Question

Gluon Inc. is considering the purchase of a new high pressure glueball. It can purchase the glueball for $90,000 and sell its old low-pressure glueball, which is fully depreciated, for $16,000. The new equipment has a 10-year useful life and will save $20,000 a year in expenses. The opportunity cost of capital is 8%, and the firm’s tax rate is 21%. What is the equivalent annual saving from the purchase if Gluon can depreciate 100% of the investment immediately. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

First, compute the operating cash flow for the new machine. Since the new machine will reduce expenses, the cash expense amount will be a negative value.

Operating cash flow

= [(Revenues – Cash expenses) × (1 – Tax rate)] + (Tax rate × Depreciation)

= [$0 – (–$20,000) × (1 – .21)] + [.21 × ($90,000 / 10)]

= $17,690

Now, compute the net present value of purchasing the new machine.

NPV= -Cost new machine + After-tax salvage value of old machine + Operating cash flow × PVIFA8%,10

= –$90,000 + [$16,000 × (1 – .21)] + $17,690 × ((1 / .08) – {1 / [.08(1 + .08)^10]})= $41,341.34

The last step is to compute the annuity payment that has the same NPV as the new machine purchase.

NPV = C× PVIFA r%,t

$41,341.34= C× ((1 / .08) – {1 / [.08(1 + .08)10]})

C= $6,161.08

Since the annuity payment is positive, the new machine will produce an annual cash savings of $6,161.08.

Scenario 2: If we depreciate the equipment immediately

Operating cash flow for year 1

= [(Revenues – Cash expenses) × (1 – Tax rate)] + (Tax rate × Depreciation)

= [$0 – (–$20,000) × (1 – .21)] + [.21 × $90,000]

=$15,800 + $18,900

= $34,700

Operating cash flow from year 2 to 10

= [(Revenues – Cash expenses) × (1 – Tax rate)]

= [$0 – (–$20,000) × (1 – .21)]

= $15800

NPV= -Cost new machine + After-tax salvage value of old machine + Operating cash flow × PVIFA8%,10

= –$90,000 + [$16,000 × (1 – .21)] + $18,900/(1+0.8) +$15,800 × ((1 / .08) – {1 / [.08(1 + .08)^10]})= $46,159.29

NPV = C× PVIFA r%,t

$46,159.29 = C× ((1 / .08) – {1 / [.08(1 + .08)10]})

C= $6,879.10

Since the annuity payment is positive, the new machine will produce an annual cash savings of $6,879.10.