11CHAPTER 142• This chapter examines tools used to evaluate potential projects/investments• Accountants–Simple Rate of Return (SRR)• Based on NI• AKA Accounting Rate of Return3• Financiers–Don’t like NI• Too much discretion• Prefer ATCF to NI–Use PBP, NPV, and IRR–Concept of ATCF is discussed in Appendix 14C24• SRR & PBP are non-discounting models–Don’t use PV• NPV & IRR are discounting models–Use PV 5Present Value(Appendix 14A)6• Instinctively, you know $1 in future ≠ $1 today• You can put $1 in bank:–Earn interest on deposit–Have $1 + interest in future37• PV tells you what you put in bank today to have $1 in future:PVIF =__1___(1+ d)n• “d” – interest rate• “n” – number of periods8• E.g., $1 received at end of 1 year–10% interest compounded annually–Deposit following at start of year: PVIF = (1/(1.10)1)PVIF = 90.909¢9You can test this:One Year's Interest (.1 x 90.909¢ )= 9.0909¢Original Principal = 90.9090¢After 1 Year:99.9999¢Off due to rounding410• E.g., $1 is received at end of 2 years • 10% interest compounded annually• Deposit following at start of period: PVIF = (1/(1.10)2)PVIF = 82.6446¢111stYear's Interest(.1 x 82.6446¢)= 8.26446¢Original Principal = 82.64460¢After 1 year: 90.90906¢2ndYear's Interest(.1 x 90.90906¢)= 9.090906¢Balance At Start of Year = 90.909060¢After 2 years: 99.999966¢12• If you get $1 a year for a number of years– “Annuity”– You could calculate PV of each $1 to be received– Or use PV of Annuity formula:PVIFannuity =1/d ( 1- [ __1___])(1+d)n513• E.g., $1 received at end of each year for 2 years– 10% interest compounded annually– Deposit following:PV of $1 received 1 year from now:90.9090¢PV of $1 received 2 years from now:82.6446¢$1.735536• Using PVA formula: PVIFannuity= [1-(1/(1.10)2]/.1 PVIFannuity= $ 1.7355371914• If you deposit $1.73553719@ 10% interest• You can withdraw $1 at end of each year for 2 years:Initial Deposit:$1.735537190 1stYear’s Interest: 17.355372¢Balance after 1 Year: $1.909091Withdrawal of $1: -$1.000000Balance Remaining: 90.9091¢2ndYear’s Interest: 9.0909¢Balance after 2 Years: $1.000000Withdrawal of $1: -$1.000000Balance after Withdrawal of $1: 015Net Present Value616• Problem with evaluating investment –You invest present $s & receive future $s –Like comparing apples & oranges17• NPV– Convert payoff into PV & subtract investment• Now comparing apples & apples– If positive receiving return > discount factor18• Discount rate minimum return required• Traditionally weighted average cost of capital of firm– Weights are % capital coming from a particular source of capital• E.g., 20% from equity vs. 80% from debt– Cost of capital is after-tax cost of capital:• interest is deductible• dividends are not deductible719• NPV payoff is in ATCF (not NI)– Difference between NI & ATCF depreciation & other non-cash expenses• We will assume that:– Investment made on 1stday of investment & – Payoffs received at end of each year20Depreciation Tax Shield (Appx 14C)• Depreciation is not a cash expense– Not directly part of ATCF• But depreciation is tax deduction– Taxes are a cash expense & included in calculation of ATCF• For tax purposes, Depreciation follows MACRS– Unless you are told otherwise, we will assume S/L method21• Most Books:A Revenue: $100KB Less: Cash Expenses: -40KC BTCF (A-B): $60K $60KD x Tax Rate: X .4E Taxes (CxD): -$24KF Prelim ATCF (B-E): $36KG Depreciation: $10KH x Tax Rate: X .4I Tax Shield (GxH): +$4KJ ATCF (F+I): $40K822• My Approach Same Result:A Revenue: $100KB Less: Cash Expenses: -40KC BTCF (A-B): $60K $60KD Depreciation: -10KE OP (C-D): $50KF x Tax Rate: X .4G Taxes (ExF): -$20KH ATCF (C-G): $40K23• E.g., Co. considering new project• Investment of $420,000• no salvage value• tax rate 40%• required minimum return 10%• S/L depreciation with no SV Cash Flow1 $ 100K 4 150K2 200K 5 100K3 250K 6 100K$ 900K24• Depreciation Tax Shield approach– Assume depreciation deduction is $70,000/year ($420,000/6):: CF - Taxes(.4) +Tx Shd ATCF1 $ 100K - $40K + $28K 88K2 200K - $80K + 28K 148K3 250K - 100K + 28K 178K4 150K - 60K + 28K 118K5 100K - 40K + 28K 88K6 100K - 40K + 28K 88K$ 900K $708K925• Alternative approach:(A) (B) (C=A-B) (D=.4C)BTCF Dep TI Tx Rt Taxes1 $ 100K - $70K = $30K x.4= 12K2 200K - $70K = 130K x.4= 52K3 250K - $70K = 180K x.4= 72K4 150K - $70K = 80K x.4= 32K5 100K - $70K = 30K x.4= 12K6 100K - $70K = 30K x.4= 12K$ 900K $420K $480K $192K26• Next, subtract taxes from BTCF: (A) (D) (A-D)BTCF -Taxes ATCF1 $ 100K 12K 88K2 200K 52K 148K3 250K 72K 178K4 150K 32K 118K5 100K 12K 88K6 100K 12K 88K$ 900K $708K27• Now, Calculate PV of ATCF:ATCF x PVIF PV of CF1 88K x .90909 $ 80,0002 148K x .82645 122,3153 178K x .75131 133,7334 118K x .68301 80,5955 88K x .62092 54,6416 88K x .56447 49,673$708K $520,957Less Investment: -420,000NPV: $100,9571028• If NPV > 0 Co. receiving > minimum required return–You don’t know actual return–Turns out you are receiving 18.1% return29How Do You Handle Salvage Value in NPV?30• Treat the Salvage Value as an additional cash flow in the last year of the investment.– It can be a separate line, but it has the same PVIF as the last year’s payoff1131• Remember that the payoffs are ATCF• You need to subtract the taxes from the assumed sale of the Salvage Value.32• Are there any taxes on the assumed sale of the Salvage Value?• This depends on whether there is a gain from the assumed sale.33• If you used accounting depreciation, then you never depreciated the asset below its salvage value.• Thus, it still has a BV equal to its salvage value, and the sale produces no gain:Sale Proceeds – BV = GainSalvage Value – Salvage Value = 0 gain1234• If you used MACRS, then you depreciated the asset below its salvage value.• Thus, it has no BV on the assumed sale• You therefore have a gain on the assumed sale:• Sale Proceeds – BV = gain• Salvage Value – 0 = Salvage Value (gain)35• If you used MACRS, you have to assume that the Salvage Value taxable• Thus, you have to reduce it by the tax amount in order to have the ATCF36Internal Rate of Return1337• IRR is same analysis as NPV with following modifications:–Assume NPV = 0 –Solve for discount (interest) rate• IRR is very popular in business world• Academics don’t like IRR •
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