$2.$ After recently receiving a bonus, you have decided to add some bonds to your investment portfolio. You have narrowed your choice down to the following bonds $($assume semiannual payments$)$:

Bond A

Bond B

Bond C

Settlement Date

$2/15/2015$

$2/15/2015$

$2/15/2015$

Maturity Date

$8/15/2025$

$5/15/2035$

$6/15/2045$

Coupon Rate

$5\mathrm{.}00\%$

$7\mathrm{.}50\%$

$8\mathrm{.}00\%$

Market Price

$$987$

$$1,040$

$$1,098$

Face Value

$$1,000$

$$1,000$

$$1,000$

Required Return

$5\mathrm{.}25\%$

$7\mathrm{.}00\%$

$7\mathrm{.}25\%$

a$.$ Using the PRICE function, calculate the intrinsic value of each bond. Are any of the bonds currently undervalued? How much accrued interest would you have to pay for each bond?

b$.$ Calculate the current yield of each bond. Is this the total return that you would earn each year? If you were on a fixed income, would you care about this number?

c$.$ Using the YIELD function, calculate the yield to maturity of each bond using the current market prices. How do the YTMs compare to the current yields of the bonds?

d$.$ Calculate the duration and modified duration of each bond. Create a chart that shows both measures versus term to maturity. Does duration increase linearly with term? If not, what relationship do you see?

e$.$ Which bond would you rather own if you expect market rates to fall by $2\%$ for all bonds? What if rates will rise by $2\%?$ Why?