Comparing Mutually Exclusive Projects – Hagar industrial systems Company (HISC) is trying to decide between two different conveyor belt systems. System A cost $360,000, has a four – year life, and requires $105,000 in pretax annual operating cost. System B costs $480,000, has a six year life, and requires $65,000 in pretax annual operating costs. Both systems are to be depreciated straight – line to zero over their lives and will have zero salvage value. Whichever system is chosen, it will not be replaced when it wears out. If the tax rate is 34 percent and the discount rate is 11 percent, which system should the firm choose?
If we are trying to decide between two projects that will not be replaced when they wear out, the proper capital budgeting method to use is NPV. Both projects only has costs associated with them, not sales, so we will use these to calculate the NPV of each project. Using the tax shield approach to calculate the OCF, the NPV of system A is:
OCFA = -$105,000(1-0.34) + 0.34($360,000/4)
OCFA = - $38,700
NPVA = - $360,000 - $38,700 (PVIFA11%,4)
NPVA = - $ 480,064.65
And the NPV of system B is:
OCFB = -$65,000 (1 – 0.34) + 0.34($480,000/6)
OCFB = -$15,700
NPVB = - $480,000 - $15,700(PVIFA11%,6)
NPVB = -$546,419.44
If the system will not be replaced when it wears out, then system A should be chosen, because it has the less negative NPV.
Comparing Mutually Exclusive Projects – Suppose in the previous problem that HISC always needs a conveyor belt system; when one wears out, it must be replaced. Which system should the firm choose now?
If the equipment will be replaced at the end of its useful life, the correct capital budgeting techniques is EAC. Using the NPVs we calculated in the previous problems, the EAC for each system is:
EACA = - $ 480, 064.64 / (PVIFA11%,4)
EACA = -$154, 737.49
EACB = -$546,419.44 / (PVIFA11%,6)
EACB = - $129,160.75
If the conveyor belt system will be continually replaced, we should choose system B since it has the last negative EAC.
Comparing Mutually Exclusive Projects – Vandalay Industries is considering the purchase of a new machine for the production of latex. Machine A costs $2,400,000 and will last for six years. Variable costs are 35 percent of sales, and fixed costs are $180,000 per year. Machine B costs $5,400,000 and will last for nine years. Variable costs for this machine are 30 percent and fixed cost are $110,000 per year. The sales for each machine will be $10,5 million per year. The required return is 10 percent and the tax rate is 35 percent. Both machines will be depreciated on a straight – line basis. If the company plants to replace the machine when it wears out on a perpetual basis, which machine should you choose?
Since we need to calculate the EAC for each machine, sales are irrelevant. EAC only uses the costs of operating the equipment, not the sales. Using the bottom – up approach, or net income plus depreciation, method to calculate the OCF, we get:
machine A | machine B | ||
variable costs | - $3,675,000 | -$3.150.000 | |
fixed costs | -180.000 | -180.000 | |
depreciation | -400.000 | -600.000 | |
EBT | -$4.255.000 | -$3.860.000 | |
tax | 1.489.250 | 1.351.000 | |
net income | -$2.765.750 | -$2.509.000 | |
depreciation | 400.000 | 600.000 | |
OCF | -$2.365.750 | -$1.909.000 |
The NPV and EAC for machine A is:
NPVA = -$2,400,000 - $2,365,750(PVIFA10%,6)
NPVA = -$12,703,458.00
EACA = -$12,703,458.00 / (PVIFA10%,6)
EACA = -$2,916, 807.71
And The NPV and EAC for machine B is:
NPVB = - $5,400,000 - $1,909,000 (PVIFA10%,9)
NPVB = -$16,393,976.47
EACB = -$16,393,976.47 / (PVIFA10%,6)
EACB= -$2,846, 658.91
You should choose machine B since it has a less negative EAC.
Reference: Corporate Finance Book, Stephen A.Ross, Randolph W.Westerfield and Jeffrey Jaffe, Ninth Edition. Chapter 5, questions number 12,13,14, page 196 - 197
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