Question

You are considering purchasing a $2,000, 20-year, 8% bond. Interest is paid semi-annually and comparable issues with similar risk are yielding 7%. If the bond has 12 years until maturity, what is the most you should pay for the bond today?

Answer 1

Price of this bond is the present value of cash flows of this bond.

Present value of coupon

$       80.00

*

16.05837

=

$              1,284.67

Present value of face value

$ 2,000.00

*

0.437957

=

$                  875.91

Present value of cash flows

$              2,160.58

So, price of bond is $ 2,160.58 and I should pay $ 2,160.58 for this bond.

Working:

# 1

Semi annually coupon paid in cash

=

Face Value * Semi annual coupon rate

=

2000*8%*6/12

=

$    80.00

# 2

Present value of annuity of 1

=

(1-(1+i)^-n)/i

Where,

=

(1-(1+0.035)^-24)/0.035

i

7%/2

=

0.035

=

16.05837

n

12*2

=

24

# 3

Present value of 1

=

(1+i)^-n

=

(1+0.035)^-24

=

0.437957