Question

Zero-coupon bond. Wesley Company will issue a zero-coupon bond this coming month. The projected bond yield is 8%. If the par value is ​$100,000, what is the​ bond's price using a

semiannual convention if a. the maturity is 10 ​years?

b.the maturity is 40 ​years?

c.the maturity is 50 ​years?

d.the maturity is 80 ​years?

Answer 1

(a)-Price of the Zero-coupon bond if the maturity is 10 years

Par Value of the Bond = $100,000

Yield to Maturity (YTM) = 4.00% [8.00% x ½]

Maturity Period = 20 Years [10 Years x 2]

Therefore, the Price of Zero-Coupon Bond = Par Value / (1 + YTM)ⁿ

= $100,000 / (1 + 0.04)²⁰

= $100,000 / 2.191123

= $45,638.69

(b)-Price of the Zero-coupon bond if the maturity is 40 years

Par Value of the Bond = $100,000

Yield to Maturity (YTM) = 4.00% [8.00% x ½]

Maturity Period = 80 Years [40 Years x 2]

Therefore, the Price of Zero-Coupon Bond = Par Value / (1 + YTM)ⁿ

= $100,000 / (1 + 0.04)⁸⁰

= $100,000 / 23.049799

= $4,338.43

(c)-Price of the Zero-coupon bond if the maturity is 50 years

Par Value of the Bond = $100,000

Yield to Maturity (YTM) = 4.00% [8.00% x ½]

Maturity Period = 100 Years [50 Years x 2]

Therefore, the Price of Zero-Coupon Bond = Par Value / (1 + YTM)ⁿ

= $100,000 / (1 + 0.04)¹⁰⁰

= $100,000 / 50.504948

= $1,980.00

(d)-Price of the Zero-coupon bond if the maturity is 80 years

Par Value of the Bond = $100,000

Yield to Maturity (YTM) = 4.00% [8.00% x ½]

Maturity Period = 160 Years [80 Years x 2]

Therefore, the Price of Zero-Coupon Bond = Par Value / (1 + YTM)ⁿ

= $100,000 / (1 + 0.04)¹⁶⁰

= $100,000 / 531.293237

= $188.22