Question

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 10 years. The first is a zero-coupon bond that pays \(1,000 at maturity. The second has an 8% coupon rate and pays the \)80 coupon once per year. The third has a 10% coupon rate and pays the $100 coupon once per year.

a. If all three bonds are now priced to yield 8% to maturity, what are their prices?

b. If you expect their yields to maturity to be 8% at the beginning of next year, what will their prices be then? What is your rate of return on each bond during the one-year holding period?

Short answer

Answer

a.

	Zero	8% coupon	10% coupon
Current Prices (A)	$463	$1000	$1134.20

b.

Rate of return (Income / Current Prices)

8.00%

8.00%

8.00%

Step-by-step solution

Given information

Maturity period = 10 Years

Zero coupons matures at $1000

Coupon income for all three is $0, $80 and $100

Calculation of Current prices

If the yield to maturity of three bonds is 8% at the beginning of the next year, it would be calculated using 9 years of maturity in place of 10 years.

Therefore,

	Zero	8% coupon	10% coupon
Current Prices (A)	$463	$1000	$1134.20

Calculation of rate of return 

	Zero	8% coupon	10% coupon
Current Prices (A) PV= (0.8, 10, PMT, 1000)	$463	$1000	$1134.20
Price one year from now (B) PV= (0.8, 9, PMT, 1000)	$500.25	$1000	$1124.94
Price increase (B-A)	$37.06	$0.00	$-9.26
Coupon income (Given)	$0.00	$80	$100
Income (Price increase + Coupon Income)	$37.06	$80	$90.74
Rate of return (Income / Current Prices)	8.00%	8.00%	8.00%