Today, we will talk about. Profit Revisited. No! Profit is not zero. Depreciation and Taxes. Depreciation Calculations- Information Needed

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Amos Booker
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1 Today, we will talk about. Profit Revisited 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 = 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 DEPRECIATIO Depreciation and Taxes Suppose a company has $10 million in profits on December 1, 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 1 Is the profit = 0? o! Profit is not zero The company has merely converted one asset (cash) to another (equipment). This is why Uncle Same controls how equipment is expensed -- i.e. you cannot declare items of capital equipment as expenses when purchased. Instead, they are depreciated. Depreciation Calculations- Information eeded 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 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

2 Mmmm. Math C i = Initial cost of an asset C s = Final salvage value of an asset C d =Depreciable cost =(C i - C s ) m = lifetime for tax purposes (often differs from actual lifetime) d k = fractional depreciation in year k D k = Dollar amount of depreciation, year k D k = d k C d, Book Value = C i - C d Σ d k Book Value is often not true asset value. Depreciation Methods Straight Line D k = C d /m (same over lifetime) Accelerated Depreciation Double Declining Balance D 1 = C i (2/m) B 1 = C i - D 1 D 2 = B 1 (2/m) = [C i (1-2/m)](2/m)],etc. Sum of the Years Digits D k = C d (Useful years left = m-k +1)/Σ Σ = m + (m-1) + (m-2) k = current year m = lifetime Link to Summary of Depreciation Methods 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 earnings Earnings = 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 i T = i(1 - T) So, real after tax earnings = Pi T 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 = -C i Reflects that C i of cash of unavailable for other investments ow, we need to consider the fact that depreciation gives us a tax savings each year We will use i T in after-tax comparisons Cash Flow Time Line for Investments C S D 1 T D 2 T D T D 4 T D T C i Cash outflow is shown below the line Savings and/or revenues above the line C s is salvage value Cash Flow Time Line for Investments C S D 1 T D 2 T D T D 4 T D T C i DT m Cs d s m m1 = (1+ (1+ i) T C i P = (C + C) = DT m Cd 1 Cd 1 (1+ = T m = T m m1 = (1+ m1 = (1+ it 1 T 1 (1+ P= Cs 1 C + d 1 (1 + i T ) i T

3 After-Tax Cost Comparison Formulae Link to After-Tax Cost Comparison Formulae 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) R(1 - T) R(1 - T) R(1 - T) R(1 - T) Expenses in After-Tax Comparisons After-Tax Cash Flow Time Line Showing Revenues, Expenses and Depreciation 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 (π) - Expense (X) = Profit After Expense (π x ) Tax = π x T = πt - XT Profit after Taxes = π x - π x T = π x (1 - T) Therefore, Effect of Expense = -X(1 - T) C S DT DT DT DT R(1 - T) R(1 - T) R(1 - T) R(1 - T) C i X(1 - T) X(1 - T) X(1 - T) X(1 - T) ote! Depreciation is not a real cash flow into company. It has the effect of reducing taxes. ote! o taxes associated with C i or C s terms. Profitability vs. Cash Flow Assume Companies A & B make the same product, in same quantities and have the same revenues R = $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 taxes For A = $100,000 - $50,000 = $50,000/yr For B = $100,000 - $50,000 = $50,000/yr O DIFFERECE! Yet, we know that B is more profitable because it consumes less of its capital assets. Profits (Including Depreciation) before Taxes For A = $100,000 - $50,000 - (0.20)(200,000) = $10,000/yr For B = $100,000 - $50,000 - (0.15)(200,000) = $20,000/yr B shows itself to be better! (50%) A = 0.50($10,000) = $5000 B = 0.50($20,000) = $10,000 After-Tax Income (Before Tax Profit) - (Taxes) A = 10, = $5000 B = 20,000-10,000 = $10,000 But after tax cash flow [R - X - Taxes] A = $100,000 - $50,000 - $5000 = $45,000 B = $100,000 - $50,000 - $10,000 = $40,000 Which company is better?

4 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 Sales Other income Depreciation - a Source of Cash?? Variable Costs (raw materials, labor, etc.) Fixed Costs (excluding depreciation) Profit Depreciation (paid to yourself) Taxes Buildup of cash Real cash buildup Buy new equipment Uncle Sam s perspective Payout time / Payback period - Many definitions of this - Generally Profitability Measures Payback Period (, in years) = Initial Investment Income/yr Initial investment is C i total investment for some people, only C d (depreciable investment) for others ROI (Return on Original Investment) ROI = Income / yr Initial investment either payback period nor ROI explicitly considers the time value of money! 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? Preferred Methods et Present Value (PV) Also known as Venture Worth (VW) t DT k (RX) k(1t) Cs Iw P= Ci+ + k + I k w+ k1 = (1+ k= 1 (1+ (1+ (1+ Discounted Cash Flow Rate of Return (DCFRR) Same as PV = 0, solve for i T Which Method is Better? et Present Value Requires setting a value of i T before you start Any PV > 0 means a worthwhile project In choosing between alternatives with unequal lifetimes, need to choose on an annualized income basis DCFRR o need to have same time basis or to choose i T a priori Go down list from highest i T to lowest (down to a minimum acceptable

5 Revenues ($/yr) Costs ($/yr) Required Investment ($) Salvage Value at End ($) Project Life (yrs) Depreciation Lifetime (yrs) Example - Two Competing Investment Opportunities Opportunity 1 Opportunity 2 60,000 75,000 10,000 15,000 10, ,000 10,000 0,000 After tax interest rate = 0.10/yr = i T Combined Fed/State tax rate = 0.48 = T Depreciation method = Straight line 5 4 Opportunity 1 Cash Flow Time Lines (Amounts in 1000 s) 60(1 - T) 60(1 - T) 60(1 - T) 60(1 - T) 60(1 - T) (1- T) 10(1- T) 10(1- T) 10(1- T) 10(1- T) C ote: d CiCs 1010 D= = = = 40 D D 10 D = depreciation lifetime = = Project Lifetime Opportunity 2 Cash Flow Time Lines (Amounts in 1000 s) Present Value Calculations 5 Cs 1 (1+ 1 (1+ P1= Ci + + (RX)(1 T) DT 5 + (1+ i i T) T it 75(1 - T) 0 75(1 - T) 75(1 - T) 75(1 - T) (1- T) 15(1- T) 15(1- T) 15(1- T) ote: D = = (1+ 0.1) 1 (1+ 0.1) = (6010)(1 0.48) 40(0.48) 5 + (1+ 0.1) = (thousands of dollars) 0 1(10.1) 4 + 1(10.1) + 2= = con t Since P 1 > 0 and P 2 > 0, do both projects, if possible If can only choose one or the other X1= = = $5.94x10 /yr 1 (1+ 0.1) X2 = = = $5.42x10 /yr 1 (1+ 0.1).16 Choose Opportunity 1 over Opportunity 2 (X 1 > X 2) ote, if P 1 had been just a bit less, could have had P 1 > P 2 but X 1 < X 2 In this case, choose Opportunity 2 DCFRR Let P 1 = 0 and solve for i T eed a root finding technique Know i T > 0.1 / yr In this case 5 (i T ) 1 from 10 1(1i) + T 1(1i) (50)(.52) 40(0.48) T = % 5 + (1i) + T it it 4 0 1(1i) + T 1(1i) + T (i T ) 2 from 0= (60)(.52) 40(0.48) 15% 4 + (1i) + T it it Choose projects based on i T, 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 i T

6 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+ i annual = (1 + i cont /k) k where there are k compounding periods per year. ow let k, (1 + i cont /k) k e icont Thus Continuous Discounting i annual = e icont -1 and S = P (1 + i annual ) n = P (1 + e icont -1) n = P e i n where it is now understood that in these types of calculations, i = i cont Link to Continuous Interest Formulae

CAPITAL BUDGETING Shenandoah Furniture, Inc.

CAPITAL BUDGETING Shenandoah Furniture, Inc. Shenandoah Furniture is considering replacing one of the machines in its manufacturing facility. The cost of the new machine will be $76,120. Transportation