，則 HPR= ？ B 1 = 100/ /(1.11) 2 = 983 HPR = (B 1 -B 0 +I 1 ) / B 0 = ( ) / 1000 = HPR = (B 1 -B 0 )/B 0 +I 1 /B 0 = expected capital gain return + current yield HPR≠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 1 /P 0 + g For example, if the firm expects to pay $1 dividend in first year on a $25 stock and the dividend is expected to grow at 7%, the expected return is: E(r) = 1/ = 11% Expected return on stock Expected $1 dividend in year one

Stock Valuation Models The Basic Stock Valuation Equation

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 on Excel. A non-functional excerpt from the spreadsheet appears on the following slide. Stock Valuation Models The Zero Growth Model

Stock Valuation Models The Zero Growth Model Using Excel

Stock Valuation Models The Zero Growth Model Using Excel 注意： preferred stock 的價值

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 Excel A non-functional excerpt from the spreadsheet appears on the following slide. Stock Valuation Models The Constant Growth Model

Stock Valuation Models The Constant Growth Model Using Excel

Stock Valuation Models The Constant Growth Model Using Excel ∴當市場均衡時， k= 股價沒被高估也沒被 低估， 此時為效率 市場。 在效率市場之 下，價格充份反應所 有公開資訊 =expected first year dividend yield 再加上 g ，這樣算出來的 k 是 股東預期的報酬率，若大於股東 所要求的報酬率 ( 亦即 CAPM 算出 來的 ) ， 則該股票目前價格被低估∴投資者 應買進。但投資者一買，價格就 會上升，使得 同理若 ，則表示目前股價被 高估，∴投資者應賣出。但投資者 一賣出，價格就會下跌，使得 k 直到 為止。

The non-constant 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. For assistance and illustration purposes, I have developed a spreadsheet tutorial available under the heading “Course Materials” on Course Web-Page. A non-functional excerpt from the spreadsheet appears on the following slide. Stock Valuation Models Variable Growth Model

Stock Valuation Models Variable Growth Model Using Excel

Stock Valuation Models Variable Growth Model =2.5×(1+10%) 1 =2.5×(1+10%) 2

Stock Valuation Models Variable Growth Model V0V0 V2V

Variable Growth Model Stock Valuation Models

股票評價模式：剩餘現金流量折現法 (free cash flow discounted model) (1) FCF s = (EBIT-Int)*(1-T) + Dep - CE - ∆NWC – RP + New Debt (2) FCF B = Int* (1-T) + RP - New Debt (3) FCF A = EBIT*(1-T) + Dep – CE - ∆NWC = EBIT* (1-T) - ∆NFA – ∆NWC Note ： CE= 資本支出 (capital expenditure) = ∆PPE ( property, plant, equipment) = ∆GFA ( 期末減去期初的固定資產毛額 ) RP= 當期償還的本金 (principal repayment) ∆NFA= 期末減期初的固定資產淨額 NWC = (CA – Cash - marketable security) - (CL - Long- term Debt matured in one year) ( 一 ) 每股股價 =[ ∑ FCF s,t / (1+K s ) t ] / number of shares ( 二 ) 每股股價 = {[ ∑ FCF A,t / (1+K A ) t ] -B] / number of shares K A = WACC = K S *S / (B+S) + K B *(1-T)*B / (B+S)

Other Approaches to Stock Valuation Book value per share is the amount per share that would be received if all the firm’s assets were sold for their exact book value and if the proceeds remaining after paying all liabilities were divided among common stockholders. This method lacks sophistication and its reliance on historical balance sheet data ignores the firm’s earnings potential and lacks any true relationship to the firm’s value in the marketplace. Book Value

Other Approaches to Stock Valuation Liquidation value per share is the actual amount per share of common stock to be received if al of the firm’s assets were sold for their market values, liabilities were paid, and any remaining funds were divided among common stockholders. This measure is more realistic than book value because it is based on current market values of the firm’s assets. However, it still fails to consider the earning power of those assets. Liquidation Value

Other Approaches to Stock Valuation Some stocks pay no dividends. Using P/E ratios are one way to evaluate a stock under these circumstances. The model may be written as: –P = (m)(EPS) –where m = the estimated P/E multiple. For example, if the estimated P/E is 15, and a stock’s earnings are $5.00/share, the estimated value of the stock would be P = 15*5 = $75/share. Valuation Using P/E Ratios

Determining the appropriate P/E ratio. –Possible Solution: use the industry average P/E ratio Determining the appropriate definition of earnings. – Possible Solution: adjust EPS for extraordinary items Determining estimated future earnings –forecasting future earnings is extremely difficult Other Approaches to Stock Valuation Weaknesses of Using P/E Ratios

Valuation equations measure the stock value at a point in time based on expected return and risk. 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.

Decision Making and Common Stock Value Changes in Risk and Required Return Changes in risk or required return can have a profound impact on the value of a stock. 注意： k s 越大， p 越小，而 ，所以當經理人之決策使得 系統風險增加時， k s 變大，則股票價值會下跌。

Combined effect Decision Making and Common Stock Value Changes in Risk and Required Return