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 $4\mathrm{.}70\%,10-$year $4\mathrm{.}25\%$

$10-$year A rated bonds should yield $($return$)0\mathrm{.}75\%$ 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 $1\mathrm{.}25\%.$

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 today$$s price. Given your calculations estimate what would

happen to the price of the bonds if interest rates were to decline $0\mathrm{.}50\%$

from current $($today$$s 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?