Question

Please provide the relevant formulas and calculate the results.

There are three different bonds

• Bond A has a 5% annual coupon, matures in 12 years, and has a $5,000 face value.
• Bond B has a 9% annual coupon, matures in 12 years, and has a $2,000 face value.
• Bond C has an 15% annual coupon, matures in 12 years, and has a $1,000 face value

The interest rate is 9%

1. Calculate the price of each of the three bonds at time zero. compounded annually.
2. For bond A, keep other variables in constant, the compounded period is monthlyright now, what’s the bond A ‘s valuation?
3. For bond C, keep other variables in constant, the compounded period is quarterlyright now, what’s the bond C ‘s valuation?
4. Can you figure out the relationshipbetween compounded period and bond valuation?

Answer 1

(a) Price of the bond = Facevalue/ ( 1+interest rate)^no.of years

Price of bond (A) = 5000/(1+0.05)^12 = 5000/1.79= 2793

Price of bond (B) = 2000/(1+0.09)^12 = 2000/2.81 = 711

Price of bond (C) = 1000/(1+0.15)^12 = 1000/5.35 = 186

(b) price of bond (A) = 5000/(1+0.05/12)^12×12 = 5000/1.80 = 2777

(c) price of bond (C) = 1000/(1+0.15/4)^12*4 = 1000/5.64 = 177

(d) Bond valuation in effect is calculating the present value of a bonds expected future coupon payments. The theoretical fair value of bond is calculated by discounting the present value of its coupon payments by an appropriate discount rate which can be compounded annually,monthly, semiannually and quarterly. The discount rate used is the yield to maturity which is the rate of return that an investor will get if he reinvested every coupon payment from the bond at a fixed interest rate until the bond matures. It takes into account the price of the bond,par value, coupon rate and time to maturity.