A newly issued bond pays its coupons once annually. Its coupon rate is 5%, its maturity is 20 years, and its yield to maturity is 6%.
Boston University Bond Pricing Calculations Excel Worksheet
Homework 4
Unless stated otherwise, round your answers to two decimal points, and do not round intermediate calculations.
Problem 1. A newly issued bond pays its coupons once annually. Its coupon rate is 5%, its maturity is 20 years, and its yield to maturity is 6%.
a) Find the price of the bond.
b) After one year, the bond is selling at a yield to maturity of 5.5%. Find the holding period return if you sell the bond after one year.
c) If you sell the bond after one year, what taxes will you owe? Assume that the tax rate on interest income is 40% and the tax rate on capital gains income is 30%.
d) What is the after-tax holding period return on the bond?
Problem 2. A 30-year maturity, 8% coupon bond paying coupons semiannually is callable in five years at a call price of $1,020. The bond currently sells for $1,059.34.
a) What are the yield to maturity and the yield to call of the bond?
b) What would be the yield to call annually if the call price were only $970?
c) What would be the yield to call annually if the call price were $1,020, but the bond could be called in two years instead of five years? d) Sketch the price of the bond as a function of the interest rate.
Problem 3: Bond Research. Consider the following tradeable bonds. Company Apple Disney McDonald’s Ticker AAPL DIS MCD Bond ID US037833CX61 US25468PDB94 US58013MFQ24 Par Value $1,000.00 $1,000.00 $1,000.00 Coupon 3.000% 4.125% 3.600% Maturity Jun 20, 2027 Jun 1, 2044 Jul 1, 2030
a) For the bonds listed, find the current bid and ask prices. Compute their yields to maturity.
b) Based on the stock you were assigned at the beginning of the semester, study the appropriate stock. If your stock was $AAPL, consider the Apple bond, etc.
i) Research the details of the bond for example, how often and at what dates is the bonds paying coupons; is the bond international or domestic; what is the size of the issue; is the bond fixed or floating rate; is the bond convertible, callable, or puttable.
ii) What is the credit rating of the issuer of the bond? How is this credit rating reflected in the yield of the bond? If possible, quantify the credit spread.
Problem 4. A five-year bond with a yield of 11% pays an 8% coupon at the end of each year. a) b) c) d) What is the bond’s price? What is the bond’s duration? Use the duration to calculate the effect on the bond’s price of a 0.2% decrease in its yield. Recalculate the bond’s price on the basis of a 10.8% per annum yield, and verify that the result agrees with your answer to c.
Problem 5. An investor is deciding between investing in the bonds issued by two companies operating in the same industry using the information listed below: Revenue Interest Expense Earnings before interest, taxes Assets Company A $20 million $2 million $4 million $10 million Company B $50 million $5 million $7 million $25 million Based on the companies’ financials listed above, use two financial ratios to identify the company that is less likely to default.
Problem 6. A newly issued bond has a maturity of 10 years and pays a 5.5% coupon rate (with coupon payments coming once annually). The bond sells at par value.
a) What are the convexity and the duration of the bond?
b) Find the actual price of the bond assuming that its yield to maturity immediately increases from 5.5% to 6.5% (with maturity still 10 years). Assume a par value of 100.
c) What price would be predicted by the modified duration rule?
d) What is the percentage error of that rule? What price would be predicted by the modified durationwith-convexity rule? What is the percentage error of that rule? Problem 7. An insurance company has the liabilities with the following payment pattern, each at the end of the respective year: • • • Year 3: Year 7: Year 20: $2.5 million $4.2 million $6.0 million There are no other liabilities to consider. The discount rate for the insurance’s liabilities is 3%.
The insurance company has the following investment opportunities in bonds and stocks: Coupon Bonds Maturity Yield Common Stocks Duration Stock Zero-Coupon Bonds Dividend Duration Maturity Yield 4 7.0% 3 A 5.0% 20 3 1.5% 10 9.0% 7 B 9.3% 11 5 2.0% 20 30 10.0% 11.0% 11 20 C D 10.0% 14.3% 10 7 7 10 2.0% 3.0% 15 3.5% 20 4.0% (Note: As for bonds, it is possible to compute something like duration for dividend paying stocks. More about that in later classes.)
a) Using the information about the zero-coupon bonds, draw the yield curve and compute two forward rates of your choice.
b) Calculate the duration of the liability.
c) The insurance company desires a rate of return of 11% for its investments. Using the securities listed above, design an investment portfolio that is immunized from small interest rate changes and provides an expected return of at least 11%. If such a portfolio is impossible to achieve with the securities listed above, what return can be achieved?
d) How can the liabilities of the insurance completely immunized from all interest changes? Explain your approach and build the portfolio. The following problems are for your practice only. They will help you prepare for the exam, but you need not submit them.
Practice Problems
Chapter 14, Problems 8-10, 25-27
Chapter 15, Problems 7, 12
Chapter 16, Problems 3-5, 11-12 3
Collepals.com Plagiarism Free Papers
Are you looking for custom essay writing service or even dissertation writing services? Just request for our write my paper service, and we'll match you with the best essay writer in your subject! With an exceptional team of professional academic experts in a wide range of subjects, we can guarantee you an unrivaled quality of custom-written papers.
Get ZERO PLAGIARISM, HUMAN WRITTEN ESSAYS
Why Hire Collepals.com writers to do your paper?
Quality- We are experienced and have access to ample research materials.
We write plagiarism Free Content
Confidential- We never share or sell your personal information to third parties.
Support-Chat with us today! We are always waiting to answer all your questions.
