Corporate Finance (Chapter 6)

Explain why two coupon bonds with the same maturity may each have a different yield to maturity.

When the yield curve is not flat, bonds with the same maturity but different coupon rates will have different yields to maturity. If the yield curve is upward sloping, the resulting yield to maturity decreases with the coupon rate of the bond. Alternatively, when the zero-coupon is downward sloping, the YTM will increase with the coupon rate.

How do we compute the bond yields from forward rates?

(1+f₁)*(1+f₂)*..*(1+fn)=(1+YTMn)ⁿ

Whate are the properties of coupon bond prices?

* bond price > face value, bond trades above par or at a premium, this occurs when coupon rate>yield to maturity; *bond price = face value, bond trades at par, coupon rate = yield to maturity; *bond price < face value, bond trades below par or at a discount, coupon rate < yield to maturity

What are the two reasons that after the issue date the market price of a bond generally changes over time?

1. As time passes, the bond gets closer to its maturity date. Holding fixed the bond's yield to maturity, the PV of the bond's remaining cash flows changes as the time to maturity decreases. 2. Changes in market interest rates affect the bond's yield to maturity and its price.

Which two types of payments make bonds typically to their holders?

1. Coupons = the promised interest payments of a bond (periodically to maturity date); 2. Principal or face value payments

Which two types of U.S. Treasury coupon securities are currently traded in financial markets?

1. Treasury notes = original maturities from 1 to 10 years; 2. Treasury bonds = orginial maturities of more than 10 years.

There are two reasons the yield of a defaultable bond exceeds the yield of an otherwise identical default-free bond. What are they?

1. calculate the YTM using the promised cash flows rather than the expected cashflows 2.The expected return of a corporate bond, which is the firm's debt cost of capital, equals the risk-free rate of interest plus a risk premium.

What is the definition of an interest rate forward contract?

A contract today that fixes the interest rate for a loan or investment in the future.

What options does a country have if it decides it cannot meet its debt obligations?

A country facing difficulty meetings its financial obligations typically has the option to print additional currency to pay its debts (leads to high inflation and sharp devaluation of the currency) When infalting away the debt is infeasible or politically unattractive, countries may choose to default on their debt (schulden riskeren)

What is the definition of a bond?

A security sold by governments and corporations to raise money from investors today in exchange for promised future payments.

What is the definition of a forward interest rate?

An interest rate that we can guarantee today for a loan or investment that will occur in the future. (1+YTMn)ⁿ=(1+YTMn-1)^(n-1)*(1+fn) fn = (1+YTMn)ⁿ/(1+YTMn-1)^(n-1) -1 Note: yield curve increasing in year n than is fn>YTMn, yield curve decreasing fn<YTMn, yield curve flat fn=zero-coupon yield

Why do sovereign debt yields differ across countries?

Because most sovereign debt is risky, the prices and yield of sovereign debt behave mucht like corporate debt: The bonds issued by countries with high probabilities of default have high hields and low prices.

How do you calculate the price of a coupon bond from the yields of zero-coupon bonds?

Because we can replicate a coupon-paying bond using a portofolio of zero-coupon bonds, the price of a coupon-paying bond can be determined based on the zero-coupon yield curve is the Law of One Price: P=PV(Bond Cash Flows)=CPN/(1+YTM₁)+..+(CPN+FV)/(1+YTMn)ⁿ

Give the bond terminology.

Bond certificate = indicates the amounts and dates of all payments to be made; Maturity date = final payment date; Term = time remaining until the repayment date

How does a bond's coupon rate affect its duration-the bond price's sensitivity to interest rate changes?

Bond prices change as interest rate change. When interest rate rise, bond prices fall, and vice versa. - Long-term zero-coupon bonds are more sensitive to changes in interest rates than are short-term zero-coupon bonds - Bonds with low coupon rates are more sensitive to chang0es in interest rates than similar maturity bonds with high coupon rates. - The duration of a bond measures the sensitivity of its price to changes in interest rates.

How do we calculate the coupon payment?

CPN = (Coupon Rate x Face Value)/Number of Coupon Payments per Year Face Value = the notional amount we use to compute the interest payment; Coupon Rate = The amount of each coupon payment.

What is the similarity and difference between a zero-coupon bond and a coupon bond?

Similarity: pay investors their face value at maturity; Difference: a coupon bond make regular coupon interest payments.

How does the forward rate compare tot the future interest rate?

It is a good predictor only when investors do not care about risk. "break even rate"= forward rate Expected future spot interest rate = forward interest rate + risk premium

What is a bond rating?

It summarize the creditworthiness of bonds for investors. Investmen-grade bonds: low default risk Speculative bonds, junk bonds or high-yield bonds: default is high. The rating depends on the risk of bankruptcy as well as the bondholders' ability to lay claim to the firm's assets.

What are sovereing bonds?

Sovereign bonds are issued by national governments. Sovereign bonds yields reflect investor expectations of inflation, currency, and default risk.

What is the relationship between expected return and YTM?

The bond's expected return is less than the YTM if there is a risk of default. Moreover, a higher YTM does not necessarily imply a bond's expected return is higher.

Give the definition of default spread or credit spread.

The difference between yields on Treasury securities and yield on corporate bonds. The credit spread compensates investors for the difference between promised and expected cashflows and for the risk of default.

How do you calculate the price of a coupon bond from the prices of zero-coupon bonds?

We match each coupon payment to a zero-coupon bond with a face value equal to the coupon payment and a term equal tot he time remaining tot he coupon date. Similarly, we match the final bond payment.

Give the defintion of credit risk.

The risk of default, means that that the bond's cash flows are not known with certainty, because the issuer might not pay back the full amount promised.

The risk-free interest rate for a maturity of n-years can be determined from the yield of what type of bond?

The risk-free interest rate for an investement until date n equals the YTM of a risk-free zero-coupon bond that matures on date n. A plot of these rates against maturity is called the zero-coupon yield curve. rn=YTMn "spot interest rate"=rn=yields of default-free zero-coupon bonds

Give the definition of yield to maturity (YTM)

The yield of maturity of a bond is the discount rate that sets the present value of the promised bond payments equal to the current market price of the bond.

How do we calculate the yield to maturity of a coupon bond?

The yield to maturity for a coupon bond is the discount rate,y, that equates the present value of the bond's future cashflows with its price: P = CPN*(1/y)*(1-1/(1+y)ⁿ)+FV/(1+y)ⁿ

What is the relationship between a bond's price and its yield to maturity?

YTMn = (FV/P)^(1/n)-1 P=FV/(1+YTMn)^n

What is the definition of a zero-coupon bond?

Zero-coupon bonds make no coupon payments, so investors receive only the bond's face value. Example Treasury bills

Which assumption is made to U.S. securities?

generally considered free of default risk.

If a bond's yield to maturity does not change, how does its cash price change between coupon payments?

the IRR of an investement in a bond equals its yield to maturity even if you sell the bond early.