Answer :
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.