A 10-year maturity zero-coupon bond selling at a yield to maturity of 7.25% (effective annual yield) has convexity of 157.5 and modified duration of 9.06 years. A 30-year maturity 7.5% coupon bond making annual coupon payments also selling at a yield to maturity of 7.25% has nearly identical duration—9.04 years—but considerably higher convexity of 251.6.

Acompany manufactures hair dryers. it buys some of the components, but it makes the heating element, which it can produce at the rate of 920 per day. hair dryers are assembled daily, 250 days a year, at a rate of 360 per day. because of the disparity between the production and usage rates, the heating elements are periodically produced in batches of 2,300 units. a. approximately how many batches of heating elements are produced annually? b. if production on a batch begins when there is no inventory of heating elements on hand, how much inventory will be on hand 4 days later? c. what is the average inventory of elements, assuming each production cycle begins when there are none on hand?

Alandlord rented an art studio to an artist. under the terms of the signed, written, two-year lease, the artist agreed to pay the landlord $1,000 per month and to assume responsibility for all necessary repairs. after the first year of the lease, the artist assigned the balance of his lease to a sculptor. the landlord approved the sculptor as a tenant and accepted two rent payments from her, and then the landlord sold the building to an investor. the sculptor had made two payments to the investor when an electrical fire broke out in the studio, injuring the sculptor. the fire was caused by faulty wiring. the landlord was aware that there was a dangerous wiring problem when he leased the property to the artist. but when the landlord discovered how costly repairs would be, he decided it would be more profitable to sell the property than to repair it. the problem was not easily discoverable by anyone other than an expert electrician, and the landlord did not tell the artist, the sculptor, or the investor about the problem. the sculptor sues to recover damages for her injuries. from whom can the sculptor recover?

Verizon communications, inc., provides the following footnote relating to its leasing activities in its 10-k report. the aggregate minimum rental commitments under noncancelable leases for the periods shown at december 31, 2010, are as follows: years (dollars in millions) capital leases operatingleases 2011 $97 $1,898 2012 74 1,720 2013 70 1,471 2014 54 1,255 2015 42 1,012 thereafter 81 5,277 total minimum 418 $ 12,633 rental commitments less interest and (86) executory costs present value of 332 minimum lease payments less current (75) installments long-term obligation $257 at december 31, 2010 (a) confirm that verizon capitalized its capital leases using a rate of 7.4 %. (b) compute the present value of verizon's operating leases, assuming an 7.4% discount rate and rounding the remaining lease term to 3 decimal places. (use a financial calculator or excel to compute. do not round until your final answers. round each answer to the nearest whole number.)