Question

A six-year annual payment corporate bond has a required return of 9.5 percent and an 8 percent coupon. Its market value is $20 over its PV. the bond's E(r)?

A corporate bond returns 12 percent of its cost (in PV terms) in the first year, 11 percent in the second year, 10 percent in the third year and the remainder in the fourth year. What is the bond's duration in years? step by step please

Answer 1

1st we need to find price of bond.

Lets take face value of bond as $1000.

Presnet value of bond is given by following formula:

PV = C * (1 - (1 + r)^(-n))/r + FV/(1+r)^n

where C is annual coupon

r is required return

n is number of year.

PV = 80*(1 - (1.095)^(-6))/.095 + 1000/(1.095)^6

= $353.59 + 580.12

= $933.71

But its market value is $20 more than fair value so we need to find E(r) using given formula only by taking bond value as $953.71

$953.71 = 80* (1 - (1+E(r))^(-6)/E(r) + 1000/(1 + E(r))^(6)

while using trail and error method we will get the value of E(r) = 9.03%

Ans 2) Duration in year = summation of (year* percent of its cost in PV terms in respectivce year)

Duration in year = 1*12% + 2*11% + 3*10% + 4*(100 - 12 - 11 - 10)%

= 3.32 years