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Assume today is April 1 , 2 0 2 4 , and that all bonds pay interest semi - annually with a face value of

Assume today is April 1,2024, and that all bonds pay interest semi-annually
with a face value of $1,000. YTM = Current yield + Capital Gains yield; CY =
Annual Interest/Current Price
ABC is currently A rated; AAA Treasuries yield 1-year is 4.70%,10-year 4.25%
10-year A rated bonds should yield (return)0.75% more than AAA bonds.
2 Years ago, ABC issued 7% coupon, semi-annual paying bonds with a $1000 face
value set to mature on April 1,2033. These bonds are callable, 1 year from
today at $1050. At the time these bonds were issued ABC was dealing with
financial problems as their new product, a state-of-the-art semiconductor, was
not selling well. Also, at that time 10-year treasury rates were about 1.25%.
Today all is well for ABC as their product has taken off and sales are through
the roof. The current price for these bonds today is $1070.
1. What is the yield to maturity for an investor who buys the bonds today
at the current price?
2. Is the bond trading at a premium, discount or at par? Explain what your
answer means.
3. What is the current yield of this bond?
4. What is the capital gains yield of this bond?
5. Do you think ABC would call these bonds in 1 year? WHY? Calculate the
yield to call. Which rate here is more relevant, the YTM or the YTC?
Explain why.
For Questions 6 and 7 Assume that the bonds pay interest annually
this will simplify the work!!!
IBM has a 5-year, 4% coupon, annual interest bonds that are currently
priced at $950 that have a face of $1000. Use these bonds for the
questions below.
6. Calculate the Macaulay Duration and Modified Duration for this bond
based on todays price. Given your calculations estimate what would
happen to the price of the bonds if interest rates were to decline 0.50%
from current (todays levels). Assume the change is immediate and
dissect the change in price due to duration and compare it to the actual
calculated change in price.
Show expected price predicted by duration and actual price by
calculation they should be similar but slightly different!
7. Calculate your annualized return if you assume that you buy the bonds
today at the price given and that you sell the bond in 3 years when the
YTM of the bond is at 3%. Assume that the interest you are paid is
reinvested at an annual rate of 3%. Make sure you calculate your
annualized return using the EAR formula. This is a 3-year return
problem!! Comment on why your return is different than the YTM when you
buy the bond today.
8. If you purchase a bond with a YTM of 4% and reinvested the coupon
payments at an annualized rate of 5% what will the realized annual
return be in relation to the YTM?
Realized annual return will be greater than, equal to, or less than YTM
at purchase.
9. True or False if a company issues bonds at a very high interest rate
due to their riskiness and afterwards their fundamentals improve
dramatically but during that time interest rates in the economy rise,
there is likely no chance of them calling their bonds early?

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