Question

Yelverton Metals wants to issue new 14-year bonds for some much-needed expansion projects. The company currently has 10 percent coupon bonds on the market that sell for $1,300, make semiannual payments, and mature in 14 years. What should the coupon rate be on the new bonds if the firm wants to sell these new bonds at par? (Hint: These new bonds have the same risk as the outstanding bonds.)

a.) 6.57%

b.) 6.67%

c.) 6.77%

d.) 6.87%

e.) 6.97%

Answer 1

Face Value = $1,000
Current Price = $1,300

Annual Coupon Rate = 10%
Semiannual Coupon Rate = 5%
Semiannual Coupon = 5% * $1,000
Semiannual Coupon = $50

Time to Maturity = 14 years
Semiannual Period = 28

Let Semiannual YTM be i%

$1,300 = $50 * PVIFA(i%, 28) + $1,000 * PVIF(i%, 28)

Using financial calculator:

N = 28
PV = -1300
PMT = 50
FV = 1000

I = 3.335%

Semiannual YTM = 3.335%
Annual YTM = 2 * 3.335%
Annual YTM = 6.67%

So, the firm should set the coupon rate of 6.67% if they want to sell these bonds at par.