Question

 

​Beryl's Iced Tea currently rents a bottling machine for $52,000per​ year, including all maintenance expenses. It is considering purchasing a machine instead and is comparing two​ options:

a. Purchase the machine it is currently renting for$160,000.

This machine will require$22,000per year in ongoing maintenance expenses.

b. Purchase a​ new, more advanced machine for$255,000.

This machine will require$19,000per year in ongoing maintenance expenses and will lower bottling costs by$10,000per year.​ Also,$35,000

will be spent up front to train the new operators of the machine.

Suppose the appropriate discount rate is 9%per year and the machine is purchased today. Maintenance and bottling costs are paid at the end of each​ year, as is the cost of the rental machine. Assume also that the machines will be depreciated via the​ straight-line method over seven years and that they have a​ 10-year life with a negligible salvage value. The marginal corporate tax rate is38%.

Should​ Beryl's Iced Tea continue to​ rent, purchase its current​ machine, or purchase the advanced​ machine? To make this​ decision, calculate the NPV of the FCF associated with each alternative.

Answer 1

Renting

After tax renting cost per year = $52000 * (1-0.38) = $32240

NPV of Renting = - $32240/0.09*(1-1/1.09^10)

= - $206905.28

Purchasing the current machine

Year	0	1 to 7	08-Oct
Machine Cost	-160000
maintenance cost		-22000	-22000
Depreciation		-22857.14286	0
Total Cost		-44857.14286	-22000
After tax cost		-27811.42857	-13640
Add Depreciation		22857.14286	0
FCF	-160000	-4954.285714	-13640

So, NPV =

-160000 - 4954.29/1.09- 4954.29/1.09^2- .. -4954.29/1.09^7 - 13640/1.09^8-13640/1.09^9-13640/1.09^10

= -160000-4954.09/0.09*(1-1/1.09^7)- 13640/1.09^8-13640/1.09^9-13640/1.09^10

= -$203821.08

Purchasing the advanced machine

Year	0	1 to 7	8 to 10
Machine Cost	-255000
After tax training cost	-21700
maintenance cost		-19000	-19000
benefit of lowering bottling costs		10000	10000
Depreciation		-36428.5714	0
Total Cost		-45428.5714	-9000
After tax cost		-28165.7143	-5580
Add Depreciation		-36428.5714	0
FCF	-276700	8262.857143	-5580

So, NPV

=-276700 + 8262.86/1.09+8262.86/1.09^2- .. +8262.86/1.09^7 - 5580/1.09^8-5580/1.09^9-5580/1.09^10

= -276700+8262.86/0.09*(1-1/1.09^7)-5580/1.09^8-5580/1.09^9-5580/1.09^10

= -$242840.07

As the NPV is least negative in case of purchasing the current machine, the current machine should be purhased