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Capital Investment Analysis • Determine whether an investment should be undertaken or not – Capacity expansion (machines, facilities) – Equipment replacement • Selects between investment opportunities (mutually exclusive choices) • Selects best portfolio of investment within a budget Basics • Cash Flow Diagram: the financial description of a project • Time Value of Money: the value of money changes with time • Interest: used to move money through time for comparisons • Measure of Worth: method in which to financially evaluate a project Cash Flow • Movement of money (in or out) of a project • Inflows: revenues or receipts • Outflows: expenses or disbursements • Net Cash Flow: receipts - disbursements Cash Flow Diagram • Describes type, magnitude and timing of cash flows over some horizon • Used to describe any investment opportunity. • Typical investment: Cash Flow Analysis • Given that any investment opportunity can be drawn by a cash flow diagram, how can we select the best? • Transform all cash flow diagrams into something similar for comparison. – Use a Common Interest Rate – Use Time Value of Money Calculations Time Value of Money • Money has value because it gives us utility. • Generally, money is preferred now, as opposed to later (same amount) – One can spend it now and get utility – One can invest it and watch it grow into larger sums for greater future utility – One can put it under the mattress and watch it lose purchasing power Time Value of Money • To describe the same amount of money at different periods of time requires the use of interest. • Generally, money grows (compounds) into larger future sums. • Similarly, money is smaller (discounted ) in the past. Interest • Cost of Money – Rental amount charged by lender for use of money – In any transaction, someone “earns” and someone pays • Savings Account: • Home/Auto Loan: Definitions • Principal: P – Amount invested or loaned • Interest Rate: i – Rental charge for money defined as a percentage of principal per time period • Compounding Period – Defines how often interest is calculated (may not be paid, however) • Length of loan/investment: n periods Simple Interest • Interest earned/paid is directly proportional to capital involved. Compound Interest • Interest is paid on both the capital and accrued interest. Compound Interest and Cash Flow Diagrams Effective Interest Rates • Rate of interest charged for a given period • i % per period Compound Interest and Cash Flow Diagrams • To perform any analysis, cash flow diagrams and interest rate must use same measure of a period (i.e. years, months, days, etc.) • Match cash flows and interest rate by converting rate to proper period. Converting Effective Interest Rates • Cash flows occur every month. Given annual interest rate of 12 %. • Cash flows occur every year. Given quarterly interest rate of 4 %. Nominal Interest Rates or APRs • Annual interest rate that does not incorporate the effects of compounding • r % per year compounded periodically • r % compounded periodically • Nominal interest rate: r Converting Nominal Interest Rates to Effective Interest Rates • First, convert to compounding period • Then convert to required period Nominal to Effective Rates • Nominal Rate: r% compounded periodically (m) • Effective Rate: i% = r%/m • Example: 12% compounded quarterly • Example: 14% compounded monthly Effective to Nominal Rates • Effective Rate: i% per period • Nominal rate: r% = i% * number of compounding periods in a year • Example: 2% per month • Example: 4% per quarter Nominal vs. Effective Interest Rates • For comparison: compare effective interest rates over common period • Auto Loan: – Bank: 12% compounded quarterly – Dealer: 1.5% per month • Which is better? Cash Flow Evaluation • With interest, ready to move money through time. • Common calculations: – Convert all cash flows to time zero (present value) – Convert all cash flows to time n (future value) – Convert all cash flows to a set of n equal cash flows from time 1 through n (annual equivalent) • Can learn formulas or use spreadsheets. After-Tax Cash Flows • Need to calculate after-tax cash flows for analysis. • Income Taxes -- paid on profits from operations and profitable sale of assets • Capital Gains Taxes -- paid on the profitable sale of assets (greater than purchase price) • Tax Credits -- received due to loss from operations or sales and possibly for investments Income Taxes Revenue - Expense = Income Taxes Paid = Income * Tax Rate => Expenses actually reduce our taxable income! Expenses • Labor • Materials • Operations... • Interest • Depreciation Depreciation • Buying an asset does not constitute an “expense” in the government’s eyes. • When you purchase an asset (depreciable), you may “expense” it over time. The depreciation in a given year is the amount of expense. • Depreciation is an expense, but NOT a cash flow. Depreciation • Effect on income taxes: – Depreciation is an expense and therefore reduces the before-tax income. • Effect on sales of assets: – The total depreciation accumulated over time by an asset determines its book value. The difference between the sale price of an asset and its book value determines whether the sale is a gain or loss. • Calculation – Requires depreciation method and number of periods allowed Book Value • Depreciation: – Dt in time t • Book value at the end of time n: – Initial book value B0 is generally the purchase price – Bn = B0 - Dt Current Law: MACRS • Asset Classes and Methods – Personal property (equipment, etc. -- not buildings or land) • 3, 5, 7, 10-year properties: 200% DB to SL • 15, 20 -year properties: 150% DB to SL – Real property (buildings, bridges, parking facilities, etc. -- not personal property or land) • 27.5, 31.5 -years -- Alternative SL • No Salvage Value • 1/2 year convention (years 1 and n+1) • Asset sold before year n, 1/2 depreciation MACRS Percentages • 3-year Class Year % 1 33.33% 2 44.44% 3 14.81% 4 7.41% Sales of Assets • If you sell your asset (at any time) for a value SV, you calculate the gain or loss as : SV - BVt • If SV - BV > 0, gain • If SV - BV < 0, loss • Note, if sold before year “n”, only half depreciation is received. • Tax Paid = Income Tax Rate * (SV - BV) After-Tax Cash Flows • Once we calculate taxes and subtract them from our profits, we still have to CALCULATE the after-tax cash flow. • After-Tax Cash Flow Calculation: • Reason to use spreadsheets Single Project Evaluation • Goal: Determine if an investment project is worth doing. • Answer the following question: Will it make money? • Better question: Will it make enough money? • Assume – Cash flows (value and timing) are known – Interest rate and compounding periods are known – Decision is to accept or reject project Selecting an Interest Rate • Generally specified by management • MARR: Minimum Attractive Rate of Return, defines minimum amount you are willing to make on an investment • Assume you can ALWAYS make the interest rate -- so your project must beat it to be worth the investment. • PW is a measure of worth above the baseline Present Worth Analysis Project Evaluation • Present and Future Worth and Annual Equivalent – Require knowledge of cash flows and MARR – Equivalent measures of worth -- same decision • MARR represents your baseline – Only invest in project if you can beat it – PW(MARR) > 0 means you make profit above the MARR – Think of PW as “discounted” profit Internal Rate of Return • Interest rate i* where PW(i*) = 0 • The periodic rate at which your investment earns money Internal Rate of Return Pitfalls • More than one rate? Example • Purchase piece of equipment for $30,000. It is expected to bring in revenues of $15,000 per year against $1,000 of operating expenses. Assume alternative straight-line depreciation and a tax rate of 34% per year. At the end of three years, the equipment is discarded at no cost (or revenue). The asset is a 5-year class asset. The interest rate is 12%. Should you consider this investment? Inputs: MARR: Cash Flows 12.00% Depreciation: 2 Method: 3 Tax Rate: 34.00% Life: 5 Principal: Periods: 3 Salvage: $0.00 Interest: Policy: 2 Periods: n: Revenues Inflation % 0 1 2 3 Totals Inflow 1: 0.00% $15,000.00 $15,000.00 $15,000.00 $45,000.00 Inflow 2: 0.00% $0.00 $0.00 $0.00 $0.00 Inflow 3: 0.00% $0.00 $0.00 $0.00 $0.00 Inflow 4: 0.00% $0.00 $0.00 $0.00 $0.00 Total Inflows: $15,000.00 $15,000.00 $15,000.00 $45,000.00 Expenses Outflow 1: 0.00% ($1,000.00) ($1,000.00) ($1,000.00) ($3,000.00) Outflow 2: 0.00% $0.00 $0.00 $0.00 $0.00 Outflow 3: 0.00% $0.00 $0.00 $0.00 $0.00 Interest: $0.00 $0.00 $0.00 $0.00 Depreciation: ($3,000.00) ($6,000.00) ($3,000.00) ($12,000.00) Total Expenses: ($4,000.00) ($7,000.00) ($4,000.00) ($15,000.00) Taxable Income: $11,000.00 $8,000.00 $11,000.00 $30,000.00 Income Tax: ($3,740.00) ($2,720.00) ($3,740.00) ($10,200.00) Profit A/T: $7,260.00 $5,280.00 $7,260.00 $19,800.00 Loan Principal: $0.00 $0.00 $0.00 $0.00 $0.00 Purchase: ($30,000.00) ($30,000.00) Cash Flow A/T: ($30,000.00) $10,260.00 $11,280.00 $10,260.00 $1,800.00 Analysis Cash Flow PW: ($4,544.07) Cash Flow AE: ($1,891.92) Cash Flow FW: ($6,384.10) IRR: 2.97% $5,000.00 $0.00 0 0.4 0.8 0.08 0.16 0.24 0.32 0.48 0.56 0.64 0.72 0.88 0.96 ($5,000.00) PV(MARR) ($10,000.00) ($15,000.00) ($20,000.00) ($25,000.00) MARR Example • What if you sold the equipment for $10,000 after year three? Cash Flows Inputs: MARR: 12.00% Depreciation: 2 Method: 3 Tax Rate: 34.00% Lif e: 5 Principal: Periods: 3 Salvage: $0.00 Interest: Policy: 2 Periods: n: Revenues Inf lation % 0 1 2 3 Totals Inf low 1: 0.00% $15,000.00 $15,000.00 $15,000.00 $45,000.00 Inf low 2: 0.00% $0.00 $0.00 $0.00 $0.00 Inf low 3: 0.00% $0.00 $0.00 $0.00 $0.00 Inf low 4: 0.00% $0.00 $0.00 $0.00 $0.00 Total Inf low s: $15,000.00 $15,000.00 $15,000.00 $45,000.00 Expenses Outf low 1: 0.00% ($1,000.00) ($1,000.00) ($1,000.00) ($3,000.00) Outf low 2: 0.00% $0.00 $0.00 $0.00 $0.00 Outf low 3: 0.00% $0.00 $0.00 $0.00 $0.00 Interest: $0.00 $0.00 $0.00 $0.00 Depreciation: ($3,000.00) ($6,000.00) ($3,000.00) ($12,000.00) Total Expenses: ($4,000.00) ($7,000.00) ($4,000.00) ($15,000.00) Taxable Income: $11,000.00 $8,000.00 $11,000.00 $30,000.00 Income Tax: ($3,740.00) ($2,720.00) ($3,740.00) ($10,200.00) Prof it A/T: $7,260.00 $5,280.00 $7,260.00 $19,800.00 Loan Principal: $0.00 $0.00 $0.00 $0.00 $0.00 Purchase/Sale: ($30,000.00) $10,000.00 ($30,000.00) Tax on Asset Sale: $2,720.00 Cash Flow A/T: ($30,000.00) $10,260.00 $11,280.00 $22,980.00 $14,520.00 Analysis Cash Flow PW: $4,566.71 Cash Flow AE: $1,901.35 Cash Flow FW: $6,415.90 IRR: 19.50% $20,000.00 $15,000.00 $10,000.00 $5,000.00 PV(MARR) $0.00 0 0.4 0.8 0.08 0.16 0.24 0.32 0.48 0.56 0.64 0.72 0.88 0.96 ($5,000.00) ($10,000.00) ($15,000.00) ($20,000.00) ($25,000.00) MARR Next Steps • Multiple Projects • Capital Budgets • Uncertainty Payback Period • Answers the question: How many periods does it take us to earn back our investment? Example • Invest $50,000 in a machine at time zero. It brings in income (revenues - expenses) of $10,000 in year 1, growing by $10,000 per year for 4 years. What is n*? Payback Period Characteristics • Bad – Does not include time-value-of money – Does not consider cash flows past time period n* – Does not provide a measure of worth or return – May deter investment in potentially worthy projects • Good – Gives some measure of “risk” of a project – Determines “breakeven point” for an investment – Can be used to “enhance” evaluation of a project with a traditional measure of worth Project Balance • Evaluates a project at each period of its estimated life. • Calculate the FW(MARR) at each period. Example • Invest $50,000 in a machine at time zero. It brings in income (revenues - expenses) of $10,000 in year 1, growing by $10,000 per year for 4 years. Visualizing PB Project Balance Characteristics • PB=FW of a project at each period • PBn = FW of a project – PB provides same investment decision as FW • Graph of PB defines payback period with interest – Point when PB graph crosses over time axis • Graph defines “good” investments – Low payback period with interest – Large positive area under graph – Small negative area under graph – High FW Sensitivity Analysis • Allows one to consider errors in parameter estimates – Helps determine which parameters values are critical (most sensitive) – Also determines which parameters are NOT critical • Provides ranges of estimates where projects are acceptable

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