The Dinosaur Adventure Theme Park needs $200 million to build a monorail that will run through the park. The park's financial advisors believe that it will be able to borrow the the money by issuing a 30-year bond with an annual coupon rate of 4.8 percent that pays interest every 6 months. However, interest rates have been very volatile over the last year, ranging from 4.6 percent to 5.1 percent for borrowers with Dinosaur's credit rating. As a result, Dinosaur's manager is concerned. If rates rise while the offering is in registration, Dinosaur will not get the $200 million it needs from the sale of its bonds. To make sure they will be able to raise enough money, Dinosaur’s financial advisors have recommended that Dinosaur register a total of $250 million worth of bonds. In the event that rates rise above 4.8 percent, Dinosaur will sell enough additional bonds to get the $200 million it needs for the monorail system.
a. If rates rise to 4.95 percent on the day the bonds are sold, how much would Dinosaur receive from the sale of $200 million worth of bonds?
b. What is the par value of the additional bonds that Dinosaur must sell to raise the required $200 million.