JRJ Corporation issued 10-year bonds at a price of $1,000. These bonds pay $60 interest every six months. Their price has remained the same since they were issued; that is, the bonds still sell for $1,000. Due to additional financing needs, the firm wishes to issue new bonds that would have a maturity of 10 years and a par value of $1,000 and pay $40 interest every six months. If both bonds have the same yield, how many new bonds must JRJ issue to raise additional capital of $2 million

JRJ must issue 2,596 bonds to raise additional capital of $2 million.

Explanation:

From the question, we have the following:

Amount needed to be raised = $2 million = $2,000,000

Coupon rate = 8.0%, or 0.08

FV = Face value = 1000

Year to maturity = 10

NPER = Number of period = Year to maturity * Number of semiannuals in a year = 10 * 2 = 20

PMT = (FV * Coupon rate) / Number of semiannuals in a year  =(1000 * 0.08) / 2 = 40

Rate = Semiannual interest / FV = $60 / $1000 = 0.06

The net proceeds can be calculated using the following excel function:

Net proceed = PV(rate, NPER, -PMT, -FV) (1)

Substituting all the relevant value into equation (1), we have:

Net proceed = PV(6%, 20, -40, -1000)

Inputing =PV(6%, 20, -40, -1000) in any cell in excel sheet (Note: as done in the attached excel file), we have:

Net proceed = $770.60

Therefore, we have:

Number of bonds that must be raised = Amount needed to be raised / Net proceed = $2,000,000 / $770.60 = 2,596

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