Question

a series of $1,000 par value bonds outstanding. Each bond pays interest semi-annually and carries an annual coupon rate of 6%. Some bonds are due in 4 years, while others are due in 10 years. If the required rate of return on bonds is 10%, what is the current price of: a) the bonds with four years to maturity? b) the bonds with 10 years to maturity? c) Explain the relationship between the number of years until a bond matures and its price.

Answer 1

a. Semi annual coupon = $1,000 * 6% / 2 = $30

Par Value = $1,000

PVIFA (n=8, i=5%) = 6.4632 & PV of 4th year with semiannual compounding at n=8 and i=5% = 0.6768

Price of bond with 4 year of maturity = $1,000 * 0.6768 + $30*6.4632

= 676.80 + 193.90 = $870.70

b. Semi annual coupon = $1,000 * 6% / 2 = $30

Par Value = $1,000

PVIFA (n=20, i=5%) = 12.4622 & PV of 10th year with semiannual compounding at n=20 and i=5% = 0.3769

Price of bond with 4 year of maturity = $1,000 * 0.3769 + $30*12.4622

= 376.90 + 373.87 = $750.77

c. The longer the years, the less the current price of the bonds to maturity as it the loses the compounding interest benefit.