会计投资分析：回报期、净现值与内部收益率计算

A new cutting machine would initially cost $320,000 and would lead to equal annual sales revenue $200,000 for each of the next 6 years，Contribution margin ratio is forty percent, as well as have an estimated salvage value at the end of 6 years of $20,000. The business has a required rate of return of 18% per annum. REQUIRED: A)Calculate the pay-back period for this project, and briefly describe what this measure indicates about a project. B)Ignoring tax, calculate the Net Present Value of the above investment proposal. Would you accept or reject this proposal? C) Ignoring the estimated salvage value at the end of 6 years, calculate the Value of this project’s Internal Rate of Return (IRR)? D) Assuming now that there is a tax rate of 30%, and that this machine would be depreciated (i.e. written down) to a zero value at the end of year 6, calculate the Net Present Value of the above investment proposal. The business still requires a 18% rate of return on the after-tax cash flows. Would you accept or reject this proposal?

A) Pay-Back Period Calculation

Initial Investment: $320,000 Annual Cash Inflow (Contribution Margin): $200,000 * 0.40 = $80,000

Pay-Back Period = Initial Investment / Annual Cash Inflow = $320,000 / $80,000 = 4 years

Description: The pay-back period indicates that it will take 4 years to recover the initial investment of $320,000. This measure is useful for assessing the liquidity of the investment and the risk associated with the time it takes to recover the initial outlay.

B) Net Present Value (NPV) Calculation

Initial Investment: $320,000 Annual Cash Inflow (Contribution Margin): $80,000 Salvage Value: $20,000 Required Rate of Return: 18%

NPV Calculation: 1. Discount the annual cash inflows: Year 1-6: $80,000 / (1 + 0.18)^n Sum of discounted cash inflows = $80,000 * [1 - (1 / 1.18^6)] / 0.18 ≈ $293,017.84

Discount the salvage value: Year 6: $20,000 / (1 + 0.18)^6 ≈ $7,988.85
Calculate NPV: NPV = -$320,000 + $293,017.84 + $7,988.85 ≈ -$18,993.31

Decision: Reject the proposal because the NPV is negative.

C) Internal Rate of Return (IRR) Calculation

Initial Investment: $320,000 Annual Cash Inflow (Contribution Margin): $80,000 Salvage Value: Ignored

IRR Calculation: 1. Set up the equation: $320,000 = $80,000 * [1 - (1 / (1 + IRR)^6)] / IRR

Solve for IRR: Using a financial calculator or trial and error, the IRR is approximately 15.24%.

Decision: If the required rate of return is 18%, reject the proposal because the IRR (15.24%) is less than the required rate.

D) Net Present Value (NPV) Calculation with Tax

Initial Investment: $320,000 Annual Cash Inflow (Contribution Margin): $80,000 Salvage Value: $20,000 Tax Rate: 30% Depreciation: Straight-line to zero over 6 years = $320,000 / 6 = $53,333.33 per year Tax Shield from Depreciation: $53,333.33 * 0.30 = $16,000 per year

After-Tax Cash Inflow: $80,000 - ($80,000 * 0.30) + $16,000 = $72,000 per year

NPV Calculation: 1. Discount the annual after-tax cash inflows: Year 1-6: $72,000 / (1 + 0.18)^n Sum of discounted cash inflows ≈ $263,716.06

Discount the salvage value (after tax): Year 6: $20,000 * (1 - 0.30) = $14,000 Discounted salvage value ≈ $5,592.19
Calculate NPV: NPV = -$320,000 + $263,716.06 + $5,592.19 ≈ -$50,691.75

Decision: Reject the proposal because the NPV is negative.

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