Answer these questions and show your work: Assume that the company that you sele
ID: 2738188 • Letter: A
Question
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?
Explanation / Answer
Solution:-
Current price of bond = Interest amount * Cumulative P.V. factor @ 8 % for 20 Years + Principal amount * P.V. Factor @ 8 % of 20TH Year
= (1000 * 6.5%) * 9.8181 + 1000 * 0.2145
= 65 * 9.8181 + 1000 * 0.2145
= $ 852.68 (approx)
YTM is more than coupon rate, market price is less than face value i.e. at Discount.
The bond is selling for Discount.
2.
Current price of the bond = Interest amount * Cumulative P.V. factor @ 4 % for 40 Years + Principal amount * P.V. Factor @ 4 % of 40TH Year.
= (1000 * 6.5 % * 6/12) * 19.7928 + 1000 * 0.2083
= 32.5 * 19.7928 + 1000 * 0.2083
= $ 852 (approx)
Note:- Bonds pay interest semi-annually:-
The annual interest payment is divided by 2 to obtain semi-annual interest payment. The number of YTM is multiplied by 2 to get number of half-yearly periods. The discount rate is divided by 2 to get discount rate applicable to half-yearly periods.
3.
Whene bond’s yield to maturity is 5%, paid annually
The bond’s new price is $1252.03
Since Yield to maturity has been reduced, current price of bond has been increased.
Price is at premium since YTM<Coupon rate and is just opposit to part a
Since the market enters into recession and interest rate falls, exeptation from risk free instrument will decrease and bond will be purchased even at premium.
Let the bond’s current yield be X, so
Conditionally, 360 + 5.951 X = 1125
=> X = (1125-360)/5.951 = 128.55
As the amount of Current yeild is $ 128.55, rate of current yield = 128.55/1000 * 100 = 12.85%
Year Interest income DF @5% Present value (PV) 1 to 20 65 13.462 875.03 20 1000 0.377 377 Total 1252.03Related Questions
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