JRJ Corporation recently issued 10-year bonds at a price of $1,000. These bonds pay $89 in interest each six months.

JRJ Corporation recently issued 10-year bonds at a price of $1,000. These bonds pay $89 in interest each six months. Their price has remained stable since they were issued, i.e., they still sell for $1,000. Due to additional financing needs, the firm wishes to issue new bonds that would have a maturity of 16 years, a par value of $1,000, and pay $69 in interest every six months. If both bonds have the same yield, how many new bonds must JRJ issue to raise $2,000,000 cash?(round your answer)

Solutions

Expert Solution

If a bond is priced at its par value, then its yield (YTM) equals it coupon rate.

Yield (YTM) of old bonds = coupon rate = annual coupon payment / face value = ($89 * 2) / $1,000 = 17.8%

Price of a bond is the present value of its cash flows. The cash flows are the coupon payments and the face value receivable on maturity.

Issue price of new bond is calculated using PV function in Excel :

rate = 17.8%/2 (Semiannual YTM of bonds = annual YTM / 2)

nper = 16 * 2 (16 years remaining until maturity with 2 semiannual coupon payments each year)

pmt = 69 (semiannual coupon payment)

fv = 1000 (face value receivable on maturity)

PV is calculated to be $789.96

Number of bonds to issue = amount to raise / issue price per bond

Number of bonds to issue = $2,000,000 cash / $789.96

Number of bonds to issue = 2,532

jeff jeffy answered 1 year ago

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