Question

Motron has two bonds outstanding, Series E and Series F. Both bonds have face values of $10,000 and, because both bonds are backed by Motron, share a 5.25% YTM. The Series E is a zero coupon bond with a maturity in 5 years. The Series F, maturing in 4 years, is a hybridized bond that pays no coupon for the first year; then pays $350 every six months for two years (four total payments); and finally makes two $850 payments in the last year.

Series E;

YTM: 5.25%

Issuance: 10/01/2018

Maturity: 10/01/2023

Term: 5 years

Face: $10,000

Coupons/Yr: 2

Coupon: 0%

Series F:

YTM: 5.25%

Issuance: 10/01/2018

Maturity: 10/01/2022

Term: 4 years

Face: $10,000

Coupons/ Yr : 2

Coupon 1: 0% annually, begins year 0

Coupon 2: 7% begins after year 1

Coupon 3: 17% annually begins after 3

What is the current price of a Series F bond? (Hint: Even if you utilize formulas to solve this, you should lay out and discount the stream of cash flows as a check on your work.)

A. $10,098.06

B. $10,034.54

C. $10,774.14

D. $11,001.42

E. $13,413.23

Answer 1

Solution:

Annual effective YTM=[1+(YTM/No. of compounding)]^2-1

=[1+(0.0525/2)]^2-1

=0.05319 or 5.319%

thus effctive YTM per coupon period=0.05319/2=0.026595

Price of bond is the sum of present value of future coupon on it and its maturity value:

Price=Coupon/(1+effctive YTM per coupon period)^no. of period+Maturity value/(1+effctive YTM)^no of period to maturity

=$350/(1+0.026595)^3+$350/(1+0.026595)^4+$350/(1+0.026595)^5+$350/(1+0.026595)^6+$850/(1+0.026595)^7+[($850+$10,000)(1+0.026595)^8]

=$10,746.92

Thus correct answer is Option C,i.e $10,774.14

Difference between calculated answer(10,746.92) and actual answer(10,774.14) is due to rounding of present value factor.