Question

show work in excel with formulas please

Clipboard Font Nigament Number E38 4 А B 35 19. TJ Machine bonds have a coupon rate of 5.3 percent, a face value of $1,000, and pay interest semiannually. The bonds mature in 23 years and have a yield to 16 maturity of 5.4 percent. What will be the percentage change in the bond's price if the market rate increases by 1 percent to 6.4 percent? 39 60 41 42 44 45 46

Answer 1

Let us first find orice of bond when YTM = 5.4%
Here face value = $1000
YTM = 5.4%/2 = 2.7%
Interest = Face value x Interest rate x 1/2
= 1000 x 5.3% x 1/2
= 26.5$
n = no of interest payments = 23 x 2 = 46

Price of bond = Interest x PVIFA(YTM% , n) + Redemption value x PVIF(YTM%,n)

PVIFA(YTM% , n) = [1-(1/(1+r)^n) / r ]
PVIFA(2.7% , 46) = [ 1-(1/(1+2.7%)^46 / 2.7%]
= [ 1 -(1/(1+0.027)^46 / 0.027]
=[1-(1/(1.027)^46 / 0.027]
=[1-0.2936 / 0.027]
=[0.7063976/0.027]
=26.1629

PVIF(YTM%,n) = 1/(1+r)^n
= (1/(1+0.027)^46)
=(1/(1.027)^46 )
= 0.2936024

Thus price of bond = 26.5 x 26.1629 + 1000 x 0.2936024
= 693.3162 + 293.6024
= 986.92 $

Now Let us first find orice of bond when YTM = 6.4%
Here face value = $1000
YTM = 6.4%/2 = 3.4%
Interest = Face value x Interest rate x 1/2
= 1000 x 5.3% x 1/2
= 26.5$
n = no of interest payments = 23 x 2 = 46

Price of bond = Interest x PVIFA(YTM% , n) + Redemption value x PVIF(YTM%,n)

PVIFA(YTM% , n) = [1-(1/(1+r)^n) / r ]
PVIFA(3.2% , 46) = [ 1-(1/(1+3.2%)^46 / 3.2%]
= [ 1 -(1/(1+0.032)^46 / 0.032]
=[1-(1/(1.032)^46 / 0.032]
=[1-0.2348 / 0.032]
=[0.7652/0.032]
=23.9119

PVIF(YTM%,n) = 1/(1+r)^n
= (1/(1+0.032)^46)
=(1/(1.032)^46 )
= 0.234819

Thus price of bond = 26.5 x 23.9119 + 1000 x 0.234819
= 633.6652 + 234.8194
= 868.48 $

Thus % change in price = 868.48-986.92/986.92

= -118.44/986.92

=-0.12

i.e -12%