Question

A 2-year maturity bond with face value of $1,000 makes annual coupon payments of $80 and is selling at face value. What will be the rate of return on the bond if its yield to maturity at the end of the year is: (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.) Rate of Return a. | 6% b. | 8% c. | 10%

Answer 1

Solution:

Annual coupon payment of the bond is $80

At the beginning of the year, remaining maturity period is 2 years.

Price of the bond is equal to face value, i.e. the initial price of the bond is $1000.

New price of the bond = present value of the final coupon payment + present value of the maturity amount.

New price of the bond = $\frac{80}{1+r} +\frac{1000}{1+r}$

where, r is the yield to maturity at the end of the year.

Substitute 0.06 for r in the above equation,

Therefore new price of the bond is  = $\frac{80}{1+0.06} +\frac{1000}{1+0.06}$

                                                           = $\frac{1080}{1.06}$

                                                           = $ 1010.87

Calculating the rate of return of the bond as

$\text{rate of return}=\frac{\text{coupon+new price-old price}}{\text{initial price}}$

                     $=\frac{80+1018.87-1000}{1000}$

                     = 0.09887

Therefore, the rate of return on the bond is 9.887%

                                                                    ≈ 10 %