Question

Assume that the term structure is flat with a 20% rate. At the end of one year there is the possibility of a single, parallel shift in interest rates either to 24% or to 16% or rates could stay the same. Assume annual compounding. Suppose you have a two- year holding period. Under the three interest rate scenarios, what would be the future value of your investment at the end of two years for the following bond investments if you reinvest the coupon payments at the then-prevailing market rate?

A $1000, 2-year bond with a 20% coupon payment.

b. A $1000, 5-year bond with a 20% coupon payment (i.e., you sell the bond after two years).

c. A 2-year zero coupon bond with a face value of $1,440.

Answer 1

A.)

Part 1

if Interest rate = 20%

Future value (FV)= $1000

Part 2

if Interest rate = 24%

Future value (FV)= 200*1.24 (Reinvested coupon received at the end of year 1@ 24%)+1200 (200+1000=Coupon +Principal at the end of year 2)=1448

Part 3

if Interest rate = 16%

Future value (FV)= 200*1.16 (Reinvested coupon received at the end of year 1@ 16%)+1200 (200+1000=Coupon +Principal at the end of year 2)=1432

B

Part 1

if Interest rate = 20%

Future value (FV)= 200*1.20 (Reinvested coupon received at the end of year 1@ 20%)+200 (Coupon at the end of the year 2)+1000(Amount received after selling the bond at the end of year 2)=1440

Part 2

if Interest rate = 24%

Future value (FV)= 200*1.24 (Reinvested coupon received at the end of year 1@ 20%)

+200 (Coupon at the end of the year 2)

+920.75(Amount received after selling the bond at the end of year 2= present value of all the future cash flows discounted at 24% =( (200/1.24)+200/(1.24)²+ 1200/(1.24)³ )

=1368.75

Part 3

if Interest rate = 16%

Solve similar to part 2 as above.

C

For a 2year Zero coupon bond, FV will not change. It will mature after 2 years at $1440.