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Unformatted text preview: Bond Valuation Bond Mind Map Mind
s Why?: One of the most important sources of financing is the bond market. In the bond market, firm’s raise debt financing directly from investors (i.e., no “middledirectly man”). For large corporations, this is a man”). primary source of external financing. From a personal finance perspective, bonds account for a very large percentage of retirement savings (especially for older savers). Mind Map Mind
s Learning objective:
– Develop familiarity with bond attributes and Develop terminology terminology – Calculate bond values – Calculate yields – Demonstrate an understanding of bond price Demonstrate sensitivities Mind Map Mind
s Key words/concepts:
– – – – – – Par/face value; coupon rate; maturity Current yield Yield to maturity (YTM) Annual vs. semi-annual payment Indenture Duration Duration Warm-up: Warm-up: What are they worth?
Suppose you were promised the following Suppose cash flow: $100 in one year, $100 in two years, $100 in three years, and $1000 also in three years. in s What would these be worth to you if you What discounted them at 10%? At 12%? discounted
s Service Opportunity Service
s Still looking for a project for your class service Still requirement? requirement? s Set a goal to sell 4 or 5 copies of the Set joke book by creating awareness among non-Marriott-School friends and family. and s This will satisfy your class service This requirement! requirement! Quick Reminder Quick
s s s s Recall that during the first day of class, I asked Recall you to consider praying about this class and praying for your fellow students in this class. praying Are you? If so, thanks! If not, why? Characteristics of Bonds Characteristics
• Bonds pay fixed coupon (interest) Bonds coupon payments at fixed intervals (usually every 6 months) and pay the par value at par maturity. maturity
$I 0 $I 1 $I $I 2 $I ... $I+$M n example: AT&T 10s of 2011 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 1 $100 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
Vb = Σ n t=1 $I (1 + kb) 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 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 = ????? LOS 67.c / Book 5, p. 223 Valuing a Swap: Example Valuing PV of fixed rate bond! LOS 67.c / Book 5, p. 223 Valuing a Swap: Example Valuing PV of floating bond! LOS 66.b / Book 5, p. 190 Derivative Investments Options on Fixed-Income Securities 16 LOS 66.c / Book 5, p. 202 Derivative Investments The Black-Scholes-Merton Model The Black-Scholes-Merton (BSM) model prices European options on non-dividend paying stock: X × e –Rc ×T × N ( d ) f C0 = S0 × N ( d1 ) – 2 S0 + Rc + 0.5 ×σ× T 2 ln X f d1 = σ× T It’s not that hard – can ( ) d2 = d1 –σ× T ( ) you add, subtract, multiply and divide?
17 WITH THE FINANCIAL CALCULATOR CALCULATOR
s s s s Bonds are a “5 find 4” game Bonds “5 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 Q: Are you going to have ugly grandchildren? Q: s Tip: enter PV as a negative.
s THERE ARE 2 KINDS OF BOND QUESTIONS BOND
s Questions 1: Given the discount rate, find the market price find Question 2: Given the market price, find the discount rate (aka “Yield to Maturity”) Maturity”) s 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 s aka the “promised yield” aka s Note: this is NOT the same as the Note: Current Yield. Current 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 V = $I (PVIFA i, n) + $M (PVIF i, n) $I n) b
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 a n T h is rta n t im p o ide!! sl Using the Financial Calculator Using
P/YR = 1 P/YR Mode = end N = 16 (huh?) PV = -898.90 PMT = 50 (why?) PMT
is a n T h is rta n t im p o 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 offshore – no regulation). (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! What is the impact on YTM? YTM? 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. Thought for the Day Thought
Elder Joseph B. Wirthlin said: Elder Kindness is the essence of greatness essence and the fundamental characteristic of the noblest men and women I have known. Kindness is a passport that opens doors and fashions friends. It softens hearts and molds relationships that can last lifetimes. 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 1 120 2 120 3 ... ... 1000 120 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 (why?) 10 PMT = 120 (why?) PMT FV = 1000 Solve PV = -$1,170.27 Solve 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 = 120 FV = 1000 FV Point: If theSolve PV = -$867.54 rate, the coupon Point coupon discount the Solve rate < discount bond will sell for a discount. discount Prices vs. Yields Prices
Big point: There is an inverse relationship between prices and yields. yields. s If interest rates 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” 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 sensitivity
– Longer maturity = greater sensitivity – Lower coupon = greater sensitivity Duration captures both effects s Literally, a weighted average time to Literally, maturity maturity s Testable topic – more in lab on Friday
s Job Search (2) Minutes Job
The secret to preparing for an The internship: RESEARCH! internship: s Know your company s How? Vault! (for starters)
s – – –
s Lib.byu.edu Business mgmt Vault Do it The Financial Pages: The
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
Bonds Cur Yld Vol Close Net Chg AlldC zr 09 AlldC ... 30 43 5/8 +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
Maturity Rate Mo/Yr Bid Asked Rate 9 Nov 18 128:18 128:24
s 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 = 1, N = 36, FV = 1000, PMT = 45, P/YR 36 FV 1000 PMT 45 PV = - 1,287.50 (128.75% of par) 1,287.50
s Solve: Solve: I/YR = 6.31% 6.31% ...
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