Suppose you purchase a two-year bond that has a $450 coupon and a face value of $5000,and immediately after you purchase the bond,new bonds are issued that are otherwise identical,except they have coupons of $375.If you sell your bond,you will receive a gain of

Question

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First, we need to calculate the yield to maturity (YTM) of the original bond. We can do this by using the bond pricing formula:

$5000 = [$450/(1 + YTM)^1] + [$450/(1 + YTM)^2] + … + [$450/(1 + YTM)^4] + [$5000/(1 + YTM)^4]

Simplifying the equation, we get:

$5000 = $450 [(1 - 1/(1 + YTM)^4)/YTM] + $5000/(1 + YTM)^4

Solving for YTM using trial and error or a financial calculator, we get YTM = 4.5%.

Next, we need to calculate the price of the original bond after the new bonds are issued. Since the new bonds have a lower coupon rate, they will be priced lower than the original bond. We can use the same bond pricing formula, but with a coupon of $375 instead of $450:

$P = [$375/(1 + YTM)^1] + [$375/(1 + YTM)^2] + … + [$375/(1 + YTM)^4] + [$5000/(1 + YTM)^4]

Solving for P using YTM = 4.5%, we get P = $4,865.34.

Therefore, the gain from selling the original bond is:

$4,865.34 - $5,000 = -$134.66

This means that you would experience a loss of $134.66 if you sold the original bond after the new bonds were issued.

Suppose You Purchase a Two-Year Bond That Has a $450