Question

Assume you have a one-year investment horizon and are trying to choose among three bonds. All have the same degree of default risk and mature in 8 years. The first is a zero-coupon bond that pays $1,000 at maturity. The second has an 7.6% coupon rate and pays the $76 coupon once per year. The third has a 9.6% coupon rate and pays the $96 coupon once per year.

a.	If all three bonds are now priced to yield 7.6% to maturity, what are their prices? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

	Zero	7.6% Coupon	9.6% Coupon
Current prices	$	$	$

b-1.	If you expect their yields to maturity to be 7.6% at the beginning of next year, what will their prices be then? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

	Zero	7.6% Coupon	9.6% Coupon
Price one year from now	$	$	$

b-2.	What is your rate of return on each bond during the one-year holding period? (Do not round intermediate calculations.Round your answers to 2 decimal places.)

	Zero	7.6% Coupon	9.6% Coupon
Rate of return	%	%	%

Answer 1

(a) Common Yield for Three Bonds = 7.6%, Common Tenure = 8 years, Common Par Value = $ 1000

Zero Coupon Bond:

Price = 1000 / (1.076)^(8) = $ 556.55

7.6% Coupon Bond:

Annual Coupon = 0.076 x 1000 = $ 76

Price = 76 x (1/0.076) x [1-{1/(1.076)^(8)}] + 1000 / (1.076)^(8) = $ 1000

9.6% Coupon Bond:

Annual Coupon = 0.096 x 1000 = $ 96

Price = 96 x (1/0.076) x [1-{1/(1.06)^(8)}] + 1000 / (1.076)^(8) = $ 1116.698 ~ $ 1116.7

(b) At the beginning of the next year, the tenure for all the bonds become 7 years. All other conditions remain the same and the bond's price will still equal the total present value of their coupons and par value redeemed at maturity.

Yield to Maturity = 7.6 %

Zero Coupon Bond:

Price = 1000 / (1.076)^(7) = $ 598.84

7.6% Coupon Bond:

Annual Coupon = 0.076 x 1000 = $ 76

Price = 76 x (1/0.076) x [1-{1/(1.076)^(7)}] + 1000 / (1.076)^(7) = $ 1000

9.6% Coupon Bond:

Annual Coupon = 0.096 x 1000 = $ 96

Price = 96 x (1/0.076) x [1-{1/(1.06)^(7)}] + 1000 / (1.076)^(7) = $ 1105.57

(c) Return Over 1-Year Holding Period = [(Price after 1 Year - Initial Price) + Bond Coupn / Initial Price] x 100

Zero Coupon Bond Return = [(598.84 - 556.55) + 0 / 556.55] x 100 = 7.5986% ~ 7.6 %

7.6% Bond Return = [(1000 - 1000) + 76  / 1000] x 100 = 7.6 %

9.6% Bond Return = [(1105.57 - 1116.7) + 96 / 1116.7] x 100 = 7.6 %