One of the ways to value bonds issued by a corporation is to use the risk-neutral valuation model. Consider a 1-year zero-coupon bond issued by a pharmaceutical firm called Designer Drugs with a face value of $1,000 that is currently trading at $950.50. Suppose that if Designer Drugs defaults, the recovery rate of the bond is 65 percent. Assume that the annual risk-free interest rate is 3.5 percent.

(i) Find the risk-neutral probability of default.

(ii) Bloomberg just released news that a new drug to treat COVID-19 from Designer Drugs got approved by the government for large scale human testing. This event decreased the risk-neutral probability of default by 1 percent. In other words, if the probability of default was x percent in part (a), now it is going to be (x 1) percent. At what price will the bond be trading after the news?

(iii) In addition to the information given in part (b) above, assume now that the risk-free interest rate is decreased from 3.5 percent to 3.0 percent. Find the price of the bond.