Untitled Flashcards Set

1. Bond Features (Concepts #1, 2, 6, 7)

A bond is defined as "A long-term debt instrument in which a borrower agrees to make payments of principal and interest, on specific dates, to the holders of the bond." Key features of a bond include:

• Par Value: The "face amount of the bond, which is paid at maturity (assume $1,000)."

• Coupon Interest Rate: The "stated interest rate (generally fixed) paid by the issuer. Multiply by par value to get dollar payment of interest."

• Maturity Date: The "years until the bond must be repaid."

• Issue Date: The "when the bond was issued."

• Yield to Maturity (YTM): The "rate of return earned on a bond held until maturity (also called the “promised yield”)."

Beyond these basic features, some bonds include specific provisions:

• Call Provision: "Allows issuer to refund the bond issue if rates decline (helps the issuer, but hurts the investor). Bond investors require higher yields on callable bonds." These provisions often include a "deferred call provision and a declining call premium."

• Sinking Fund: A "Provision to pay off a loan over its life rather than all at maturity... Reduces risk to investor, shortens average maturity. But not good for investors if rates decline after issuance." Sinking funds can be executed by calling a percentage of the issue at par (likely when the required rate of return is below the coupon rate) or by buying bonds in the open market (likely when the required rate of return is above the coupon rate).

Bonds can be categorized into different types based on their security and risk:

• Mortgage bonds

• Debentures

• Subordinated debentures

• Investment-grade bonds

• Junk bonds

Evaluating Default Risk and Bond Ratings: Bond ratings "are designed to reflect the probability of a bond issue going into default." Factors affecting default risk and bond ratings include:

• Financial performance: Debt ratio, Times Interest Earned (TIE) ratio, Current ratio.

• Qualitative factors (Bond contract terms): Secured vs. unsecured debt, senior vs. subordinated debt, guarantee and sinking fund provisions, debt maturity.

• Miscellaneous qualitative factors: Earnings stability, regulatory environment, potential antitrust or product liabilities, pension liabilities, potential labor problems.

Other types or features of bonds include:

• Convertible bond: "may be exchanged for common stock of the firm, at the holder’s option."

• Warrant: A "long-term option to buy a stated number of shares of common stock at a specified price."

• Puttable bond: "allows holder to sell the bond back to the company prior to maturity."

• Income bond: "pays interest only when interest is earned by the firm."

• Indexed bond: "interest rate paid is based upon the rate of inflation."

The "discount rate (ri) is the opportunity cost of capital, and is the rate that could be earned on alternative investments of equal risk." This rate is composed of several components: ri = r* + IP + MRP + DRP + LP.

2. Calculating Bond Price (Sample Problems #1, 2)

The value of a bond is the present value of its expected future cash flows, which include periodic coupon payments and the par value at maturity. The general formula for bond valuation is:

Value (VB) = CF1/(1+r)^1 + CF2/(1+r)^2 + ... + (CFN + Par Value)/(1+r)^N

Where:

• CF is the coupon payment per period

• r is the discount rate (yield to maturity) per period

• N is the number of periods to maturity

The excerpt provides examples of calculating the value of a 10-year bond with a $1,000 par value and different annual coupon rates (10%, 13%, and 7%) when the required rate of return (rd) is 10%.

• Par Bond: A bond with a coupon rate equal to the yield to maturity will sell at par value. For the 10% coupon bond with a 10% YTM, the value is approximately $1,000. "VB = ... = $1,000"

• Premium Bond: A bond with a coupon rate greater than the yield to maturity will sell at a premium. For the 13% coupon bond with a 10% YTM, the value is approximately $1,184.34. "This bond sells at a premium because the coupon rate > the yield to maturity."

• Discount Bond: A bond with a coupon rate less than the yield to maturity will sell at a discount. For the 7% coupon bond with a 10% YTM, the value is approximately $815.66. "This bond sells at a discount because the coupon rate < the yield to maturity."

Non-annual Coupon Payments: For bonds that pay coupons semi-annually, the following adjustments are necessary:

1. Multiply the number of years to maturity by 2 (Number of periods = 2N).

2. Divide the nominal annual interest rate by 2 (Periodic rate (I/YR) = rd/2).

3. Divide the annual coupon payment by 2 (PMT = Annual coupon/2).

An example is provided for a 10-year, 10% semiannual coupon bond with a required rate of return of 13%, resulting in a bond value of approximately $834.72.

3. Relationship of Coupon Rate, Yield to Maturity, and Current Yield (Concepts #3-5, 8)

The relationship between the coupon rate and the yield to maturity determines whether a bond sells at a premium, discount, or par:

• If coupon rate < YTM (kd), discount.

• If coupon rate = YTM (kd), par bond.

• If coupon rate > YTM (kd), premium.

Changes in Bond Value Over Time: Assuming the required rate of return remains constant:

• The value of a premium bond will decrease over time until it reaches its par value at maturity.

• The value of a discount bond will increase over time until it reaches its par value at maturity.

• The value of a par bond will remain at its par value.

• "At maturity, the value of any bond must equal its par value."

4. Finding Yield to Maturity (YTM) (Sample Problems #3, 4)

Yield to maturity (YTM) is the discount rate that equates the present value of the bond's cash flows (coupon payments and par value) to its current market price. It represents the total return an investor can expect to receive if they hold the bond until maturity.

The YTM is found by solving for the interest rate (I/YR on a financial calculator or using a function like RATE in Excel) given the bond's current price, coupon payments, time to maturity, and par value.

Examples are provided:

• A 10-year, 9% annual coupon bond selling for $887 has a YTM of 10.91%. "This bond sells at a discount, because YTM > coupon rate."

• A 10-year, 9% annual coupon bond selling for $1,134.20 has a YTM of 7.08%. "This bond sells at a premium, because YTM < coupon rate."

5. Computing Yield to Call (YTC) for Callable Bonds (Problems #5, 6)

Yield to call (YTC) is the rate of return an investor earns if a callable bond is called before its maturity date. The calculation is similar to YTM, but it uses the call price and the number of periods until the bond can be called.

The formula and calculator inputs are adjusted:

• N = total number of coupon payments until bonds are callable

• FV = Call price of bond

An example is given for a 10-year, 10% semiannual coupon bond selling for $1,135.90, callable in 4 years for $1,050. The semiannual YTC is 3.568%, resulting in a nominal annual YTC of 7.137%.

Investors holding premium callable bonds should expect to earn the lower of the YTM and YTC. "Investors should expect a call, and to earn the YTC of 7.137%, rather than the YTM of 8%." A call is more likely when a bond sells at a premium because "(1) coupon > rd, so (2) a call is more likely." Therefore, "expect to earn: YTC on premium bonds. YTM on par and discount bonds."

6. Calculating Current Yield and Capital Gains Yield (Sample Problems #7, 8)

• Current Yield (CY): The annual coupon payment divided by the current market price of the bond.

• "Current yield = Annual coupon payment / Current price"

• Capital Gains Yield (CGY): The expected change in the bond's price divided by the beginning price.

• "Capital gains yield = (Ending price - Beginning price) / Beginning price"

The relationship between YTM, current yield, and capital gains yield is:

• YTM = Current yield + Capital gains yield

An example is provided for a 10-year, 9% annual coupon bond selling for $887:

• Current Yield = $90 / $887 = 10.15%

• Capital Gains Yield = YTM - Current Yield = 10.91% - 10.15% = 0.76%

7. Understanding Interest Rate Risk and Reinvestment Risk (Concepts #9, 10)

• Interest Rate Risk (Price Risk): The risk that rising required rates of return (rd) will cause the value of a bond to fall. Bonds with longer maturities are more sensitive to interest rate changes and thus have higher price risk.

• "Price risk is the concern that rising rd will cause the value of a bond to fall. The 10-year bond is more sensitive to interest rate changes, and hence has more price risk."

• Reinvestment Risk: The risk that when coupon payments or the principal are received, they will have to be reinvested at lower interest rates, thus reducing the overall return. This risk is higher for short-term bonds and high-coupon bonds.

• "Reinvestment risk is the concern that rd will fall, and future CFs will have to be reinvested at lower rates, hence reducing income."