Question

On November 1, 2009, Riley Corp. sold a $700 million bond issue to finance the purchase of a new distribution facility. These bonds were issued in $1,000 denominations with a maturity date of November 1, 2049. The bonds have a coupon rate of 6.00% with interest paid semiannually. Required: a) Determine the value today, November 1, 2019 of one of these bonds to an investor who requires an 8 percent return on these bonds. Why is the value today different from the par value? b) Assume that the bonds are selling for $890.00. Determine the current yield and the yield-to-maturity. Explain what these terms mean. c) Explain what layers or textures of risk play a role in the determination of the required rate of return on Riley’s bonds.

Answer 1

Solution to question a

To find out the current price of the bond, we have to discount the cash flow of the bonds using the required rate of 8%.

Alternatively, we can also use a financial calculator.

n is the total number of periods for maturity. since coupons are paid semiannually, n is twice the number of years.

n = (2049-2019) * 2 = 30 * 2 = 60

I/Y is the yield-to-maturity or the required rate . since semiannual payments are being made, we have to divide that by 2

I/Y = 8/2 = 4

PMT is the amount of coupon payment for the period = (coupon payment for 1 year) /2

coupon payment for one year = coupon rate * par value of bond = 0.06*$1000 = $60

PMT for the period = $60/2 = $30

FV is the future value of the bond. This is the price of the bond at maturity, which is the par value = $1,000

Inputting these details, PV, which is the current value of the bond will stand at - $773.76. The negative sign means that the investor has to pay that amount to purchase that bond today in order to receive positive coupon payments of $30 every 6 months and par value of $1,000 in the future.

Hence the value of the bond today if required rate is 8% is $773.76

Solution to question B

we need to use a financial calculator to find out the yield- to- maturity

n is the total number of periods for maturity. since coupons are paid semiannually, n is twice the number of years.

n = (2049-2019) * 2 = 30 * 2 = 60

PMT is the amount of coupon payment for the period = (coupon payment for 1 year) /2

coupon payment for one year = coupon rate * par value of bond = 0.06*$1000 = $60

PMT for the period = $60/2 = $30. These are coupon payments the investor will receive, hence the sign is positive.

FV is the future value of the bond. This is the price of the bond at maturity, which is the par value = $1,000. Again this is the money the investor will receive upon maturity, hence the positive sign.

PV, which is the current value of the bond is given as $890. You need to enter the (-) sign in the calculator for PV, as it is the amount the investor would pay to purchase the bond

I/Y will be computed as 3.44%. Since this is a rate for 6 months, we have to double it for annual YTM = 3.435 *2 = 6.87%

current yield = annual coupon payment / current price of the bond = $60/$890 = 0.0674 = 6.74%

current yield gives you how much coupon the bond gives as a ratio of the amount you have to pay to acquire the bond.

yield-to-maturity is the rate of return expected by a bond investor given the bond's risk profile .

Solution to c

A bond usually has two major risks, interest rate risk and credit risk. The interest rate risk is the risk that higher interest rates in the future would erode the value of future coupon payments of the bond. Credit risk is the risk that the bond issuer may default on paying the coupons or the par value.

The higher the perceived risk on the bond the higher will be the required rate of return or the yield -to -maturity on the bond.

In case of Riley's bond issues, there is a high interest rate risk because the bond matures 30 years from now. However, a higher credit risk could also cause yield-to-maturity to rise and bond prices to fall.