Question

# Bond price: Pierre Dupont just received a cash gift from his grandfather. He plants to invest...

 Bond price: Pierre Dupont just received a cash gift from his grandfather. He plants to invest in a five-year bond issued by Venice Corp. that pays an annual coupon rate of 5.5 percent. If the current market rate is 7.25 percent, what is the maximum amount Pierre should be willing to pay for this bond?

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

Here face value is assumed to be = \$1000 ,
Interest = face value x coupon rate
= 1000 x 5.5%
= 55\$
n = no of coupon payments= 5
YTM = 7.5%

PVIF(YTM%,n)
PVIFA(YTM%,n) = [1-(1/(1+r)^n / r ]
PVIFA(7.5%,5) = [1-(1/(1+7.5%)^5 / 7.5%]
=[1-(1/(1+0.075)^5 / 0.075]
=[1-(1/(1.075)^5 / 0.075]
=[1-0.6966 / 0.075]
=0.3034/0.075
=4.0459
PVIF(7.5%,5) = 1/(1+7.5%)^5
=1/(1.075)^5
= 0.69656
Value of bond = 55 x 4.0459 + 1000 x 0.69656
= 222.52 + 696.56

= 919.08 \$

Thus he should be 919.08 \$ for the bond

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