IBM wants to issue new 20-year bonds. The company currently has 8.5 percent bonds with face value of $1000 on the market that sell for $994, make semiannual payments, and mature in 7 years. What should the coupon rate be on the new bonds if the firm wants to sell them at par

8.62%

Explanation:

Based on the information given, the coupon rate on the new bonds if the firm wants to sell them at par will be calculated thus:

The following information can be gotten from the question:

Par Value = $1,000

Current Price = $994

Time to Maturity = 7 years

Annual Coupon Rate = 8.50%

Semiannual Coupon Rate = 8.50%/2 = 4.25%

Semiannual Coupon = 4.25% × $1,000 = $42.50

Semiannual Period to Maturity = 7/½ = 14

Let the semiannual Yield to maturity be represented by x Therefore,

994 = 42.50 × PVIFA(x, 14) + 1,000 × PVIF(x, 14)

Then, we'll use the financial calculator where,

N = 14

PV = -994

PMT = 42.50

FV = 1000

Based on this, the value of x will be 4.308%.

Since the Semiannual YTM is 4.308%, then the Annual YTM will be:

= 2 × 4.308%

= 8.616%

= 8.62%

Therefore, the coupon rate should be 8.62%