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 a 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. Assume that all bonds are compounded annually.

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.)

b. 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.)

c. What is your rate of return on each bond during the one-year holding period?

Answer 1

Bond Par Value = $1,000

Time to Maturity = 8 years

Bond A,

Coupon Rate = 0%

Bond B,

Coupon Rate = 7.6%

Bond C,

Coupon Rate = 9.6%

a.

If YTM = 7.6%

Present Value of Bond A,

PV = [FV = 1000, T = 8, I = 0.076, PMT = 0]

PV = $556.55

Present Value of Bond B,

PV = [FV = 1000, T = 8, I = 0.076, PMT = 76]

PV = $1,000

Present Value of Bond C,

PV = [FV = 1000, T = 8, I = 0.076, PMT = 96]

PV = $1116.7

2.

After 1 year YTM = 7.6%

Present Value of Bond A,

PV = [FV = 1000, T = 7, I = 0.076, PMT = 0]

PV = $598.84

Present Value of Bond B,

PV = [FV = 1000, T = 7, I = 0.076, PMT = 76]

PV = $1,000

Present Value of Bond C,

PV = [FV = 1000, T = 7, I = 0.076, PMT = 96]

PV = $1,105.57

3.

Holding Period Return of Bond A = (598.84 - 556.55)/556.55 = 7.60%

Holding Period Return of Bond B = (1000 - 1000 + 76)/1000 = 7.60%

Holding Period Return of Bond C = (1105.57 - 1116.70 + 96)/1116.70 = 7.60%