Question

Suppose that you are considering investing in a four-year bond that has a face value of $1000 and a coupon rate of 5.5 %.

a.) If the market interest rate on similar bonds is 5.5 %, the price of the bond is $ (Round your response to the nearest cent.)

The bond's current yield is % (Round your response to two decimal places.)

b.) Suppose that you purchase the bond, and the next day the market interest rate on similar bonds falls to 4 .5 %.

The price of the bond will be $ . (Round your response to the nearest cent.)

c.) Now suppose that one year has gone by since you bought the bond, and you have received the first coupon payment. The market interest rate on similar bonds is still 4.5 %.

The price of the bond another investor will be willing to pay is ? $

The total return on the bond was $

if another investor had bought the bond a year ago for the amount that was calculated in? (b), the total return would have been %

d.) Now suppose that two years have gone by since you bought the bond and that you have received the first two coupon payments. At this? point, the market interest rate on similar bonds unexpectedly rises to

9?%.

The price of the bond another investor will be willing to pay is  $. (Round your response to the nearest? cent.)

The total return on the bond was     %. (Round your response to two decimal? places.)

Suppose that another investor had bought the bond at the price you calculated in? (c).

The total return would have been

     %. (Round your response to two decimal? places.)

Answer 1

coupon rate = 5.5% = 0.055

par value of bond = $1000

annual coupon , C = par value * coupon rate = 1000*0.055 = 55

maturity of bond , n = 4 years

a)

market interest rate = 5.5%

since coupon rate = market interest rate = 5.5%

the price of bond will be = par value of bond = $1000

current yield = annual coupon / market price of bond = 55/1000 = 5.5%

b)

market rate next day , r = 4.5% = 0.045

maturity of bond = 3 years + 364 days =3 +( 364/365 years) = 3.99726 years

price of bond = present value of coupons + present value of maturity amount

Present value of coupons = C*PVIFA( 4.5% , 3.99726 years)

PVIFA( 4.5% , 3.99726 years) = present value interest rate factor of annuity

= [((1+m)ⁿ - 1)/((1+m)ⁿ*m)] = [((1.045)^3.99726 - 1)/((1.045)^3.99726*0.045)] = 3.585278

Present value(PV) of coupons = C*PVIFA( 4.5% , 3.99726 years) = 55*3.585278 = 197.190295

PV of maturity amount = par value/(1+m)ⁿ = 1000/(1.045)^3.99726 = 838.662485

Price of bond when YTM is 4.5% = 197.190295 + 838.662485 = $1035.85278 or $ 1035.85 ( rounding off to 2 decimal places)

c)

market rate , r = 4.5% = 0.045

maturity of bond = 3 years

price of bond = present value of coupons + present value of maturity amount

Present value of coupons = C*PVIFA( 4.5% , 3 years)

PVIFA( 4.5% , 3 years) = present value interest rate factor of annuity

= [((1+m)ⁿ - 1)/((1+m)ⁿ*m)] = [((1.045)³ - 1)/((1.045)³*0.045)] = 2.74896435

Present value(PV) of coupons = C*PVIFA( 4.5% , 3.99726 years) = 55*2.74896435 = 151.19303949

PV of maturity amount = par value/(1+m)ⁿ = 1000/(1.045)³ = 876.29660405

Price of bond when YTM is 4.5% = 151.19303949 + 876.29660405 = $1027.48964354 or $ 1027.49 ( rounding off to 2 decimal places)

return on bond for new investor = annual coupon/ price of bond = 55/1027.48964354 = 0.053529 = 5.3529% or 5.35% ( rounding off to 2 decimal places)

return on bond when bought an year ago =

[C + ( price of bond today - price of bond a year ago)]/ price of bond a year ago =

[55 + (1027.48964354- 1035.85278)]/1035.85278 = 46.6368635/1035.85278 = 0.045022 = 4.50%

d)

market rate , r = 9% = 0.09

maturity of bond = 2 years

price of bond = present value of coupons + present value of maturity amount

Present value of coupons = C*PVIFA( 9% , 2 years)

PVIFA( 9% , 2 years) = present value interest rate factor of annuity

= [((1+m)ⁿ - 1)/((1+m)ⁿ*m)] = [((1.09)² - 1)/((1.09)²*0.09)] = 1.75911119

Present value(PV) of coupons = C*PVIFA( 9% , 2 years) = 55*1.75911119 = 96.75111523

PV of maturity amount = par value/(1+m)ⁿ = 1000/(1.09)² = 841.67999327

Price of bond when YTM is 4.5% = 96.75111523 + 841.67999327 = $938.431108493 or $ 938.43 ( rounding off to 2 decimal places)

return on bond for new investor = annual coupon/ price of bond = 55/938.431108493 = 0.058608458= 5.8608458% or 5.86% ( rounding off to 2 decimal places)

return on bond when bought an year ago =

[C + ( price of bond today - price of bond a year ago)]/ price of bond a year ago =

[55 + (938.431108493- 1027.48964354)]/1027.48964354 = -34.058535051/1027.48964354 = -0.033147= -3.31%