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	%	%	%

We do not use excel in this class only the Texas Instruments BA II plus calculator or equations. Please do not use excel when explaining, please!

Answer 1

a)

zero coupon bond:

gieven YTM = 7.6%

incase of zero coupon bonds price = 1000 / (1+Y)^n

where , Y = YTM ; n = number of periods untillmaturity

current price = 1000 / (1+7.6%)^8

= $556.55

7.6% coupon :

in calculator you have to give the following inputs

(N = 8 , I/Y = 7.6 , PMT = 76 , FV = 1000) and then press CPT(compute) then Press PV

where N = number of periods

I/Y = YTM

PMT = coupon Payments

FV = Redemption value

Price of the Bond = $1000

9.6% coupon :

in calculator you have to give the following inputs

(N = 8 , I/Y = 7.6 , PMT = 96 , FV = 1000) and then press CPT(compute) then Press PV

where N = number of periods

I/Y = YTM

PMT = coupon Payments

FV = Redemption value

Price of the Bond = $1116.70 (ignore negative symbol)

b)1

Zero couponbond:

price after 1year = 1000 / (1.076)^7

= $598.84

7.6% coupon :

in calculator you have to give the following inputs

(N = 7 , I/Y = 7.6 , PMT = 76 , FV = 1000) and then press CPT(compute) then Press PV

where N = number of periods

I/Y = YTM

PMT = coupon Payments

FV = Redemption value

Price of the Bond = $1000

9.6% coupon :

in calculator you have to give the following inputs

(N = 7 , I/Y = 7.6 , PMT = 96 , FV = 1000) and then press CPT(compute) then Press PV

where N = number of periods

I/Y = YTM

PMT = coupon Payments

FV = Redemption value

Price of the Bond = $1,105.57

b-2)

holding period return = (current year price + coupon - last year price) / last year price

zero coupon bond:

return = (598.84 - 556.55) / 556.55 = 7.60%

7.6% bond:

return = (1000 + 76 -1000) / 1000 = 7.60%

9.6% bond:

return = (1105.57 + 96 - 1116.70) / 1116.70 = 7.60%

(in case of any further clarification please comment below)