Question

3) Consider two bonds, all with a par value of $100 and pays interest annually: B Coupon Rate Coupon Rate Required return rate Maturity A 3% 6% 4 years 8% 6% 4 years a. What is the price of Bond A and Bond B? (5 marks) b. If the market rate (Required return rate) increased by 2%, how much will the price change of these bonds (5 marks)

Answer 1

Answer :

Price of Bond =( Coupon * Present Value Annuity Factor @ r% for n years) + (Par Value * Present Value Factor @ r% for nth year)

(a.) Calculation of Price of Bond A

Price of Bond A =( 3 * Present Value Annuity Factor @ 6% for 4 years) + (100 * Present Value Factor @ 6% for 4th year)

where Coupon = 100 * 3% = 3

r = Required Return i.e 6%

n = Number of Years to maturity i.e 4 years

Par Value = 100

Price of Bond A =( 3 * 3.46510561263) + (100 * 0.79209366321)

= 10.3953168378 + 79.209366321

= $89.6046831588 or $89.60

Calculation of Price of Bond B

Price of Bond B =( 8 * Present Value Annuity Factor @ 6% for 4 years) + (100 * Present Value Factor @ 6% for 4th year)

where Coupon = 100 * 8% = 8

r = Required Return i.e 6%

n = Number of Years to maturity i.e 4 years

Par Value = 100

Price of Bond B =( 8 * 3.46510561263) + (100 * 0.79209366321)

= 27.720844901 + 79.209366321

= $106.930211222 or $106.93

(b.) Calculation of price Change in Bond if Required return increses by 2%

Calculation of Price of Bond A

Price of Bond A =( 3 * Present Value Annuity Factor @ 8% for 4 years) + (100 * Present Value Factor @ 8% for 4th year)

where Coupon = 100 * 3% = 3

r = Required Return i.e 6% + 2% = 8%

n = Number of Years to maturity i.e 4 years

Par Value = 100

Price of Bond A =( 3 * 3.31212683998) + (100 * 0.73502985277)

= 9.93638051994 + 73.502985277

= $83.4393657969 or $83.44

Price of Bond A reduces from 89.60 to 83.44 by increasing the required Return

Calculation of Price of Bond B

Price of Bond B =( 8 * Present Value Annuity Factor @ 8% for 4 years) + (100 * Present Value Factor @ 8% for 4th year)

where Coupon = 100 * 8% = 8

r = Required Return i.e 6% + 2% = 8%

n = Number of Years to maturity i.e 4 years

Par Value = 100

Price of Bond B =( 8 * 3.31212683998) + (100 * 0.73502985277 )

= 26.4970147198 + 73.502985277

= $99.999999 or $100

When required return is equal to coupon rate price of the bond will be same as par value .

Threfore by Increasing the required return by 2 % the price of Bond B reduces from 106.93 to 100.