Question

A 25-year, $1,000 par value zero-coupon rate bond is to be issued to yield 8 percent. Use Appendix B for an approximate answer but calculate your final answer using the formula and financial calculator methods.

a. What should be the initial price of the bond? (Assume annual compounding. Do not round intermediate calculations and round your answer to 2 decimal places.)

b. If immediately upon issue, interest rates dropped to 7 percent, what would be the value of the zero-coupon rate bond? (Assume annual compounding. Do not round intermediate calculations and round your answer to 2 decimal places.)

c. If immediately upon issue, interest rates increased to 10 percent, what would be the value of the zero-coupon rate bond? (Assume annual compounding. Do not round intermediate calculations and round your answer to 2 decimal places.)

Answer 1

Requirement (a) – Initial Price of the Bond at 8 percent YTM

Price of a Zero-Coupon Bond is the Present Value of the Par Value of the Bond

Par Value = $1,000

Yield to Maturity (YTM) = 8%

Number of period = 25 Years

The Price of the Bond = Par Value x [1 / (1 +YTM) ⁿ]

= $1,000 x [1/(1 + 0.08)²⁵]

= $1,000 / 6.84848

= $146.02

Requirement (b) – Value of the zero-coupon rate bond if the interest rates dropped to 7 percent

Par Value = $1,000

Yield to Maturity (YTM) = 7%

Number of period = 25 Years

The Value of the Bond = Par Value x [1 / (1 +YTM) ⁿ]

= $1,000 x [1/(1 + 0.07)²⁵]

= $1,000 / 5.42743

= $184.25

Requirement (c) – Value of the zero-coupon rate bond if the interest rates increase to 10 percent

Par Value = $1,000

Yield to Maturity (YTM) = 10%

Number of period = 25 Years

The Value of the Bond = Par Value x [1 / (1 +YTM) ⁿ]

= $1,000 x [1/(1 + 0.10)²⁵]

= $1,000 / 10.83471

= $92.30