Question

Apple Inc. recently issued 15-year bonds at $950 per share. These bonds pay $25 coupons every six months. Their price has remained stable since they were issued, i.e., they still sell for $950 share today. Due to additional financing needs, the firm wishes to issue new bonds that would have a maturity of 15 years, a par value of $1,000, and it will pay $40 coupons every six months. If both bonds have the same yield to maturity, how many shares of new bonds must Apple Inc. issue today to raise $2,188,000 cash today?

Answer 1

CalCulation of YTM from old issued Bonds

Current Price = 950

Coupon 25 every six months

Maturity = 15 years * 2 = 30

SInce the Current Price of Bond > Par Value, the TYM will be less than Coupon.

Let's assume the YTM be 5%

Value of the Bond will be 1000 only as the coupon rate is also 5%

Now,

Let's assume the YTM be 6% / 2 = 0.03

Value of Bond =

=

= 902

YTM =

= 5% + ((1000 - 950) / (1000 - 950) + (950 - 902)) * (6-5)

= 5% + 0.49%

= 5.49%

value of New Bond to be issued =   

r = 0.0549 / 2= 0.02745

n = 15 years * 2 = 30

Coupon 40

=

= 1254.30

No of Bonds to be issued = 2188,000 / 1254.30

= 1206.87 OR 1207 shares