Occurs when someone adds value to an item of personal property by use of labor or materials. generally, the owns the property after this occurs. if the improvement was made without the permission of the owner, the owner pay for it. is the commingling of goods to the extent that the goods of one owner cannot be distinguished from the goods of another owner. this often occurs with goods. if this occurs because of agreement, mistake or the act of a third party, the owners share in proportion to their contributions. if it happens because of the wrongful act of one owner, the acquires title to the whole lot of goods.

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.)

Anew 2-lane road is needed in a part of town that is growing. at some point the road will need 4 lanes to handle the anticipated traffic. if the city's optimistic estimate of growth is used, the expansion will be needed in 4 years and has a probability of happening of 40%. for the most likely and pessimistic estimates, the expansion will be needed in 8 and 15 years respectively. the probability of the pessimistic estimate happening is 20%. the expansion will cost $ 4.2 million and the interest rate is 8%. what is the expected pw the expansion will cost?

Consider the following two projects. both have costs of $5,000 in year 1. project 1 provides benefits of $2,000 in each of the first four years only. the second provides benefits of $2,000 for each of years 6 to 10 only. compute the net benefits using a discount rate of 6 percent. repeat using a discount rate of 12 percent. what can you conclude from this exercise?