Lecture 3 Managerial Finance FINA 6335 Ronald F. Singer

3-2 Present Value of Bonds & Stocks At this point, we apply the concept of present value developed earlier to price bonds and stocks. Price of Bond = Present Value of Coupon Annuity Present Value of Principal +

3-3 Example Consider a 20 year bond with 6% coupon rate paid annually. The market interest rate is 8%. The face value of the bond is $100,000. PV of coupon annuity =  = t=1 ( ) PV of principal = 100,000 = 21,455 ( ) 20 Present Value of Total = 80,363 OR

3-4 By Calculator 20 N 8I%YR 6000 PMT FV PV 80, By Bond tables in calculator = % of Par OR Price of bond = PVAF(20, 8%) x 6,000 + PVF(20, 8%) x 100,000 = x 6, x 100,000 = 58, ,500 = 80,408 Example

3-5 Yield to Maturity YTM: The Annual Yield you would have to earn to exactly achieve the cash flow promised by the bond It is the internal rate of return of the bond It is that interest rate which makes the price of the bond equal the present value of the promised payments.

3-6 Consider a bond with principal of $100,000 and a coupon, paid semiannually, of 9%, selling for (This is percent of the face value, so that the actual price is 100,000 x = $99,375. Maturity date is August 30, The semiannual coupon payments are: 4.5% of 100,000 or 4,500. (As of August ) 4,500 4,500 4, , /01 8/02 99,375 99,375 = ,500 (1+YTM) (1+YTM) 2 (1+YTM) 3 (1+YTM) The Yield to Maturity is 9.35%.

3-7 By Calculator 4 N PV PMT FV CPTI/Y x 2 = 9.35

3-8 US Exchange Bonds From the Wall Street Journal (January 26, 2001) U.S. Exchange Bonds BONDS CUR VOL. CLOSE NET YLD CHG DukeEn6 7 /823… / 8 _ (coupon is 6.875) /01 12/01 6/02 6/23

3-9 Note: We assume that the bond matures at the end of June, and pays interest at the end of June and December. This is an arbitrary assumption. Also, U.S. Bonds are quoted "cum" coupon, so that the next coupon is always included in the calculation: NB: See Moody's Bond Guide or S & P for actual dates. –Principal: $1,000 (most US Corporate bonds have $1,000 principal). –Coupon (Annual): $68.75 –Maturity : 2023 –Current yield: 7.3% Current = Coupon = = 7.3% Yield Price Price = x 1000 = $ What is the bond's Yield to Maturity? YTM = Accrual = Note in this case: YTM > Current Yield > Coupon: Why?

3-10 Calculation of YTM Suppose we know the appropriate Yield to Maturity ("Discount Rate") For Example: 10% (NB: Bond Quotes are in simple interest) The Bond Value is P 0 =  t=1 (1.05) t (1.05) └────┴───┴───┴───────────────────── ─────┘

3-11 Treasury Bonds, Notes and Bills Maturity Ask Rate Mo/Yr Bid Asked chg. Yld. 10 5/8 Aug 15149:08 149: Bid Price: what government security dealers were willing to buy the bonds for at the end of the day Asked Price: what government security dealers were willing to sell the bonds for at he end of the day The amount after the : is the quote in 32nd of a percentage point and the quote is in percent of par. so the quotes are, /32% of par bid % and /32% of par asked %

3-12 Treasury Bonds, Notes and Bills Rate: the coupon rate as a percent of par. the coupon is % of $100,000 or $10,625 per year in two equal installments of $ each. Chg.: the change in the asked price from the prior day's close (in 32nds). YLD.: the Yield to Maturity based on the closing asked price

3-13 Valuation of Common Stock The Annual Expected Return on a share of common stock is composed of two components: Dividends and Capital Gains Expected Returns: E(R 0 ) = Dollar Return = E(Div 1 ) + E (P 1 ) - P o Price P 0 Where P 0 = The current per share price E(Div 1 ) = Expected dividend per share at time 1 E(P 1 ) = Expected price per share at time 1 E(R o ) = Expected Return E(R 0 ) = expected dividend yield + expected capital gain return

3-14 New York Stock Exchange Composite Transactions 52 Weeks Yld Vol Net High Low Stock Sym Div % PE 100s Hi Lo Close Chg 223/8 151/8 OcciPete OXY dd /8 193/8 191/2... Current (Annual) Yield = Dividend = Price P-E Ratio = Closing Price = (dd) Current Earnings Current = Closing Price Earnings P-E Ratio

3-15 Note, we don't observe E(R o ) but we observe prices and promised payoffs. If we solve for P o, the current value of the stock P o = E(Div 1 ) + E (P 1 ) 1 + E(R) = Expected Payoff x Discount at Time 1 Factor This relation will hold through time, therefore, P 1 = E (Div 2 ) + E(P 2 ) 1 + E(R) Substitute for P 1 P o = E(Div 1 ) + E(Div 2 ) + E(P 2 ) 1 + E(R) (1 + E(R)) 2 (1 + E(R)) 2

3-16 In general, P o =  T E (Div t ) + E(P T ) t=1 (1 + E(R)) t (1 + E(R)) T You can think of E(P T ) as a liquidating dividend equal to the value of firm's assets at time T. As T ----> 00, Present Value of E(P T )----> 0 And the stock price is the present value of all future dividends paid to existing stockholders P o =  00 E (Div t ) t=1 (1 + E(r)) t What happened to capital gain?

3-17 Consider the value of the stock (or the per share Price of the stock) The basic rule is: The value of the stock is the present value of the cash flows to the stockholder. This means that it will be the present value of total dividends (or dividends per share), paid to current stockholders over the indefinite future. That is: V(o) = Ó E{ Dividend(t)} t=1 (1 + r) t or:P(0) = Ó E{ DPS(t) } t=1 (1 + r) t This equation represents: The Capitalized Value of Dividends Capitalized Value of Dividends

3-18 Capitalized Value of Dividends The problem is how to make this OPERATIONAL. That is, how do we use the above result to get at actual valuation? We can use two general concepts to get at this result: They all involve the above equation under different forms. (1) P0 = EPS1 + PVGO r (2) P0 = Ó (Free Cash Flow per Share)t t=1 (1 + r) t EPS 1 is the expected earnings per share over the next period. PVGO is the "present value of growth opportunities. r is the "appropriate discount rate Free Cash Flow per Share is the cash flow available to stockholders after the bondholders are paid off and after investment plans are met.

3-19 Capitalized Dividend Model Simple versions of the Capitalized Dividend Model DIV(1) = DIV(2) =... = DIV(t) =... The firm's dividends are not expected to grow. essentially, the firm is planning no additional investments to propel growth. thus: with investment zero: DIV(t) = EPS(t) = Free Cash Flow(t) PVGO = 0 therefore the firm (or stock) value is simply: P 0 = DIV= EPS r r

3-20 Constant Growth Model Next suppose that the firm plans to reinvest b of its earnings at a rate of return of i throughout the indefinite future. Then growth will be a constant level of: g = b x i, note that: DIV(t) = (1 - b)EPS(t) = Free Cash Flow(t) and we can write the valuation formula as: P 0 = DIV(1) = (1-b)EPS(1) = Free Cash Flow(1) r - g r - g r - g = EPS(1) + PVGO r

3-21 Example: ABC corporation has established a policy of simply maintaining its real assets and paying all earnings net of real depreciation out as a dividend. suppose that: r = 10% Net Investment = ? Current Net Earning per Share is 10. then: EPS(1) = EPS(2)..=.. EPS(t). = 10 Year growth dividends free cash flow and: P o = 10 =

3-22 Now let this firm change its policy: Let it take the first dividend (the dividend that would have been paid at time 1) and reinvest it at 10%. then continue the policy of paying all earnings out as a dividend. We want to write the value of the firm as the present value of the dividend stream, the present value of free cash flow and the present value of Constant Earnings Per Share plus PVGO. time earnings 10 dividends 0 free cash flow investment Present Value of Dividends Present Value of Free Cash Flow Present Value of current Earnings plus Present Value of growth opportunities. Suppose return on investment were 20%? Suppose it were 5% ?

3-23 This value of the firm can be represented by v o = EPS 1 + PVGO: r where, PVGO =  NPV(t) t=1 (1+r) t Notice: if the NPV of future projects is positive then the value of the stock, and its price per share will be higher, given its current earnings and its capitalization rate