Question

As the new Financial Manager, the CEO of King Fisher has asked you to review some bonds. What is the price of a 15 year, semi-annual zero-coupon bond, paying $1000 at maturity if the YTM is:

8%

10%

12%

Fill in the values and show all work

Answer 1

Solution :- i). If YTM is 8 %, Price of Semi annual bond :-

YTM = 8 % * 6 / 12 = 4 % or 0.04 (Semi-annual).

Time period = 15 * 12 / 6 = 30 Semi annual periods.

Price of semi-annual bond = Maturity value of bond / (1 + YTM on bond)Time period.

= 1000 / (1 + 0.04)30

= 1000 / (1.04)30

= 1000 / 3.2434

= $ 308.32 (approx).

ii). If YTM is 10 %, Price of Semi annual bond :-

YTM = 10 % * 6 / 12 = 5 % or 0.05 (Semi-annual).

Time period = 15 * 12 / 6 = 30 Semi annual periods.

Price of semi-annual bond = Maturity value of bond / (1 + YTM on bond)Time period.

= 1000 / (1 + 0.05)30

= 1000 / (1.05)30

= 1000 / 4.3219

= $ 231.38 (approx).

iii). If YTM is 12 %, Price of Semi annual bond :-

YTM = 12 % * 6 / 12 = 6 % or 0.06 (Semi-annual).

Time period = 15 * 12 / 6 = 30 Semi annual periods.

Price of semi-annual bond = Maturity value of bond / (1 + YTM on bond)Time period.

= 1000 / (1 + 0.06)30

= 1000 / (1.06)30

= 1000 / 5.7435

= $ 174.11 (approx).

Conclusion :-

YTM	Price of semi-annual bond
i). 8 %	$ 308.32 (approx).
ii). 10 %	$ 231.38 (approx).
iii). 12 %	$ 174.11 (approx).