Calculate the price of a bond. Show your calculations

Question

Company ROOS is partly financed with a bond loan. The bonds are so-called 'level coupon bonds'. The nominal value of each of the bonds is €1.000 and the coupon 3%. The coupon is paid annually. The remaining maturity of the bonds is 4 years. The yield to maturity of the bonds is 6%. Assume there is no default risk.

 

Questions:

a. Calculate the price of a bond. Show your calculations. (6 points)

b. At what market interest rate does the price of the bond equal the nominal value? (4 points)

Answer 1

The bond price is the discounted value of all cash flows. The is a three percent coupon or 30 Euroes Every Year for 4 years This is just like a 30 euro 4 year Annuity. The PV of the 4 year Bullet is 1000/(1+6%)^4 =792.09 Euros. The Annuitiy is worth PV=30*(1/6%)(1-(1/(1.06)^4)) - 3.465*30 = 103.95. add the two pieces together and get Bond price = 896.04