Lecture 6 Managerial Finance FINA 6335 Bond and Stock Valuation Ronald F. Singer

Present Value of Bonds & Stocks At this point, we apply the concept of present value developed earlier to price bonds and stocks.

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 +

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. (referred to as par) PV of coupon annuity =  = 58,908 t=1 ( ) PV of principal = 100,000 = 21,455 ( ) 20 Present Value of Total = 80,363 OR

Yield to Maturity By Calculator N = 20 I%YR = 8 PMT = 6,000 FV = 100,000 PV => 80, or % of par.

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 IF the promised payments are all paid. It is that interest rate which makes the price of the bond equal the present value of the promised payments.

Characteristics of US Bonds Promised Payments include Coupon Payments and Principle (Face Value or Par Value) Coupons are quoted as annualized percent of the Face Value Coupons are usually paid semi-annually, at the month of the maturity date and six months later. Principle is usually in $1,000 increments Prices are quoted as % of Face Value Quote Bond: ATT 7s ‘10

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 March 1, The semiannual coupon payments are: 4.5% of 100,000 or 4,500. (As of March 1, 2008) 4,500 4,500 4, , /08 3/10 99,375 99,375 = ,500 (1+YTM) (1+YTM) 2 (1+YTM) 3 (1+YTM) The Yield to Maturity is 9.35%.

By Calculator 4 N PV PMT FV CPT I/Y x 2 = 9.35 Note the YTM is quoted as “simple” APR Rate, (not compounded). This is the convention of how bonds are quoted, in simple “yields” not compounded

Bond Pricing From Yahoo! Finance (finance.yahoo.com) Click: Investing>bonds>Bond Center Current Fitch Type Issue Price CouponMaturity YTM Yield Rating Corp ABBOTT /15/ AA LABS ………………………… $ /08 9/08 3/09 3/11

–Principal: $1,000 (most US Corporate bonds have $1,000 principal). –Coupon (Annual): $37.50 –Maturity : March 15, 2011 –Current yield: 3.891% Current = Coupon = 3.75 = 3.891% Yield Price Price = x 1000 = $ What is the bond's Accrual (we can assume 90 day quarters) So Accrual = Coupon (Days from last Coupon/Days in coupon period) = (37.5) X (162) = Cash (Dirty) price is = $ = Note in this case: YTM > Current Yield > Coupon: Why?

Calculating Bond Price Suppose we know the appropriate Yield to Maturity ("Discount Rate") For Example: 5% (NB: Bond Quotes are in simple interest) The Bond Value is P 0 =  t=1 (1.025) t (1.025) 7 P = $ or (% of par)

Calculating YTM Suppose price was 98 ($980). What is the yield to maturity? N = 7 PV = -98 PMT = FV = 100 CPT I% = X 2 = YTM = 4.37

Treasury Bonds, Notes and Bills Current Fitch Type Issue Price Coupon Maturity YTM Yield Rating Zero US Treas /15/ AAA Treas US Treas /15/ AAA Treas US Treas /15/ AAA

Valuing Bonds Using Law of One Price Strips: Zero Coupon Treasuries. These are called “strips” because it is a regular (coupon) bond with the coupons stripped away, so that you only have the principal or face value.

From Yahoo Finance Strips Maturity Price 8/15/ /15/ /15/ /15/

Value US Treas 6.50s, 2/15/ /082/09 8/092/10

Value US Treas 6.50s, 2/15/ /082/09 8/092/10

Value US Treas 6.50s, 2/15/10 To Value this Bond using Zero’s Date Paid PV First coupon 8/15/ *3.25 = Second coupon 2/15/ *3.25 = Third coupon 8/15/ *3.25 = Fourth coupon 2/15/ * = Principal YTM = ???

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 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

From Yahoo! Finance OCCIDENTAL PET (NYSE:OXY) Last Trade:79.16 Trade Time:11:47AM ET Change: 0.46 (0.58%) Prev Close:78.70 Open: y Target Est:82.73 Day's Range: wk Range: Volume:1,884,459 Avg Vol (3m):7,065,790 Market Cap:65.36B P/E (ttm):12.30 EPS (ttm):6.44 Div & Yield:1.00 (1.30%)

Analysis of OXY Yield = Current Quarterly Dividend X 4 Price P/E Ratio = Most Recent Price EPS (ttm) ttm means the “trailing twelve months” So you can solve for Earning per Share

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) 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

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?

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: oo V(o) =  E{ Dividend(t)} t=1 (1 + r) t or:P(0) =  E{ DPS(t) } t=1 (1 + r) t 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) P = EPS 1 + PVGO r (2) P =  (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.

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

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, b is the “plowback” or “retention” rate, and 1-b is the dividend payout. and, g is the constant growth rate in dividends, earnings, earnings per share, and the stock price note that under simplifying assumptions: DIV(t) = (1 - b)Earnings(t) –  WC +DEP = Free Cash Flow to Stockholders(t).

Total Payout Model Sometimes firms substitute share repurchase for dividends. Under those circumstances we can think of the cash flow to stockholders, as the sum of Dividends plus share repurchases. Then, the Total payout model would be the present value of future dividends and repurchases, and the share price is simply that present value per CURRENT outstanding shares.

Lets assume that  WC +DEP = 0, and there are no interest payments, for simplicity, so that (EPS) = Cash Flow from Operations per share. 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 Constant Growth Model

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. Assume, Change in working capital is 0 throughout: 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 Thus: P o = 10 =

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% ?

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 dividends ………. free cash flow investment 10 0 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% ?

This value of the firm can be represented by P 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

Free Cash Flow Model Free Cash Flow = EBIT(1-t) +Depreciation - CapExp –  WC Then the Value of the Firm, V = PV of FCF And Equity value = V – Debt + Cash P = (Equity value)/(Shares outstanding)

Discounted Free Cash Flow Model Approach: Determine the (present) value of the total cash flow to all Security holders, and then subtract the value of all securities other than equity to get the Equity Value of the firm.

Cash Flow to all Security Holders The Cash flow to all security holders is the firm’s Free Cash Flow. So! Free Cash Flow = EBIT(1-t) +Depreciation – Capital Expenditures – Increase in Working Capital

A Simple Example Assume Free Cash Flow grows at a constant rate over time. Historically this has been 8% Suppose we have the following data: Earnings = 5.2 million EBIT = 10 million Depreciation = 2 million Interest = 3 million Increase in Working capital is.5 million Capital Expenditures is 3 million Legal tax rate is 35%

Free Cash Flow FCF = EBIT(1-t) + Depreciation –Increase in WC – CapEx = 10(1-.35) = = 11 If this will grow at 8% per year, and the cost of capital is 15%, then the The value of the firm is: 11 = m.07

Estimating Growth Can use historical averages or: Dividends = 8 million Return on Assets = 20% Dividend Payout = 6/11 = 54.55% Retention Rate(b) = =.4545 Since ROA (i) = 20% g = b X i =.2 X.4545 = 9.09%, so V = 11 = $186.12M ( )

The Discount Rate We are using the Cash Flow to all security holders, and we want to know what the appropriate rate to discount that cash flow. We will see that the appropriate discount rate is the WACC, which is the average return required by all security holders having a claim to that cash flow. More about this later