Question

ReNew Corporation raises funds to build renewable energy systems by issuing 3-year bonds with a coupon rate of 5% and a face value of $1,800. Assume that the market interest rate for a 3-year bond issued by a firm like ReNew is currently the same as the coupon rate. The price of each of these bonds is , which means that the bonds sell at .

Answer 1

$1,800

Step-by-step explanation:

The price of the bond today is the present value of future cash flows, which are the coupon payments and the face value receivable by bondholders at redemption in 3 years.

When a bond has the same coupon rate as the yield, the bond would sell at par which is the $1,800 par value.

This is further affirmed using the formula below:

bond price=face value/(1+r)^n+annual coupon*(1-(1+r)^-n/r

face value=$1,800

r=yield=5%

n=number of annual coupons in 3 years=3

annual coupon=face value*coupon rate=$1800*5%=$90

bond price=$1800/(1+5%)^3+$90*(1-(1+5%)^-3/5%

bond price=$1800/1.05^3+$90*(1-(1.05)^-3/0.05

bond price=$1800/1.157625+$90*(1-0.863838)/0.05

bond price=$1800/1.157625+$90*0.136162/0.05

bond price=$ 1,554.91 +$ 245.09

bond price=$ 1,800.00