Question

Orange, Inc. is a technology company that designs cell phones, computers and operating systems among other products. Orange has recently undergone a large bond issue. This bond issue includes 1,000 bonds each with a $1000 face value bonds. The bonds are due in 1 year and promise a 5% coupon. These bonds will pay 1 annual coupon payment, which is due, along with the face value, in exactly one year. The bonds have a beta of 0.10 and information from the credit rating agencies indicates that the bonds have a 7% chance of defaulting. In the event of default, investors are expected to recover 95% of the amount due to them (i.e. 95% of the coupon payment and face value due to them). The market risk premium is 5% and the risk free rate is 5%.

a.What is the opportunity cost of debt (i.e. expected return) for these bonds?
b.What price should these bonds sell for in the market?
c.What should the YTM be on these bonds?
d.Is the expected return on these bonds equal to their YTM? Why or why not?
e.Your colleague at work notes that these bonds have a ‘low yield’ and are therefore a bad investment. He says that there are other bonds in the market with much higher yields and these, he says, are clearly better investments. Is he correct?

Answer 1

a. The opportunity cost of debt for these bonds is 5.5%. b. The price of these bonds should be calculated based on their yield to maturity (YTM). c. The YTM for these bonds can be calculated using the formula provided. d. The expected return on these bonds is not necessarily equal to their YTM. e. Having a low yield does not necessarily make a bond a bad investment.

Step-by-step explanation:

a. The opportunity cost of debt, or expected return, for these bonds can be calculated using the following formula:

Expected Return = Risk-Free Rate + Beta * Market Risk Premium

In this case, the risk-free rate is 5% and the market risk premium is 5%. The beta of the bonds is 0.10. Therefore, the expected return is:

Expected Return = 5% + 0.10 * 5% = 5.5%

b. The price of the bonds in the market can be calculated by discounting the future cash flows (coupon payment and face value) of the bond at the yield to maturity (YTM). The YTM is the discount rate that makes the present value of the bond's cash flows equal to its market price. The price of the bond can be calculated using the following formula:

Price = (Coupon Payment / (1 + YTM)) + (Face Value / (1 + YTM))

c. The YTM can be calculated using the following formula:

YTM = Coupon Payment / Price + (Face Value - Price) / Price

d. The expected return on the bonds is not necessarily equal to their YTM. The expected return is the average return that an investor can expect to earn on the bonds, taking into account the risk and probability of default. The YTM, on the other hand, is the discount rate that equates the present value of the bond's cash flows to its market price. While the expected return considers the probability of default, the YTM does not.

e. Your colleague is not correct in saying that these bonds are a bad investment because they have a 'low yield'. The yield of a bond is determined by its coupon rate and its market price. A low yield does not necessarily make a bond a bad investment, as it could indicate that the bond is less risky or that the market price is lower than its intrinsic value. Additionally, different bonds have different risk profiles and yields, and it is important to consider the overall risk and return profile of an investment before determining its quality.