- QUESTION
Bond Valuation
This assignment contains two parts: Part I and Part II.
Part I
Answer these questions and show your work:
Assume that the company that you selected for the Module 1 SLP has a bond outstanding that matures in 20 years and has a coupon rate of 6.5%. The par value of the bond is $1,000.
If the yield to maturity is 8% and the bond pays interest on an annual basis, what’s the current price of the bond? Is the bond selling for a premium or discount? How can you tell?
If the yield to maturity is 8% but the bond pays interest on a semi-annual basis instead of an annual basis, what’s the current price of the bond? Is it different from the value when using annual compounding? Explain.
Now, assume that the economy enters into a recession and interest rates fall. The bond’s yield to maturity is now 5%. What’s the bond’s new price? How does the price compare with your answer in part a? Why did the bond’s value change?
A bond matures in ten years and is currently selling for $1,125. The bond pay interest annually, has a par value of $1,000, and a yield to maturity of 10.75%. What’s the bond’s current yield?
Part II:
Write a 2-page essay comparing reinvestment risk and interest rate risk and how an investor can protect his or her portfolio from those risks. Please be sure to discuss duration in your paper.
SLP Assignment Expectations
You are expected to:
Describe the purpose of the report and provide a conclusion. An introduction and a conclusion are important because many busy individuals in the business environment may only read the first and the last paragraph. If those paragraphs are not interesting, they never read the body of the paper.
Answer the SLP Assignment question(s) clearly and provide necessary details.
Write clearly and correctly—that is, no poor sentence structure, no spelling and grammar mistakes, and no run-on sentences.
Provide citations to support your argument and references on a separate page. (All the sources that you listed in the references section must be cited in the paper.) Use APA format to provide citations and references.
Type and double-space the paper
Whenever appropriate, please use Excel to show supporting computations in an appendix, present financial information in tables, and use the data computed to answer follow-up questions. In finance, in addition to being able to write well, it’s important to present information in a professional manner and to analyze financial information. This is part of the assignment expectations and will be considered for grading purposes.[/et_pb_text][et_pb_text _builder_version="4.9.3" _module_preset="default" width_tablet="" width_phone="100%" width_last_edited="on|phone" max_width="100%"]
| Subject | Business | Pages | 6 | Style | APA |
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Answer
Part I
- a)
The value of a bond is the present value of all future cash flows that is expected to be generated by the bond over a given period in time.
The formula for determining the current price or value of a bond is as follows.
B0=I/ (1+kd)1+ I/ (1+kd)2+ I/ (1+kd)3+ I/ (1+kd)4----------- I/ (1+kd)n
Whereby:
B0= The current price or value of the bond
I = Annual interest paid on the bond
Kd=Required rate of return or yield to maturity
In the above case therefore:
I=6.5%*1000=65
Kd=8%
B0= 65/(1+8%)1+65/(1+8%)2+65/(1+8%)3+65/(1+8%)4+65/(1+8%)5+65/(1+8%)6+65/(1+8%)7+65/(1+8%)8+65/(1+8%)9+65/(1+8%)10+65/(1+8%)11+65/(1+8%)12+65/(1+8%)13+65/(1+8%)14+65/(1+8%)1565/(1+8%)16+65/(1+8%)17+65/(1+8%)18+65/(1+8%)19+65/(1+8%)20
=$638.18
(Ivanovski et al, 2013)
The bond will sell at a discount of $361.82 ($1000-$638.18). Whenever the required return or yield to maturity of a bond differs from its coupon interest rate, the bond will differs from it par value. If the required return or yield to maturity is higher than coupon interest rate, the bond value or price will be less than its par value and the bond sells at a discount. When the required return or yield to maturity falls below the coupon interest rate, the bond value will be greater than par value of the bond and the bond sells at a premium(Ivanovski et al, 2013).
B0= 32.5/(1+(8%/2))0.5+32.5/(1+(8%/2))1+32.5/(1+(8%/2))1.5+32.5/(1+(8%/2))2+32.5/(1+(8%/2))2.5+32.5/(1+(8%/2))3+32.5/(1+(8%/2))3.5+32.5/(1+(8%/2))4+32.5/(1+(8%/2))4.5+32.5/(1+(8%/2))5+32.5/(1+(8%/2))5.5+32.5/(1+(8%/2))6+32.5/(1+(8%/2))6.5+32.5/(1+(8%/2))7+32.5/(1+(8%/2))7.5 +32.5/(1+(8%/2))8+32.5/(1+(8%/2))8.5+32.5/(1+(8%/2))9+32.5/(1+(8%/2))9.5+32.5/(1+(8%/2))10+32.5/(1+(8%/2))10.5+32.5/(1+(8%/2))11+32.5/(1+(8%/2))11.5+32.5/(1+(8%/2))12+32.5/(1+(8%/2))12.5+32.5/(1+(8%/2))13+32.5/(1+(8%/2))13.5+32.5/(1+(8%/2))14+32.5/(1+(8%/2))14.5+32.5/(1+(8%/2))15+32.5/(1+(8%/2))15.5+32.5/(1+(8%/2))16+32.5/(1+(8%/2))16.5+32.5/(1+(8%/2))17+32.5/(1+(8%/2))17.5+ 32.5/(1+(8%/2))18+32.5/(1+(8%/2))18.5+32.5/(1+(8%/2))19+32.5/(1+(8%/2))19.5+32.5/(1+(8%/2))20
=$892.12
The current price of the bond is higher than when using annual compounding. This is because the annual interest paid is discounted twice each year i.e. semiannually and annually. The present value of future interest paid each year is higher when semiannual compounding is used than when annual compounding is used(Ivanovski et al, 2013).
B0= 65/(1+5%)1+65/(1+5%)2+65/(1+5%)3+65/(1+5%)4+65/(1+5%)5+65/(1+5%)6+65/(1+5%)7+65/(1+5%)8+65/(1+5%)9+65/(1+5%)10+65/(1+5%)11+65/(1+5%)12+65/(1+5%)13+65/(1+5%)14+65/(1+5%)1565/(1+5%)16+65/(1+5%)17+65/(1+5%)18+65/(1+5%)19+65/(1+5%)20
=$810.04
The bond value will increase to $810.04 which is higher than when the yield to maturity is 8% in part a. This is because when the yield to maturity rises the bond price reduces and when the yield to reduces, like in this case when it dropped to5%, the bond price increases(Ivanovski et al, 2013).
B0=1,125
Annual interest paid is =10.75%*1000=107.5
Kd=?
1,125=107.5/kd
Kd*1,125=(107.5/ Kd)* Kd
Kd=107.5/1.125=0.09556 or 9.6%
(Ivanovski et al, 2013)
Part II:
Interest rate risk refers to the chance that interest rates in future will change and thereby change the required return or yield to maturity and the value of a bond. The level of sensitivity a bond’s value has to changes in interest rates determines the interest rate risk of that particular bond. The level of sensitivity depends on the coupon rate and the amount of time left to maturity of the bond. Investors in the bonds market know that the longer the amount of time left to maturity the greater the interest rate risk and the lower the coupon rate, the greater the interest rate risk while all other things are kept constant. The value of a bond normally decreases when interest rates rise (Ivanovski et al, 2013).
One of the major factors that influence total return and bond market price is interest rate risk. As can be ascertained in the foregoing analysis in Part 1, bond values normally moves in the opposite direction to yield to maturity changes. Investors would normally demand to invest in bonds with a higher coupon rate when investing in a bond if inflation is projected to rise in future thus lowering the purchasing power of investors. Interest rate risk decreases for bonds with shorter maturities and higher coupon payments mainly because shorter maturities would ensure investors in the bond get interest payments in a short period which reduces the effects of time value of money on interest payments. Bonds with longer maturities and lower coupon rates have high interest rate risk (Blake, Boardman & Cairns, 2014). This is because a longer time to maturity exposes the interest payments to more adverse effects of time value of money. Lower coupon rates also expose interest paid to effects of time value of money and adverse economic challenges. Even though reinvestment risk is related to interest rate risk, it affects bonds performance differently; in an opposing manner. Reinvestment risk relates to rate of reinvesting coupon and principal cash inflows from a bond. There is a fear among investors that the expected rate may be lower than the yield to maturity when the bond was purchased(Ivanovski et al, 2013). A bond’s coupon value increases if it is paid at a fixed rate. Bonds with longer maturities and higher coupon payments have a higher reinvestment risk while reinvestment risk is lower for bonds with shorter maturities and lower coupon rates. Investors are usually concerned that a fall in interest rates in future will reduce their incomes, as the funds will be reinvested at lower rates. This is what is referred to as reinvestment risk (Ivanovski et al, 2013).
Bonds with longer maturity periods have higher reinvestment risk due to a number of reasons. One of the reasons is that the longer the maturity period, the longer the invested capital will take before it earns substantial returns (Ivanovski et al, 2013). Most of future returns will be subject to adverse economic factors. Some of these factors may include fluctuations in interest rates. Shorter periods to maturity ensure that interest payments are not affected by adverse effects of inflation. Hence, long term bonds have low reinvestment risk and high interest rate risk. On the other hand, short term bonds have high reinvestment rate risk. In conclusion, long term bonds have a high interest rate risk and a lower investment risk while short term bonds have a high reinvestment risk and high interest rate risk (Ivanovski, Stojanovski & Ivanovska, 2013).
References
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Blake, D., Boardman, T., & Cairns, A. (2014). Sharing longevity risk: Why governments should issue longevity bonds. North American Actuarial Journal,18(1), 258-277. Retrieved from http://search.proquest.com/docview/1535659618?accountid=45049 Ivanovski, Z., Stojanovski, T. D., & Ivanovska, N. (2013). Interest rate risk of bond Prices on Macedonian stock exchange - empirical test of the duration, modified duration and convexity and bonds valuation. Ekonomska Istrazivanja, 26(3), 47-62. Retrieved from http://search.proquest.com/docview/1466567571?accountid=45049
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