Here are data on $1,000 par value bonds issued by Microsoft, Ford, and Xerox at the end of 2008. Assume you are thinking about buying these bonds as of January 2009. Answer the following questions:
a.) Calculate the values of the bonds if your required rates of return are as follows: Microsoft, 6 percent; Ford, 15 percent; Xerox, 10 percent; where
coupon of interest Microsoft-5.25% Ford-7.125% Xerox-8.0%
Years to maturity Microsoft-30 Ford-25 Xerox-16
b.) At the end of 2008, the bonds were selling for the following amounts:
Microsoft $1,009.00
Ford $610.00
Xerox $805.00
What were the expected rates of return for each bond?
c.) How would the value of the bonds change if (1) your required rate of return (rb) increased 2 percentage points or (2) decreased 2 percentage points?
d.) Explain the implications of your answers in part b in terms of interest rate risk, premium bonds, and discount bonds.
e.) Should you buy the bonds? Explain.
a.) Calculate the values of the bonds if your required rates of return are as follows: Microsoft, 6 percent; Ford, 15 percent; Xerox, 10 percent; where
coupon of interest Microsoft-5.25% Ford-7.125% Xerox-8.0%
Years to maturity Microsoft-30 Ford-25 Xerox-16
To calculate the values of the bonds, you need to use the formula for present value of a bond:
Value = (Coupon Payment * (1 - (1 + r)^-n) / r) + (Par Value / (1 + r)^n)
where:
- Coupon Payment is the annual interest payment (coupon rate * par value)
- r is the required rate of return (or discount rate)
- n is the number of years to maturity
- Par Value is the face value of the bond
a) To calculate the value of each bond using the given discount rates:
For Microsoft:
Coupon Payment = 0.0525 * $1,000 = $52.5
r = 0.06 (6%)
n = 30 years
Par Value = $1,000
Value = ($52.5 * (1 - (1 + 0.06)^-30) / 0.06) + ($1,000 / (1 + 0.06)^30)
Similarly, you can calculate the values for Ford and Xerox bonds using their respective discount rates and years to maturity.
b) To calculate the expected rates of return, you need to use the formula:
Expected Rate of Return = (Ending Value - Beginning Value + Coupon Payment) / Beginning Value
For Microsoft:
Beginning Value = $1,009.00
Ending Value = $1,000.00
Coupon Payment = $52.5
Using the formula, you can calculate the expected rates of return for Ford and Xerox bonds as well.
c) To calculate how the value of the bonds would change with a 2 percentage point increase or decrease in the required rate of return, you need to recalculate the value using the adjusted rate:
New Value = ($52.5 * (1 - (1 + (r +/- 0.02))^(-30)) / (r +/- 0.02)) + ($1,000 / (1 + (r +/- 0.02))^30)
d) The implications in terms of interest rate risk, premium bonds, and discount bonds are as follows:
- Interest rate risk: When interest rates increase, the value of bonds decreases. On the other hand, when interest rates decrease, the value of bonds increases. This is because higher interest rates make existing bond yields less attractive compared to newly issued bonds with higher interest rates.
- Premium bonds: If the bond is selling for more than its face value, it is called a premium bond. In part b, Microsoft is selling for $1,009, which is higher than its par value. This suggests that the expected rate of return for the bond is lower than the coupon rate. Investors are willing to pay a premium to receive that lower expected rate of return.
- Discount bonds: If the bond is selling for less than its face value, it is called a discount bond. In part b, Ford is selling for $610, which is lower than its par value. This suggests that the expected rate of return for the bond is higher than the coupon rate. Investors require a higher return and are not willing to pay full face value for the bond.
e) Whether or not you should buy the bonds depends on your investment objectives and risk tolerance. You should consider factors such as the expected rates of return, the current market conditions, the financial health of the companies, and your own investment goals. It is recommended to consult with a financial advisor who can provide personalized advice based on your individual situation.