Question

9. Osaka Insurance Company (OIC) concentrates its underwriting in Japan. company is concerned that an earthquake will cause extensive damage. Limited The affordable reinsurance is available due to the quake risk. Financial managers at OIC decided to issue $300 million (maturity value) of "Yankee Bonds" (U.S. dollar- denominated bonds) for sale to U.S. investors. These catastrophe ("cat") bonds will mature in 3 years and each $1,000 (maturity value) bond will carry a 148 annual coupon. The bond indenture specifies that if at least one earthquake larger than 7.4 but under 7.9 on the Richter Scale occurs in Japan during a given year, the company will only pay 60 percent of that year's interest. If an earthquake of 7.9 or greater magnitude occurs in Japan, no interest is payable that year. If no earthquakes of 7.4 or greater occur, then the full interest payment must be made by OIC. The maturity value ($1,000) 18 payable in 3 years regardless of whether any earthquakes occur. Seismologists believe there's a 50 percent chance of no earthquakes exceeding 7.4 in Japan in any given year, a 40 percent chance in any given year of an earthquake between 7.4 and 7.9 in Japan, and a 10 percent chance in any given year of an earthquake of 7.9 or greater magnitude. a. How much in interest payments (total dollars) would OIC save in any year in which an earthquake occurs that is between 7.4 and 7.9 on the Richter Scale? point) b. If investors require a 10 percent return on these bonds, and they are aware of the earthquake probabilities and reduced interest payment contingency what is the most they should be willing to pay for an OIC Yankee Cat bond when issued? 12.5 points)

Answer 1

a). Annual interest payment if full paid = coupon rate*maturity value = 14%*300mn = 42mn

Only 60% of this amount will be paid if an earthquake between 7.4 & 7.9 occurs so the company will save 40% of its annual coupon.

Amount saved = 40%*42mn = 16.8mn or 16,800,000

b). Maturity value per bond = 1,000 so total number of bonds = 300,000,000/1,000 = 300,000

Annual full coupon = 14%*1,000 = 140

Expected coupon = sum of probability weighted coupons

= (50%*full coupon) + (40%*60% of full coupon) + (10%*no coupon)

= (50%*140) + (40%*60%*140) + (10%*0) = 103.6

FV = 1,000; PMT = 103.6; N = 3; rate (or required return of the investors) = 10%, solve for PV.

Price = 1,008.95

So, the investors should be willing to pay 1,008.95 per bond or 1,008.95*300,000 = 302,685,000, in total.