Bond Valuation What is Bond When a corporation
Bond Valuation
What is Bond? • When a corporation or government wishes to borrow money from public, it usually does so by issuing, or selling bonds • When investors buy a bond, they lend money to the bond issuer, the government or corporation • As a lender, investors expect to be paid back the original amount (principle) and interest over some specified period time • As a borrower, the bond issuer must repay principle and interest to buyers over some specified period time
Definition of Bond • A security that the government or corporation issue or sell to borrow money from investors today and pay promised payments later • A loan that the borrower (issuer) promises to repay the lender (investor) the amount borrowed (principle) plus interest over some specified period time
Key Features • Par value (face value, F) Ø Amount borrowed by issuers (sellers) from investors (buyers) at the beginning Ø Re-paid at the end of loan Ø Assume $1, 000 for corporate bonds • Annual Coupon (C) Ø Annual interest payments to buyers Ø Coupon Rate = Annual coupon/Par Value = C/F
Key Features • Maturity (T): Ø Number of years until par value is repaid by issuers (sellers) • Yield to maturity (YTM): Ø Discount rate used to value a bond Ø Quoted as an annual rate Ø Market rate of return
Annual Coupon Bond Price •
Annual Coupon Bond Price • The cash flows from investing on this bond are 15 years $100 plus $1, 000 in the end of year 15 0 1 P=? 100 2 100 … 14 15 100 1, 000 • How much will investors pay to buy the bond? Ø Present value of this stream of cash flows
Annual Coupon Bond Price •
Annual Coupon Bond Price •
Annual Coupon Bond Price •
Problem 6 -3 Bond Prices Lycan, Inc. , has 7. 6% coupon bonds on the market that have 9 years left to maturity. The bonds make annual payments. If the YTM on these bonds is 9. 6%, what is the current bond price?
Semiannual Coupon Bond Price •
Semiannual Coupon Bond Price •
Problem 6 -6 Bond Prices App Store Co. issued 20 -year bonds one year ago at a coupon rate of 6. 1%. The bonds make semiannual payments. If the YTM on these bonds is 5. 3%, what is the current bond price?
Bond YTM •
Annual Coupon •
Problem 6 -5 Coupon Rate Merton Enterprises has bonds on the market making annual payments, with 14 years to maturity, and selling for $953. At this price, the bonds yield 9. 4%. What must the coupon rate be on Merton’s bonds?
Annual Coupon •
Problem 6 -8 Coupon Rate Volbeat Corporation has bonds on the market with 12 years to maturity, a YTM of 9. 7%, and a current price of $948. The bonds make semiannual payments. What must the coupon rate be on the bonds?
Bond Sold at Par • Price = Par value • When are bonds sold at par? • 30 -year annual coupon bonds with $100 face value and 5% coupon rate • If YTM is 5%, how much is the bond? Ø Issuer promises $5 annual coupon (interest payment) Ø Bondholders expect $5 return Ø Actual interest payment = Expected return Ø Investors are willing to lend $100 to the issuer, so pay $100 to buy the bond
Discount Bond • Price < Par value • If YTM is 10%, how much is the bond? Ø Issuer promises $5 annual coupon (interest payment) Ø Bondholders expect $10 return Ø Actual interest payment < Expected return Ø Investors are not willing to lend $100 to the issuer Ø Investors will pay less than $100 to buy Ø Bond price is $52. 87 < $100
Premium Bond • Price > Par value • If YTM is 3%, how much is the bond? Ø Issuer promises $5 annual coupon (interest payment) Ø Bondholders expect $3 return Ø Actual interest payment > Expected return Ø Investors would like to pay more than $100 to buy Ø Investors will lend more than $100 to the issuer Ø Bond price is $139. 20 > $100
Current Yield •
Relations •
Interest Rate Risk • Interest rate movements affect investors’ expectation on bond return, so do bond price • Interest rate risk refers to the sensitivity of bond price to interest rate variations • Two features determine interest rate risk Ø Maturity Ø Coupon Rate
Interest Rate Risk • The longer the maturity, the greater the interest rate risk Ø Bond with longer maturity has more distant cash flows, which are more adversely affected by the increasing of interest rate • The lower the coupon rate, the greater the interest rate risk Ø Bond with lower coupon rate proportionally depends more on the present value of par value, so its price is more adversely affected by the increasing of interest rate
Problem 6 -16 Interest Rate Risk Both Bond Bill and Bond Ted have 12. 4% coupons, make semiannual payments, and are priced at par value. Bond Bill has 5 years to maturity, whereas Bond Ted has 22 years to maturity. If interest rates suddenly rise by 3%, what is the percentage change in the price of these bonds?
Interest Rates Rise by 3% •
Maturity • The only difference between Bond Bill and Ted is coupon rate: Ted has a longer maturity • % decline in price for Bond Ted is greater than % decline for Bill, so Bond Ted price is more sensitive to interest rate changes
Problem 6 -17 Interest Rate Risk Bond J has a coupon rate of 4. 5%. Bond S has a coupon rate of 14. 5%. Both bonds have eight years to maturity, make semiannual payments, and have a YTM of 10%. If interest rates suddenly rise by 3%, what is the percentage change in the price of these bonds? What does this problem tell you about the interest rate risk of lower-coupon bonds?
Interest Rates Rise by 3% •
Coupon Rate • The only difference between Bond J and S is coupon rate: S has a greater coupon rate • % decline in price for Bond S is smaller than % decline for S, so Bond S price is less sensitive to interest rate changes
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