Question

1. A firm is considering an investment of $480,000 in new equipment to replace old equipment with a book value of $95,000 and a market value of $63,000. If the firm replaces the old equipment with new equipment, it expects to save $120,000 in operating costs the first year. The amount of savings will grow at a rate of 8 percent per year for each of the following five years. Both pieces of equipment belong to asset class 8, which has a CCA rate of 20 percent. The salvage values of both the old equipment and the new equipment at the end of six years are $11,000 and $78,000, respectively. There are other assets in the asset class when the project terminates. In addition, replacement of the old equipment with the new equipment requires an immediate increase in net working capital of $50,000. The firm’s marginal tax rate is 35 percent and cost of capital is 11 percent.

a) What is the initial after-tax cash flow?

b) What is the present value of the incremental CCA tax savings?

c) What is the present value of the incremental after-tax operating cash flows?

d) What is the present value of the incremental ending after-tax cash flow?

e) What is the NPV of the replacement project?

Answer 1

a]

Initial after-tax cash flow = -(cost of new equipment - after tax salvage value of old equipment + increase in NWC)

after tax salvage value of old equipment = market value + ((book value - market value) * tax rate)

(We do this because the book loss on sale of old equipment is tax-deductible, and hence the after-tax salvage value = before tax salvage value + tax benefit on book loss)

after tax salvage value of old equipment = $63,000 + (($95,000 - $63,000) * 35%)

after tax salvage value of old equipment = $74,200

Initial after-tax cash flow = -($480,000 - $74,200 + $50,000)

Initial after-tax cash flow = -$455,800

b]

Incremental CCA tax saving in each year = (depreciation on new equipment - depreciation on old equipment) * tax rate

PV of incremental CCA tax saving of each year = incremental CCA tax saving / (1 + cost of capital)n

where n = number of years after which the tax saving occurs

The depreciation schedules, CCA tax savings, and the present value are calculated as below :

PV of incremental CCA tax savings = $213,575

c]

after-tax operating cash flow each year = pretax cost savings * (1 - tax rate)

PV of after-tax operating cash flow each year = after-tax operating cash flow / (1 + cost of capital)n

where n = number of years after which the cash flow occurs

PV of incremental after-tax operating cash flows = $606,369

d]

incremental ending after-tax cash flow = after tax salvage value of new equipment - after tax salvage value of old equipment + recovery of NWC

PV of incremental ending after-tax cash flow = incremental ending after-tax cash flow / (1 + cost of capital)n

where n = number of years after which the cash flow occurs

after tax salvage value = salvage value + ((book value - salvage value) * tax rate)

incremental ending after-tax cash flow = $59,416 - $15,866 + $50,000 = $93,550

PV of incremental ending after-tax cash flow = $93,550 / (1 + 11%)6

PV of incremental ending after-tax cash flow = $50,016

e]

NPV = PV of incremental after-tax operating cash flows + PV of incremental CCA tax savings +  PV of incremental ending after-tax cash flow - Initial after-tax cash flow

NPV = $606,369 + $213,575 + $50,016 - $455,800

NPV = $414,159