Question

1. As a result of improvements in product engineering, United Automation is able to sell one of its two milling machines. Both machines perform the same function but differ in age. The newer machine could be sold today for $51,500. Its operating costs are $20,200 a year, but in five years the machine will require a $19,900 overhaul. Thereafter operating costs will be $30,100 until the machine is finally sold in year 10 for $5,150.

The older machine could be sold today for $25,100. If it is kept, it will need an immediate $20,500 overhaul. Thereafter operating costs will be $29,900 a year until the machine is finally sold in year 5 for $5,150.   

Both machines are fully depreciated for tax purposes. The company pays tax at 35%. Cash flows have been forecasted in real terms. The real cost of capital is 11%.

a. Calculate the equivalent annual costs for selling the new machine and for selling the old machine.

2. Hayden Inc. has a number of copiers that were bought four years ago for $29,000. Currently maintenance costs $2,900 a year, but the maintenance agreement expires at the end of two years and thereafter the annual maintenance charge will rise to $8,900. The machines have a current resale value of $8,900, but at the end of year 2 their value will have fallen to $4,400. By the end of year 6 the machines will be valueless and would be scrapped.

Hayden is considering replacing the copiers with new machines that would do essentially the same job. These machines cost $34,000, and the company can take out an eight-year maintenance contract for $1,200 a year. The machines will have no value by the end of the eight years and will be scrapped.

Both machines are depreciated by using seven-year MACRS, and the tax rate is 40%. Assume for simplicity that the inflation rate is zero. The real cost of capital is 8%.

a. Calculate the equivalent annual cost, if the copiers are: (i) replaced now, (ii) replaced two years from now, or (iii) replaced six years from now.

3.

The president’s executive jet is not fully utilized. You judge that its use by other officers would increase direct operating costs by only $33,000 a year and would save $100,000 a year in airline bills. On the other hand, you believe that with the increased use the company will need to replace the jet at the end of three years rather than four. A new jet costs $1.23 million and (at its current low rate of use) has a life of seven years. Assume that the company does not pay taxes. All cash flows are forecasted in real terms. The real opportunity cost of capital is 7%.

a. Calculate the equivalent annual cost of a new jet.

b. Calculate the present value of the additional cost of replacing the jet one year earlier than under its current usage.

c. Calculate the present value of the savings.

Answer 1