Question

Two years ago, MTR issued $1,000 ten-year bonds that carry a coupon rate of 8% payable semi-annually.

a.) If you require an effective annual rate of return of 12%, how much are you willing to pay for the bond today?

b.) What will be the bond price if the yield to maturity falls to 6% in one year?.

C.) From the answer computed in above part (b), identify, with brief explanation (within 30 words), whether the bond is issued at par, premium or discount without involving any calculation.

Answer 1

Ans a	2 year ago , MTR issued $ 1000= 10 year Bond
	carry Interet rate 8%= payable semi annually
	Effective annual rate of return 12%
Bond Price	Interest rate * PVIFA(r%,n)+ Redemption Value *PVTF(r%,n)
Face value $		1000
Required rate of return = 12%/2			6%
N - no of installment = 8*2=16
Interest =$ 1000*8% *1/2			40
PVIFA(r%,n)
PVIFA(6%,16)		(1-(1/1+0.06)^16/0.06
(1/1.06)^16		0.393646
PVIFA(6%,16)		(1-0.393646)/0.06
PVIFA(6%,16)		10.1059
PVIF(6%,16)		(1/1.06)^16
PVIF(6%,16)		0.393646
Price of the Bond		40*10.1050+1000*0.393646
Price of the Bond $		797.846

Ans b	2 year ago , MTR issued $ 1000= 10 year Bond
	carry Interet rate 8%= payable semi annually
	Effective annual rate of return 6%
Bond Price	Interest rate * PVIFA(r%,n)+ Redemption Value *PVTF(r%,n)
Face value $		1000
Required rate of return = 6%/2			3%
N - no of installment = 8*2=16
Interest =$ 1000*8% *1/2			40
PVIFA(r%,n)
PVIFA(3%,16)		(1-(1/1+0.03)^16/0.03
(1/1.03)^16		0.623167
PVIFA(3%,16)		(1-0.623167)/0.03
PVIFA(3%,16)		12.5611
PVIF(3%,16)		(1/1.03)^16
PVIF(3%,16)		0.623167
Price of the Bond		40*12.5611+1000*0.623167
Price of the Bond $		1125.611

Bond isued at premium= Market Interest rate is Lower ( 6% ) than coupon Interest rate (8%)