Question

Here are data on ​$1,000 par value bonds issued by​ Microsoft, GE​ Capital, and Morgan Stanley. Assume you are thinking about buying these bonds. Answer the following​ questions:

a. Assuming interest is paid​ annually, calculate the values of the bonds if your required rates of return are as​ follows: Microsoft, 5.5 ​percent; GE​ Capital, 17.5 percent; and Morgan​ Stanley, 11.5 ​percent; where:

	Microsoft	GE capital	Morgan Stanley
Interest Rate	4.50%	6.75%	8%
Maturity	26	23	13

Microsoft        ​$798

GE Capital     ​$476

Morgan Stanley   ​$690

What are 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 ​(c​) in terms of interest rate​ risk, premium​ bonds, and discount bonds.

e. Should you buy the​ bonds? Explain.

Answer 1

a)

Value of Microsoft bonds = 45/0.055*(1-1/1.055^26)+1000/1.055^26 = $863.38

Value of GE-Capital bonds = 67.5/0.175*(1-1/1.175^23)+1000/1.175^23 = $400.76

Value of Morgan Stanley bonds = 80/0.115*(1-1/1.115^13)+1000/1.115^13 = $769.58

b) Given the price of the three bonds

Expected return for Microsoft bond (r) is given by

45/r*(1-1/(1+r)^26)+1000/(1+r)^26 = 798

Solving r=0.0606 or 6.06%

Expected return for GE Capital bond (r) is given by

67.5/r*(1-1/(1+r)^23)+1000/(1+r)^23 = 476

Solving r=0.1488 or 14.88%

Expected return for Morgan Stanley bond (r) is given by

80/r*(1-1/(1+r)^13)+1000/(1+r)^13 = 690

Solving r=0.1308 or 13.08%

c)

If required rates increased by 2%

Value of Microsoft bonds = 45/0.075*(1-1/1.075^26)+1000/1.075^26 = $661.02

Value of GE-Capital bonds = 67.5/0.195*(1-1/1.195^23)+1000/1.195^23 = $357.02

Value of Morgan Stanley bonds = 80/0.135*(1-1/1.135^13)+1000/1.135^13 = $671.13

If required rates decreased by 2%

Value of Microsoft bonds = 45/0.035*(1-1/1.035^26)+1000/1.035^26 = $1168.90

Value of GE-Capital bonds = 67.5/0.155*(1-1/1.155^23)+1000/1.155^23 = $456.01

Value of Morgan Stanley bonds = 80/0.095*(1-1/1.095^13)+1000/1.095^13 = $890.63

d) Interest rate poses a big risk for bonds particularly those with high maturity. In the above answers , we saw that an increase in interest rates by even 2% can decrease the value of the bond by about 23% (Microsoft bond) whereas decrease in interest rates increase the value and can even make a discount bond a premium bond. Also, the increase in value by a decrease in interest rate is higher as compared to the decrease in price.