JJM Corporation recently issued 10-year bonds at a price of $1,000. These bonds pay $60 in interest each six months. Their price has remained stable since they were issued, that is, they 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, a par value of $1,000, and pay $40 in interest every six months. If both bonds have the same yield, how many new bonds must JRJ issue to raise $2,000,000?
Question
Answer:
2,596
Step-by-step explanation:
Calculation to determine how many new bonds must JRJ issue to raise $2,000,000
Given,
Coupon rate = 8.0%
Face value = 1000
Year to maturity = 10
NPER = 20
First step is to calculate the PMT using this formula
PMT = Face value × Coupon rate / 2
Let plug in the formula
PMT=(1000 × 0.08) / 2
PMT= 80/2
PMT= 40
Second step is to calculate the Rate using this formula
Yield = 12%
Rate = Yield / 2
Let plug in the formula
Rate= 12% / 2
Rate= 6%
Third step is to calculate the net proceeds using this formula
Net proceeds= PV(rate, NPER, PMT, FV)
Let plug in the formula
Net proceeds= PV(6%, 20, 40, 1000)
Net proceeds= $770.60
Now let calculate how many new bonds must JRJ issue to raise $2,000,000
New bonds needed= $2,000,000 / 770.60
New bonds needed= 2,596 bonds
Therefore how many new bonds must JRJ issue to raise $2,000,000 will be 2,596 bonds