BBA Company is considering the purchase of a new high-speed widget grinder to replace the existing grinder. The existing grinder was purchased five years ago for $60,000 and has been depreciated under the 5-year property class of MACRS. The existing grinder doesn't have any book value. The new grinder costs $105,000 and requires $5,000 for insurance and carriage inward. The 5-year MACRS depreciation system is applicable to the new grinder. The existing grinder can be sold for $70,000 now without any other expense. The new grinder would provide before-tax and before-depreciation revenues of $43,000 per year, whereas the working capital level will be increased by $90,000. The salvage value of the new machine is zero, and the corporate tax rate on company income and capital gains is 35%.

Required:

1. Calculate after-tax relevant initial, interim incremental, and terminal cash flows.
2. Depict on a timeline the relevant cash flows associated with the replacement project.
3. Make a decision regarding the selection of the replacement project by using NPV and PI if the discount rate is 12%.

You calculated the after-tax initial, interim, and terminal cash flows for the project. You depicted these cash flows on a timeline and calculated the Net Present Value and Profitability Index. Based on these calculations, the replacement project should be accepted.

1. Calculate after tax relevant initial, interim incremental and terminal cash flows.

Initial Cash Flow:

The initial cash outlay is the net expense after replacing the old machine and purchasing the new one:

Sale of old grinder: $70,000

Purchase price of new grinder: $105,000

Insurance and carriage inward costs: $5,000

Therefore, the initial after-tax cost: $105,000 + $5,000 - $70,000 = $40,000

Interim Incremental Cash Flows:

Since we're using the 5-year MACRS depreciation system for the new grinder, let's calculate the annual depreciation. The annual revenue from the new grinder is $43,000 before tax and depreciation. Revenue after tax can be represented as: Revenue after tax = Revenue × (1 - Tax Rate).

Yearly net revenue: $43,000 × (1 - 0.35) = $27,950

Depreciation rates of 5-year MACRS: Year 1: 20%, Year 2: 32%, Year 3: 19.2%, Year 4: 11.52%, Year 5: 11.52%, Year 6: 5.76%

Year 1: $110,000 × 20% = $22,000

Year 2: $110,000 × 32% = $35,200

Year 3: $110,000 × 19.2% = $21,120

Year 4: $110,000 × 11.52% = $12,672

Year 5: $110,000 × 11.52% = $12,672

Year 6: $110,000 × 5.76% = $6,336

Now calculate the after-tax cash flow by adding back the depreciation tax shield:

Year 1: $27,950 + ($22,000 × 0.35) = $35,850

Year 2: $27,950 + ($35,200 × 0.35) = $40,270

Year 3: $27,950 + ($21,120 × 0.35) = $35,292

Year 4: $27,950 + ($12,672 × 0.35) = $32,386

Year 5: $27,950 + ($12,672 × 0.35) = $32,386

Year 6: $27,950 + ($6,336 × 0.35) = $30,162

Terminal Cash Flow:

The salvage value of the new grinder is zero. Therefore, the terminal cash flow only consists of the recovery of the working capital:

Terminal Cash Flow: $90,000

2. Depict on a time-line the relevant cash flows associated with the replacement project.

Year 0: - $40,000

Year 1: $35,850

Year 2: $40,270

Year 3: $35,292

Year 4: $32,386

Year 5: $32,386

Year 6: $30,162

Terminal (Year 6): $90,000 (Working capital recovery)

3. Make a decision regarding the selection of the replacement project by using NPV and PI if discount rate is 12%

Net Present Value (NPV):

NPV Formula: NPV = ∑ (Cash flow / [tex](1 + r)^t)[/tex]- Initial Investment

Year 0 to Year 6 and Terminal Cash Flows:

NPV = [tex](-$40,000) + [$35,850 / (1 + 0.12)^1] + [$40,270 / (1 + 0.12)^2] + [$35,292 / (1 + 0.12)^3] + [$32,386 / (1 + 0.12)^4] + [$32,386 / (1 + 0.12)^5] + ($30,162 + $90,000)/(1 + 0.12)^6[/tex]

Year 0: -$40,000

Year 1: $31,993

Year 2: $32,108

Year 3: $25,272

Year 4: $20,440

Year 5: $18,986

Year 6: $55,869

NPV = -$40,000 + $31,993 + $32,108 + $25,272 + $20,440 + $18,986 + $55,869 = $144,668

Profitability Index (PI):

PI = (Present value of future cash flows) / (Initial investment)

PI = $184,668 / $40,000 = 3.62

If NPV > 0 and PI > 1,the replacement project should be accepted.