Wyatt Oil is contemplating issuing a 20-year bond with semiannual coupons,a coupon rate of 5%,and a face value of $1000.Wyatt Oil believes it can get a AAA rating from Standard and Poor's for this bond issue.What is the difference in the price the company will receive if the rating is BBB instead of AAA?

Question

Quizplus · Accepted Answer

The difference in price between a BBB rated bond and a AAA rated bond is called the credit spread. According to historical credit spread data, the credit spread for a 20-year BBB rated bond is 80 basis points (0.80%). Therefore, Wyatt Oil's BBB rated bond would have a yield to maturity of 5% + 0.80% = 5.80%. The price of the bond can be calculated using the following formula:

Price = (Coupon Payment / Interest Rate) x (1 - 1 / (1 + Interest Rate)^Number of Payments) + Face Value / (1 + Interest Rate)^Number of Payments

For a 20-year, semiannual payment bond with a coupon rate of 5% and a face value of $1000, the coupon payment is $25 every six months. Plugging in the numbers, we get:

Price = ($25 / 0.029) x (1 - 1 / (1 + 0.029)^40) + $1000 / (1 + 0.029)^40 = $883.83

If the bond is rated AAA, the yield to maturity would be lower at 4.50% (according to historical data) and the price would be calculated as:

Price = ($25 / 0.0225) x (1 - 1 / (1 + 0.0225)^40) + $1000 / (1 + 0.0225)^40 = $910.24

The difference in price between the BBB rated and AAA rated bond is therefore $910.24 - $883.83 = $26.41. Thus, the best choice is D.

Wyatt Oil Is Contemplating Issuing a 20-Year Bond with Semiannual