Question

part a.

Madsen Motors's bonds have 25 years remaining to maturity. Interest is paid annually; they have a $1,000 par value; the coupon interest rate is 11%; and the yield to maturity is 7%. What is the bond's current market price? Round your answer to the nearest cent.

$

part b.

Nesmith Corporation's outstanding bonds have a $1,000 par value, a 7% semiannual coupon, 11 years to maturity, and a 10% YTM. What is the bond's price? Round your answer to the nearest cent.

$  

Answer 1

The Current Price of the Bond is given by the Present Value of all the cashflows associated with the bond.

Solution a:

Given:

Years until maturity = 25

Interest is paid annually

Par value of Bond = $ 1,000

Coupon interest rate = 11%

Yield to maturity (ytm) = 7%

Current price of Bond = ?

The formula for the Current price odf the bond is:

where C is the Coupon Payment = Coupon Interest rate * Bond Par value

C = 11% * 1000 = 110

P is the Par value of the Bond = 1000

ytm = 7%

n = years until maturity = 25

Upon substituting, we get,

Hence, the Current Price of the Bond = $ 1,466.14

Solution b:

Given:

Years until maturity = 11

Interest is paid semi-annually

Par value of Bond = $ 1,000

Coupon interest rate = 7%

Yield to maturity (ytm) = 10%

Current price of Bond = ?

The formula for the Current price odf the bond is:

Since, the coupon payments are semi-annual no of coupon paying periods will be 2 per year.

where C is the Coupon Payment = Coupon Interest rate per period * Bond Par value

C = (7%/2) * 1000 = 35

P is the Par value of the Bond = 1000

ytm = 10%/2 = 5%

n = years until maturity = 11* 2 = 22

Upon substituting, we get,

Hence, the Current Price of the Bond = $ 802.55