Question

The Borstal Company has to choose between two machines that do the same job but have different lives. The two machines have the following costs:   

Year Machine A   Machine B

0 $46,000   $56,000

1 11,200   10,400

2 11,200   10,400

3 11,200+ replace   10,400

4 10,400 + replace

These costs are expressed in real terms. Suppose that technological change is expected to reduce costs by 10% per year. There will be new machines in year 1 that cost 10% less to buy and operate than A and B. In year 2 there will be a second crop of new machines incorporating a further 10% reduction, and so on.

Suppose you are Borstal’s financial manager. If you had to buy one or the other machine and rent it out to the production manager for that machine’s economic life, what annual rental payment would you have to charge at the end of the first year and how would this alter in subsequent years given the expected technological changes? Assume a 8% real discount rate and ignore taxes. (Do not round intermediate calculations. Enter your answers as a positive value rounded to 2 decimal places.)

The Borstal Company has to choose between two machines that do the same job but have different lives. The two machines have the following costs: Year Machine A $46,000 11.200 11,200 11.200 replace Machine B $56.000 10,400 10,400 10,400 10,400 • replace These costs are expressed in real terms. Suppose that technological change is expected to reduce costs by 10% per year. There will be new machines in year 1 that cost 10% less to buy and operate than A and B. In year 2 there will be a second crop of new machines incorporating a further 10% reduction, and so on. Suppose you are Borstal's financial manager. If you had to buy one or the other machine and rent it out to the production manager for that machine's economic life, what annual rental payment would you have to charge at the end of the first year and how would this alter in subsequent years given the expected technological changes? Assume a 8% real discount rate and ignore taxes. (Do not round intermediate calculations. Enter your answers as a positive value rounded to 2 decimal places.) Machine A Year 1 rent Year 2 rent Year 3 rent Machine B Year 1 rent Year 2 rent Year 3 rent Year 4 rent

Answer 1

The first year rent for Machine A and B should be $17,361.15 and $20,974.81, respectively. Calculate the annual rent as follows: - Calculation for Annualized Present Value Year PV Factor (a) Machine A Machine B Amount (b) PV (axb) Amount (c) PV (a x c) 0.925925926 -$46,000 $42,592.59 $56,000 -$51,851.85 0.85733882 $11,200 -$96,02.19 $10,400 -$8,916.32 0.793832241 $11,200 $8,890.92 $10,400 $8,255.85 0.735029853 -$11,200 |-$8,232.33 -$10,400 $7,644.31 0.680583197 $10,400 -$7,078 Total 3.992710037 $(69318.03) $183,746.33) Annualized PV $17,361.15 $20,974.81