Cash Flow Estimation Byers

What We Will Learn Which cash flows are relevant How to deal with depreciation How to deal with working capital investment How to deal with selling the equipment at the end

Types of Cash Flows Cash flows matter—not accounting earnings. Sunk costs don’t matter. Incremental cash flows matter Every cash flow that changes as a result of our decision Opportunity costs matter. Side effects like cannibalism matter. Good: synergy Bad: cannibalism

Types of Cash Flows (continued) Taxes matter We want incremental after-tax cash flows. Inflation matters. Nominal cash flows and nominal discount rates Real cash flows and real discount rates (rarely used) Changes in net working capital Financing costs Not in cash flows but included in discount rate Allocation of existing costs does not matter

Depreciation The depreciation expense used for capital budgeting should be the depreciation schedule required by the IRS for tax purposes Depreciation itself is a non-cash expense It is only relevant because it affects taxes Depreciation tax shield = DT D = depreciation expense T = marginal tax rate

Types of Depreciation Straight-line depreciation MACRS D = (Initial cost – salvage) / number of years Very few assets are depreciated straight-line for tax purposes MACRS Need to know which asset class is appropriate for tax purposes Multiply percentage given in table by the initial cost Depreciate to zero Mid-year convention Simplified straight-line For learning purposes (quick and easy)

MACRS

Net Working Capital Often overlooked NWC = Current Assets – Current Liabilities Simple problems investment at time 0 Disinvestment at end of project More complex problems NWC changes from year to year Cash Accounts Receivable Inventory Accounts Payable

Salvage Value If the salvage value is different from the book value of the asset, then there is a tax effect Gain or Loss Book value = initial cost – accumulated depreciation If Salvage value > book value Gain (must pay tax) If Salvage value < book value Loss (tax refund)

Example Equipment cost $100,000 at time 0 5 year MACRS class Yearly depreciation:

What if the machine is sold after year 4 for $40,000? Tax rate = 40% We would have a gain of 40,000 – 17,280 = 22,720 We would pay tax on the gain of .40 x 22,780 = 9,088 Our cash flow from the sale would be:

What if the machine were sold after year 3 for $20,000? Now we have a loss of 20,000 – 28,800 = -8,800 We get a tax refund of .40 x 8,800 = $3,520 Our cash flow from the sale would be:

Unequal Lives Suppose Projects S and L are Mutually Exclusive and Will Be Repeated, r = 10% 1 2 3 4 S: -100 L: -100 60 33.5 Note: CFs shown in $ Thousands

NPVL > NPVS, but is L better? CF0 -100 CF1 60 33.5 NJ 2 4 I/YR 10 NPV 4.132 6.190

Put Projects on Common Basis Note that Project S could be repeated after 2 years to generate additional profits. Use replacement chain to put on common life. Note: equivalent annual annuity analysis is alternative method.

Replacement Chain Approach (000s) Franchise S with Replication NPV = $7.547. 1 2 3 4 S: -100 60 -100 60 60 -100 -40

Now Let’s Discuss a Common Framework Initial outlay Terminal Cash flow 1 2 3 4 5 n 6 . . . Operating Cash Flows

Initial Outlay (at time = 0) (Purchase price of the asset) + (shipping and installation costs) (Depreciable asset) + (Investment in working capital) + After-tax proceeds from sale of old asset (Net Initial Outlay)

Operating Cash Flows (each year) Incremental revenue - Incremental costs - Depreciation on project Incremental earnings before taxes - Tax on incremental EBT Incremental earnings after taxes + Depreciation reversal Operating Cash Flow

Terminal Cash Flow Salvage value +/- Tax effects of capital gain/loss + Recapture of net working capital Terminal Cash Flow

Putting it All Together: Let’s walk through a simple example together A firm is considering a new three-year expansion project that requires an initial fixed asset investment $2,700,000. The fixed asset will be depreciated straight line to zero over its three- year tax life. The project is estimated to generate $2,300,000 in annual sales, with costs of $970,000. The tax rate is 33% and the required return is 18%. The project requires an initial investment in net working capital of $400,000 and the fixed asset will have a market value of $230,000 at the end of the project. What is the NPV of the project?

Initial Outlay

Operating Cash Flow for years 1-3

Terminal Cash Flow

Cash Flow summary

Another Example Your firm is contemplating the purchase of a new $875,000 computer-based order entry system. The system will be depreciated straight line to zero over its five-year life. It will be worth $75,000 at the end of that time. You will save $345,000 before taxes per year in order processing costs and you will be able to reduce working capital by $105,000 (this is a one time reduction). If the tax rate is 31%, what is the IRR for this project?

Now for a more complex problem Acme Casting Company is considering adding a new line to its product mix. The production line would be set up in unused space in Acme's main plant. The machinery’s invoice price is $200,000. Another $10,000 in shipping charges would be required and it would cost an additional $30,000 to install the equipment. The machinery has an economic life of four years and will be depreciated using the MACRS three-year class. The machinery is expected to have a salvage value of $25,000 after four years of use.

The new line would generate incremental sales of 1,250 units per year for four years at an incremental cost of $100 per unit in the first year. Each unit can be sold for $200 in the first year. The sales price and cost are both expected to increase by 3% per year due to inflation. To handle the new line, the firm's net working capital would have to increase by an amount equal to 12% of sales revenues. The firm's tax rate is 40%, and its overall weighted average cost of capital is 10%.