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Last time….

Last time…. Basics of financial analysis Estimating revenues and expenses is crucial Time value of money concept The significance of present value comparisons Conversion of cash flows to present values. Profit Revisited. Profit = Revenues - Expenses

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Last time….

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  1. Last time…. • Basics of financial analysis • Estimating revenues and expenses is crucial • Time value of money concept • The significance of present value comparisons • Conversion of cash flows to present values

  2. Profit Revisited • Profit = Revenues - Expenses • Expenses should include loss of value of equipment with time due to • Wear and Tear • Obsolescence • Loss of value (“expiration of assets”) is the basis of DEPRECIATION

  3. Depreciation and Taxes • Suppose a company has $10 million in profits on December 31, i.e. Profits = Revenues - Expenses = $10,000,000 • Corporate taxes are, in simplest terms, based on a a percentage of profits • Suppose that as a way of “beating taxes” the company purchases $10 million worth of new equipment on December 31 • Is the profit = 0?

  4. No! Profit is not zero • The company has merely converted one asset (cash) to another (equipment). This is why Uncle Sam controls how equipment is “expensed”-- i.e. you cannot declare items of capital equipment as expenses when purchased. Instead, they are depreciated.

  5. Depreciation Calculations- Information Needed We need: • Price originally paid for the equipment or asset • Estimate of lifetime (IRS) • Salvage Value at the end of lifetime • Calculations to be shown neglect special circumstances, e.g. investment tax credits, additional first year allowances

  6. Depreciation • A new machine is not as good as an old machine • Depreciation is a way to account for the expiration of the machine, or any asset • Many methods: straight line versus accelerated • Has important tax consequences, which need to be considered in present value calculations

  7. Mmmm…. Math Ci = Initial cost of an asset Cs = Final salvage value of an asset Cd =Depreciable cost =(Ci- Cs) m = lifetime for tax purposes (often differs from actual lifetime) dk = fractional depreciation in year k Dk = Dollar amount of depreciation, year k Dk = dk Cd , Book Value = Ci- Cddk Book Value is often not true asset value.

  8. • Accelerated Depreciation – Double Declining Balance D = C (2/m) B = C - D 1 i 1 i 1 D = B (2/m) = [ C (1-2/m)](2/m)],etc. 2 1 i Depreciation Methods • Straight Line Dk = Cd/m (same over lifetime) Link to Summary of Depreciation Methods

  9. After-Tax Interest Rate • If we have an investment of $P yielding i interest per year, at the end of one year we have: P(1 + i) • We have to pay taxes on earningsEarnings = P(1 + i) - P = P i • Tax rate is T • Taxes = P i T • Real Earnings = Pi - P i T = Pi (1 - T) • Define after tax interest rate iT = i(1 - T) • So, real after tax earnings = PiT • We will use iT in after-tax comparisons

  10. Consider the Effect of Depreciation and Taxes on Present Value (P) • If no depreciation & taxes, the decision to invest $C i in a piece of equipment at time zero is worth P = -Ci • Reflects that Ci of cash of unavailable for other investments • Now, we need to consider the fact that depreciation gives us a tax savings each year

  11. CS D1T D2T D3T D4T DNT ••• 0 1 2 3 4 N Ci Cash Flow Time Line for Investments • Cash outflow is shown below the line • Savings and/or revenues above the line • Cs is salvage value

  12. CS D1T D2T D3T D4T DNT ••• 0 1 2 3 4 N Ci = Ci Cash Flow Time Line for Investments

  13. After-Tax Cost Comparison Formulae Link to After-Tax Cost Comparison Formulae

  14. R(1 - T) R(1 - T) R(1 - T) R(1 - T) 0 1 2 3 4 Effect of Revenues in After Tax Comparisons • For every $R of revenue, a profit making firm pays $RT in tax where T = fractional tax rate • Thus, the firm actually keeps ($R - $RT) = $R(1 - T) • An after-tax cash flow time line would therefore have amounts as shown R(1 - T) ...

  15. Expenses in After-Tax Comparisons • An expense of X in a particular tax year has two effects on cash flow -the actual out-of-pocket payment of X -the reduction of taxes as a result of the expense (XT) • Profit Before Expense (p) - Expense (X) = Profit After Expense (px) • Tax = pxT = pT - XT • Profit after Taxes = px - pxT = px(1 - T) • Therefore, Effect of Expense = -X(1 - T)

  16. CS DT DT DT DT R(1 - T) R(1 - T) R(1 - T) R(1 - T) 0 1 2 3 4 Ci X(1 - T) X(1 - T) X(1 - T) X(1 - T) After-Tax Cash Flow Time Line Showing Revenues, Expenses and Depreciation Note! Depreciation is not a real cash flow into company. It has the effect of reducing taxes. Note! No taxes associated with Ci or Cs terms.

  17. Profitability vs. Cash Flow • Assume Companies A & B make the same product, in same quantities and have the same revenuesR = $100,000/yr • Raw materials & labor $50,000/yr for both • A produces products on a machine worth $200,000 and “consumes” 20% of its useful life/yr • B’s machine also costs $200,000, but they consume 15%/yr of its useful life • Assume actual maintenance costs are the same for A & B Cash flow, before taxesFor A = $100,000 - $50,000 = $50,000/yrFor B = $100,000 - $50,000 = $50,000/yrNO DIFFERENCE!Yet, we know that B is more profitable because it consumes less of its capital assets.

  18. Profits (Including Depreciation) before Taxes • For A = $100,000 - $50,000 - (0.20)(200,000) = $10,000/yrFor B = $100,000 - $50,000 - (0.15)(200,000) = $20,000/yrB shows itself to be better! • Taxes @ (50%) A = 0.50($10,000) = $5000 B = 0.50($20,000) = $10,000 • After-Tax Income (Before Tax Profit) - (Taxes) A = 10,000 - 5000 = $5000 B = 20,000 - 10,000 = $10,000 • But after tax cash flow [R - X - Taxes]A = $100,000 - $50,000 - $5000 = $45,000B = $100,000 - $50,000 - $10,000 = $40,000 Which company is better?

  19. Which company is better? • B is the better company! • A has “turned” more of its assets into cash, but is using its assets less efficiently than B, as profit illustrates • Therefore, profitability = cash flow

  20. Depreciation - a “Source” of Cash?? Variable Costs (raw materials, labor, etc.) Fixed Costs (excluding depreciation) Sales Depreciation (paid to yourself) Other income Profit Real cash buildup Buildup of cash Buy new equipment Taxes Uncle Sam’s perspective

  21. Profitability Measures Payout time / Payback period - Many definitions of this - GenerallyPayback Period (N, in years) = • Initial investment is Ci total investment for some people, only Cd (depreciable investment) for others • Income/yr for some is average profit/yr, excluding depreciation and taxes, but some include depreciation and taxes • Basic question addressed How soon do I recoup my original investment?

  22. ROI (Return on Original Investment) ROI = • Neither payback period nor ROI explicitly considers the time value of money!

  23. Preferred Methods • Net Present Value (NPV) Also known as Venture Worth (VW) • Discounted Cash Flow Rate of Return (DCFRR) Same as NPV = 0, solve for iT • Iw = working capital (similar to initial investment in treatment)

  24. Which Method is “Better”? • Net Present Value • Requires setting a value of iT before you start • Any NPV > 0 means a worthwhile project • In choosing between alternatives with unequal lifetimes, need to choose on an annualized income basis (i.e. convert P X at end) • DCFRR • No need to have same time basis or to choose iT a priori • Go down list from highest iT to lowest (down to a minimum acceptable iT)

  25. Example - Two Competing Investment Opportunities Opportunity 1 Opportunity 2 75,000 Revenues ($/yr) 60,000 10,000 15,000 Costs ($/yr) 150,000 Required Investment ($) 130,000 30,000 10,000 Salvage Value at End ($) Project Life (yrs) 4 5 Depreciation Lifetime (yrs) 3 3 After tax interest rate = 0.10/yr = iTCombined Fed/State tax rate = 0.48 = TDepreciation method = Straight line

  26. ND = depreciation lifetime = N = Project Lifetime Cash Flow Time Lines(Amounts in 1000’s) • Opportunity 1 40T 40T 40T 10 T) 60(1 - - T) T) T) T) T) 60(1 - - T) 60(1 - - T) 60(1 - - T) 60(1 - - T) 0 0 1 1 2 2 3 3 4 5 10(1- T) 10(1- T) 10(1- T) 10(1- T) 10(1- T) 130 Note:

  27. Note: D = Cash Flow Time Lines(Amounts in 1000’s) • Opportunity 2 40T 40T 40T 30 T) 75(1 - - T) T) T) T) 75(1 - - T) 75(1 - - T) 75(1 - - T) 0 0 1 1 2 2 3 3 4 15(1- T) 15(1- T) 15(1- T) 15(1- T) 150

  28. Present Value Calculations

  29. Present Value Calculations con’t • Since P1 > 0 and P2 > 0, do both projects, if possible • If can only choose one or the other • Choose Opportunity 1 over Opportunity 2 (X1 > X2) • Note, if P1 had been just a bit less, could have had P1 > P2 but X1 < X2 . In this case, would choose Opportunity 2 instead.

  30. DCFRR • Let P1 = 0 and solve for iT • Need a root finding technique Know iT > 0.1 / yr • In this case (iT)1 from (iT)2 from • Choose projects based on iT, highest to lowest until you run out of money to invest (Here, choose 1 over 2) • Use a graphical or numerical approach to solve for iT

  31. Continuous Interest and Discounting • Treats compounding in a continuous manner, as if in every infinitesimal time period, interest accrues (instead of only at year end): 1+ iannual = (1 + icont/k)k where there are k compounding periods per year. Now let k , (1 + icont/k)k eicont

  32. Continuous Discounting Thus iannual = e icont -1 and S = P (1 + iannual )n = P (1 + e icont -1)n = P e i n where it is now understood that in these types of calculations, i = icont Link to Continuous Interest Formulae

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