Bond_Valuation

Bond_Valuation - Bond Valuation Bond What are they worth...

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Unformatted text preview: Bond Valuation Bond What are they worth? What Suppose you were promised the following Suppose cash flow: $100 in one year, $100 in two years, $100 in three years, and $1000 in three years. three s What would these be worth to you if you What discounted them at 10%? At 12%? discounted s Characteristics of Bonds Characteristics • Bonds pay fixed coupon (interest) Bonds coupon payments at fixed intervals (usually every 6 months) and pay the par value par at maturity. maturity $I 0 $I 1 $I $I 2 $I ... $I+$M n example: AT&T 10s of 2007 example: s par value = $1000 $1000 s coupon = 10% of par value per year. 10% =$100 per year (use annual payments). =$100 s maturity = 3 years. years. s issued by AT&T. $100 $100 0 $100 1 2 $100+$1000 3 Security Valuation Security KNOW THIS!!!! s In general, the value of any asset = the present value value of the stream of expected cash value flows discounted at an appropriate required rate of return. required Bond Valuation Bond s Simply discount the cash flows at the Simply investor’s required rate of return. investor’s 1) the coupon payment stream (an annuity). 1) (an 2) the par value payment (a single sum). 2) (a Bond Valuation Bond n Vb = Σ t=1 $I (1 + k b ) t $M + n (1 + kb) $I = the coupon interest payment. the s kb = the investor’s required rate of return (which depends on the riskiness of the bond). (which s Vb = the value of the bond. the s Bond Valuation Bond n Vb = Σ t=1 $I (1 + kb) t + $M n (1 + kb) Vb = $I (PVIFA i, n) + $M (PVIF i, n) So, what is the ATT bond worth? worth? s Recall, par = $1000, coupon Recall, rate = 10%, and maturity = 3 years. years. s Suppose investors require a Suppose 10% rate of return? 12%? 10% s Value = ????? WITH THE FINANCIAL CALCULATOR CALCULATOR s s s s Bonds are a “5 find 4” game Enter the 4 things you know, and solve for the Enter fifth. fifth. Pmt = 100, FV = 1000, I/Yr = 12, N = 3 Solve for PV = 951.96 s Tip: enter PV as a negative. s Q: Are you going to have ugly grandchildren? Q: THERE ARE 2 KINDS OF BOND QUESTIONS BOND s Questions 1: Given the discount rate, find the market price find s Question 2: Given the market price, find the discount rate (aka “Yield to Maturity”) Maturity”) Yield To Maturity Yield s The average annual rate of return The investors expect to receive on a bond if they hold it to maturity. if Yield To Maturity Yield s The average annual rate of return The investors expect to receive on a bond if they hold it to maturity. if Vb = $I (PVIFA i, n) + $M (PVIF i, n) $I n) Just solving for i !!! YTM Example YTM Suppose we paid $898.90 for a $1,000 Suppose par 10% coupon bond with 8 years to maturity and semi-annual coupon payments. coupon What is our yield to maturity? Using the Financial Calculator Using P/YR = 1 P/YR Mode = end N = 16 (huh?) PV = -898.90 PMT = 50 (why?) PMT is an This ant port im ide!! sl Types of Bonds Types s Debentures - unsecured bonds. unsecured s Subordinated debentures - unsecured “junior” debt. “junior” s Mortgage bonds - secured bonds. secured s Zeros - bonds that pay only par value at maturity; no coupons. maturity; s Junk bonds - speculative or belowspeculative investment grade bonds; rated BB and investment below. below. Types of Bonds Types s Eurobonds - bonds denominated in one currency and sold in another country. (Borrowing overseas). (Borrowing s example - suppose Disney decides to sell $1,000 bonds in France. These are U.S.D. denominated bonds trading in a foreign country. Why do this? country. s If borrowing rates are lower (very unlikely), s To avoid SEC regulations. Convertibility Convertibility s Some bonds may be converted to common stock. common s Is this a benefit to the investor? Yes! Yes! The Bond Indenture The s The bond contract. s Lists all of the bond’s features: coupon, par value, maturity, etc. etc. s Lists covenants which are covenants designed to protect bondholders. designed s Describes repayment provisions. Bond Example Bond s S’pose our firm decides to issue 20-year S’pose 20-year bonds with a par value of $1,000 and $1,000 annual coupon payments. The return on other bonds of similar risk is currently 12%, so we decide to offer a 12% coupon interest rate. 12% s What would be a fair price for these What bonds? bonds? 120 120 0 120 120 ... 1000 120 1 2 3 ... 20 P/YR = 1 N = 20 I%YR = 12 FV = 1,000 PMT = 120 Solve PV = -$1,000 Point: If the coupon rate = discount Point coupon discount rate, the bond will sell for par value. rate the par s Suppose interest rates fall immediately Suppose interest after we issue the bonds. The required return on bonds of similar risk drops to 10%. 10%. s What would happen to the bond What price? price? P/YR = 1 Mode = end N = 20 I%YR = 10 PMT = 120 FV = 1000 FV Solve PV = Solve $1,170.27 Point: If the coupon rate > discount rate, the Point coupon discount the bond will sell for a premium. premium s Suppose interest rates rise immediately Suppose interest after we issue the bonds. The required return on bonds of similar risk rises to 14%. 14%. s What would happen to the bond price? P/YR = 1 Mode = end N = 20 I%YR = 14 PMT = 120discount Point: If the coupon rate < discount rate, the coupon the FV discount bond will sell for a discount. FV = 1000 Prices vs. Yields Prices s Big point: There is an inverse relationship between prices and yields. If interest increase, the price of If existing bonds will fall existing s If interest rates fall, the price of If existing bonds will increase existing s Remember the pencil trick s Zero Coupon Bonds Zero No coupon interest payments. No The bond holder’s return is determined entirely by the price discount. price Zero Example Zero Suppose you pay $508 for a zeroSuppose $508 coupon bond that has 10 years left to coupon 10 maturity. What is your YTM? maturity. Zero Example Zero Suppose you pay $508 for a bond that Suppose has 10 years left to maturity. What is your yield to maturity? This is just a lump-sum problem. just -$508 0 $1000 10 Zero Example Zero P/YR = 1 Mode = End N = 10 PV = -508 FV = 1000 Solve: I/YR = 7% Solve: 7% Duration Duration s Two factors influence price Two sensitivity sensitivity – Longer maturity = greater sensitivity – Lower coupon = greater sensitivity Duration captures both effects s Literally, a weighted average time to Literally, maturity maturity s More details in lab s The Financial Pages: The Corporate Bonds Bonds Cur Yld Vol Close Net Chg Eckerd 9 1/4 04 Eckerd 8.6 20 107 1/2 ... What is Eckerd’s yield to maturity (today=00)? s P/YR = 1, N = 8 (4years x 2 pay/yr), P/YR (4years s FV = 1000, PV = $-1,075, FV 1000 PV $-1,075 s PMT = 46.25 PMT 46.25 Solve: I/YR = 7.06% (I.e., 3.5324 x 2) Solve: 7.06% The Financial Pages: The Corporate Bonds Bonds AlldC zr 09 AlldC Cur Yld ... Vol Close 30 43 5/8 Net Chg +2 What is Allied Chemical’s yield to maturity? s P/YR = 1, N = 9, FV = 1000, PV = $-436.25, P/YR FV 1000 PV $-436.25 s PMT = 0 PMT s Solve: I/YR = 9.655% Solve: 9.655% The Financial Pages: The Treasury Bonds Maturity Rate Mo/Yr Bid Asked Rate 9 Nov 18 128:18 128:24 Chg +13 Ask Ask Yld Yld 6.43 What is the yield to maturity of this Treasury What bond? (note: t-bonds are traded in 32nds) bond? s P/YR = 2, N = 40, FV = 1000, PMT = 45, P/YR 40 FV 1000 PMT 45 PV = - 1,287.50 (128.75% of par) 1,287.50 s s Solve: Solve: I/YR = 6.43% 6.43% ...
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This note was uploaded on 03/06/2012 for the course BUS M 201 taught by Professor Mcgregor during the Fall '11 term at BYU.

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