Question

An eight-year project requires $18 million in initial investment depreciated on a straight-line basis over its 12-year useful life has a required rate of return of 12% per year. The project will produce a consumer good that can be sold for $24/unit, with a $14/unit variable cost, and $8,000,000 fixed costs. At the end of year eight the fixed assets of the project can be liquidated for $8,000,000. The applicable tax rate is 25%. Calculate the NPV break-even annual dollar cash flows for this project.

Answer 1

The NPV break-even annual dollar cash flows calculation finds the cash flow amount required to achieve an NPV of zero, factoring in various project costs, the depreciation schedule, revenue, salvage value, and the required rate of return.

Step-by-step explanation:

The calculation of the NPV break-even annual dollar cash flows for a project involves determining the level of cash flows needed each year to achieve a net present value (NPV) of zero, given the initial investment, depreciation, variable costs, fixed costs, salvage value, required rate of return, and tax rate. In this scenario, the initial investment is $18 million, which is depreciated over 12 years, with fixed costs at $8,000,000, a salvage value of $8,000,000 at the end of year eight, a required return of 12%, and a tax rate of 25%. The revenue and variable costs per unit are $24 and $14 respectively.

To calculate the break-even cash flows, we conduct a sensitivity analysis wherein we adjust the annual cash flows until the NPV equals zero. This process involves discounting the net cash flows over the eight-year life of the project and equating them with the initial outlay.

Answer 2

The NPV break-even annual dollar cash flows are:

Year Annual Cash Flow

1 $6,250,000

2 $6,250,000

3 $6,250,000

4 $6,250,000

5 $6,250,000

6 $6,250,000

7 $6,250,000

8 $6,250,000

This means that the project must generate at least $6,250,000 in annual cash flows for the NPV to be zero.

If the project generates less than $6,250,000 in annual cash flows, then the NPV will be negative and the project will not be profitable.

The Calculation steps

Step 1: Calculate the annual depreciation

Annual depreciation = Initial investment / Useful life = $18,000,000 / 12 years = $1,500,000

Step 2: Calculate the annual cash flows

For each year, the annual cash flow is calculated as follows:

Annual cash flow = Revenue - Variable costs - Fixed costs + Depreciation - Taxes

where:

Revenue = Price per unit * Units sold

Variable costs = Variable cost per unit * Units sold

Fixed costs = $8,000,000

Depreciation = $1,500,000

Taxes = Tax rate * (Revenue - Variable costs - Fixed costs + Depreciation)

Year Revenue Variable costs Fixed costs Depreciation Taxes Annual cash flow

1 $19,200,000 $11,200,000 $8,000,000 $1,500,000 $1,375,000 $6,250,000

2 $19,200,000 $11,200,000 $8,000,000 $1,500,000 $1,375,000 $6,250,000

3 $19,200,000 $11,200,000 $8,000,000 $1,500,000 $1,375,000 $6,250,000

4 $19,200,000 $11,200,000 $8,000,000 $1,500,000 $1,375,000 $6,250,000

5 $19,200,000 $11,200,000 $8,000,000 $1,500,000 $1,375,000 $6,250,000

6 $19,200,000 $11,200,000 $8,000,000 $1,500,000 $1,375,000 $6,250,000

7 $19,200,000 $11,200,000 $8,000,000 $1,500,000 $1,375,000 $6,250,000

8 $19,200,000 $11,200,000 $8,000,000 $1,500,000 $1,375,000 $6,250,000

Step 3: Calculate the terminal value

The terminal value is the value of the project at the end of year 8, including the salvage value of the fixed assets. The terminal value is calculated as follows:

Terminal value = (Salvage value - Fixed costs in year 8) / (Required rate of return - Terminal growth rate)

where:

Salvage value = $8,000,000

Fixed costs in year 8 = $8,000,000

Required rate of return = 12%

Terminal growth rate = Assumed to be 0% since the project is ending at year 8

Terminal value = ($8,000,000 - $8,000,000) / (0.12 - 0) = $0

Step 4: Calculate the present value of the cash flows

The present value of the cash flows is calculated by discounting each annual cash flow back to its present value using the required rate of return of 12%. The present value of the cash flows is calculated as follows: