Question

​(Bond relationship​) ​Mason, Inc. has two bond issues​ outstanding, called Series A and Series​ B, both paying the same annual interest of ​$100. Series A has a maturity of 12 ​years, whereas Series B has a maturity of 1 year.

a. What would be the value of each of these bonds when the going interest rate is​ (1) 5 ​percent, (2) 11 ​percent, and​ (3) 12 ​percent? Assume that there is only one more interest payment to be made on the Series B bonds.

b. Why does the​ longer-term ​(12​-year) bond fluctuate more when interest rates change than does the​ shorter-term ​(1​-year) ​bond?

Answer 1

First of all lets find all PVIFA and PVIF

PVIFA(5%,1 year) = [1-(1/(1+r)^n /r] = [1-(1/1.05)^1 / 0.05] = [1-0.9524/0.05] = 0.9524

PVIFA(5%,12 years) = [1-(1/(1+r)^n /r] = [1-(1/1.05)^12 / 0.05] = [1-0.5568/0.05] = 8.8633

PVIFA ( 11%, 1 year) = [1-(1/(1+r)^n /r] = [1-(1/1.11)^1 / 0.11] = [1-0.9009/0.11] = 0.9009

PVIFA ( 11%, 12 year) = [1-(1/(1+r)^n /r] = [1-(1/1.11)^12 / 0.11] = [1-0.2858/0.11] = 6.4924

PVIFA ( 12%, 1 year) = [1-(1/(1+r)^n /r] = [1-(1/1.12)^1 / 0.12] = [1-0.8926/0.12] = 0.8926

PVIFA ( 12%, 12 year) = [1-(1/(1+r)^n /r] = [1-(1/1.12)^12 / 0.12] = [1-0.2567/0.12] = 6.1943

PVIF(5%,1 year) = 1/(1+r)^n = 1/1.05^1 = 0.9524

PVIF(5%,12 year) = 1/(1+r)^n = 1/1.05^12 = 0.5568

PVIF(11%,1 year) = 1/(1+r)^n = 1/1.11^1 = 0.9009

PVIF(11%,12 year) = 1/(1+r)^n = 1/1.11^12 = 0.2858

PVIF(12%,1 year) = 1/(1+r)^n = 1/1.12^1 = 0.0.8926

PVIF(12%,12 year) = 1/(1+r)^n = 1/1.12^12 = 0.2567

A) Now lets calculate price of bonds ( Assuming redemption value to be 1000$)

Price of Series A bond

Interest rate	Interest *PVIFA =100*PVIF	Redemption value*PVIF =1000*PVIF	Price of bond
	a	b	a+b
5%	886.33	556.8	1443.13
11%	649.24	285.8	935.04
12%	619.43	256.7	876.13

Price of series bond B

Interest rate	Interest *PVIFA =100*PVIF	Redemption value*PVIF =1000*PVIF	Price of bond
	a	b	a+b
5%	95.24	952.4	1047.64
11%	90.09	900.9	990.99
12%	89.26	892.6	981.86

B) Long term bond will fluctuate more with changes in interest rate because long term bonds carries risk that higher inflation can reduce the payments. Long term bonds have greater interest rate risk since it has more time to maturity.