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Section B: Selected interest and other rates, and ratios 1. iaf = inflation-adjusted after-tax cost of debt and owner-provided capital iaf = ridf)(1-t)+(1-r)(ief) 2. ia = inflation-free after-tax cost of debt and owner-provided (equity) capital 3. id = inflation-free before-tax cost of debt capital 4. idf = inflation-adjusted before-tax cost of debt capital = (1 +if/(1+id)-1 5. ie = inflation-free cost (i.e., expected return on) of equity capital 6. ief = inflation-adjusted cost of equity capital=(1+if)(1+ie)-1 7. if = inflation rate 8. r = debt/total (debt and equity) capital ratio 9. iaf equation (with taxes, inflation and debt) for iaf: iaf = r(idf)(1-t)+(1-r)(ief) 10.ia equation (without taxes, inflation and debt) for ia: ia = ie 11.ia equation (with taxes and debt, and no inflation) for ia: ia = r(id)(1-t)+(1-r)(ie) 3 Page AER = AEOC+[P(A/P iaf,N)-NSV(A/F,iaf,N)-t(AED)](1/(1-t) (Annual equivalent revenue) PER = PEOC+[P-NSV(P/F iaf,N)-t(PED)](1/(1-t) (Present equivalent revenue) OR AER =AEOC + [P(A/P iaf,N)CTF-SV(A/F,iaf,N)CSV]/(1-t) AEOC-annual equivalent operating expenses (including interest on debt) AED = Annual Equivalent Depreciation PED=Present Worth of annual depreciation expenses NSV = Net salvage value (i.e., market salvage value (SV) is adjusted for relevant income taxes (if any) on capital gains, recaptured depreciation or terminal loss) Section C: Detailed Example With Debt and Equity Capital, Inflation and Income Taxes Given: 1. P=$400,000 2. Expected salvage value )in 10 years)=$100,000 3. Expected life=10 years 4. Depreciation method: Declining Balance (DB) 5. DB depreciation Rate (d)= 25% 6. Half-year rule: Yes. 7. Operating expense at E01=$50,000 8. Annual operating expenses are fully responsive to inflation 9. Debt ratio (r)=40% 10. Inflation rate (if)=5% 11. Tax rate on net income, capital gains, depreciation recapturing and terminal losses) -50% 12. Inflation-free debt rate (id)= 4% 13. Inflation-free rate on equity capital (ie)=6% idf = (1 +if)(1+id)-1 = (1+0.05)(1+0.04)-1=0.092 or 9.2% ief = (1+if)(1+ie)-1 = (1+0.05)(1+0.06)-1=0.113 or 11.3% 4 Page let = (1+1)(1+le)-1 = (1+0.05)(1+0.06)-1=0.113 or 11.3% 4 Page iaf = f(idf)(1-t)+(1-r)(ief) = (0.4)(0.092)1-0.5)+(1-0.4)0.113= 0.0862 or 8.62% AEOC={50,000[EOY1](P/F,8.62%,1)+50,000(F/P,5%, 1)(P/F,8.62%,2)CEOY2] +50,000(F/P,5%,2)(P/F,8.62%,3)[EOY3]+50,000(F/P,5%,3)(P/F,8.62%,4)[EOY4] +50,000(F/P,5%,4)(P/F,8.62%,5)(EOY5]+50,000(F/P,5%,5)(P/F,8.62%,6)[EOY6] +50,000(F/P,5%,6)(P/F,8.62%,7)[EOY7+50,000(F/P,5%,7)(P/F,8.62%,8)[EOY8] +50,000(F/P,5%,8)(P/F,8.62%,9)[EOY9] +50,000(F/P,5%,9)(P/F,8.62%,10)[EOY10]}(A/P 8.62%,10) = $60,841 where (for example) 50,000(F/P,5%,1)(P/F,8.62%,2)CEOY2] is the value at EOYO (i.e., Present Worth) of the inflation-adjusted operating cost at EOY2 AED= {400,000(0.5)(0.25)(P/F, iaf,1)+(0.25)BV[EOY1](P/F,iaf,2) +(0.25)BV[EOY2](P/F,iaf,3)+(0.25)BV[EOY3](P/F iaf,4) +(0.25)BVLEOY4](P/F,iaf,5)+(0.25)BVLEOY5](P/F,iaf,6) +(0.25)BV[EOY6](P/F,iaf,7)+(0.25)BVLEOY7](P/F,iaf,8) +(0.25)BV[EOY8](P/F iaf,9) +(0.25)BV[EOY9](P/F,iaf,10)}(A/P iaf,10) = $42,457 where BVLEOY13= Book Value at end-of-year 1 AEI AED BV EOY 0 1 50,000 14.720 50,000 350,000 2 52,500 13,248 87,500 262,500 3 55,125 11.776 65,625 196,875 4 57,881 10,304 49,219 147,656 5 60.775 8,832 36,914 110,742 6 63,814 7,360 27,686 83,057 7 67,005 5,888 20,764 62,292 8 70,355 4,416 15,573 46,719 9 73,873 2,944 11,680 35,040 10 77,566 1,472 26,280 PEOC- 397,076 PEI = 59,317 PED = 277,092 AEOCO 60,841 AEI 9,089 AED 42.457 PEOC=Present Worth of Annual Operating Expenses; AEOC=Annual Equivalent Operating Expenses AEl-Annual Equivalent Interest Expense (on debt); AED=Annual Equivalent Depreciation 8,760 In the above Table, annual operating expenses are FULLY SENSITIVE to (grow exactly at the) inflation rate. 51 Page Cash Flow Approach to AER NSV= SV-t(SV-BV)=100,000-0.5(100,000-26,280)=$63,140 Section B: Annual Equivalent Revenue Requirement (Questions 14 to 19) Your decision to purchase a small business depends on the annual equivalent revenue (AER) required to meet all expenses (operating, taxes, return on capital, repayment of debt) given the values of parameters such as the inflation rate, the debt ratio, the return anticipated on your investment as shown in the following Table iafridf)(1-t)+(1-1){(1+ie)(1+if)-1] where 1. iaf inflation-adjusted after-tax cost of debt and owner-provided capital 2. id = inflation-free before-tax cost of debt capital 3. idf = inflation-adjusted before-tax cost of debt capital 4. io cost of equity (owner) capital 5. If = inflation rate 6. debt ratio 7. to tax rate 8. SV-Gross salvage value (ie., SV before taxes) 9. NSV-SV adjusted for taxes on recaptured depreciation and NSV-SV-taxes on recaptured depreciation-taxes on capital capital gains (as required) where gains (as required) Use the following equation: AER -AEOC+[P(A/P iaf,N)-NSV(A/F iaf,N)-t(AED)/(1-t) AEOC-annual equivalent operating expenses AED Annual Equivalent Depreciation AER - pre-tax annual revenues required meet annual expenses Reminder: The net salvage value (NSV) is the after-tax salvage value (SV) for relevant income taxes (if any) due to capital gains, recaptured depreciation or terminal loss. 500,000 1. Initial Cost or Purchase Price (8) 2. Projected Salvage Value (5) 3. Useful life (years) 4. Annual Operating Cost (5) at EOY1 50.000 5 60.000 14. Inflation rate (1)-0%; r0%; tw0%; le-B%. MARR (=lat) for this business environment is 15 Inflation rate (if)=0%; w0%; t-0%; le=8%. The annual equivalent revenue (AER) for this business environment is Inflation rate (if)0%; t-0%;re50%; ide12%; le=8%. If you needed to borrow 50% of the required capital (le, 50% of $500,000). MARR (-ial) for this business environment 16 3/4 17. Inflation rate (if)=0%; t=40%; r=50%;id=12%; le=8%. If you borrowed 50% of the required capital, the AER (see formula above) would be 18. Inflation rate (if)=10%; t=40%; r=50%; id=12%; le=8%; annual operating costs are fully responsive to the inflation rate. MARR (=iaf) for this business environment would be 19. Inflation rate (if)=10%; t=40%; r=50%;id=12%; ie=8%; annual operating costs are fully responsive to the inflation rate. AER for this business environment would be Section B: Selected interest and other rates, and ratios 1. iaf = inflation-adjusted after-tax cost of debt and owner-provided capital iaf = ridf)(1-t)+(1-r)(ief) 2. ia = inflation-free after-tax cost of debt and owner-provided (equity) capital 3. id = inflation-free before-tax cost of debt capital 4. idf = inflation-adjusted before-tax cost of debt capital = (1 +if/(1+id)-1 5. ie = inflation-free cost (i.e., expected return on) of equity capital 6. ief = inflation-adjusted cost of equity capital=(1+if)(1+ie)-1 7. if = inflation rate 8. r = debt/total (debt and equity) capital ratio 9. iaf equation (with taxes, inflation and debt) for iaf: iaf = r(idf)(1-t)+(1-r)(ief) 10.ia equation (without taxes, inflation and debt) for ia: ia = ie 11.ia equation (with taxes and debt, and no inflation) for ia: ia = r(id)(1-t)+(1-r)(ie) 3 Page AER = AEOC+[P(A/P iaf,N)-NSV(A/F,iaf,N)-t(AED)](1/(1-t) (Annual equivalent revenue) PER = PEOC+[P-NSV(P/F iaf,N)-t(PED)](1/(1-t) (Present equivalent revenue) OR AER =AEOC + [P(A/P iaf,N)CTF-SV(A/F,iaf,N)CSV]/(1-t) AEOC-annual equivalent operating expenses (including interest on debt) AED = Annual Equivalent Depreciation PED=Present Worth of annual depreciation expenses NSV = Net salvage value (i.e., market salvage value (SV) is adjusted for relevant income taxes (if any) on capital gains, recaptured depreciation or terminal loss) Section C: Detailed Example With Debt and Equity Capital, Inflation and Income Taxes Given: 1. P=$400,000 2. Expected salvage value )in 10 years)=$100,000 3. Expected life=10 years 4. Depreciation method: Declining Balance (DB) 5. DB depreciation Rate (d)= 25% 6. Half-year rule: Yes. 7. Operating expense at E01=$50,000 8. Annual operating expenses are fully responsive to inflation 9. Debt ratio (r)=40% 10. Inflation rate (if)=5% 11. Tax rate on net income, capital gains, depreciation recapturing and terminal losses) -50% 12. Inflation-free debt rate (id)= 4% 13. Inflation-free rate on equity capital (ie)=6% idf = (1 +if)(1+id)-1 = (1+0.05)(1+0.04)-1=0.092 or 9.2% ief = (1+if)(1+ie)-1 = (1+0.05)(1+0.06)-1=0.113 or 11.3% 4 Page let = (1+1)(1+le)-1 = (1+0.05)(1+0.06)-1=0.113 or 11.3% 4 Page iaf = f(idf)(1-t)+(1-r)(ief) = (0.4)(0.092)1-0.5)+(1-0.4)0.113= 0.0862 or 8.62% AEOC={50,000[EOY1](P/F,8.62%,1)+50,000(F/P,5%, 1)(P/F,8.62%,2)CEOY2] +50,000(F/P,5%,2)(P/F,8.62%,3)[EOY3]+50,000(F/P,5%,3)(P/F,8.62%,4)[EOY4] +50,000(F/P,5%,4)(P/F,8.62%,5)(EOY5]+50,000(F/P,5%,5)(P/F,8.62%,6)[EOY6] +50,000(F/P,5%,6)(P/F,8.62%,7)[EOY7+50,000(F/P,5%,7)(P/F,8.62%,8)[EOY8] +50,000(F/P,5%,8)(P/F,8.62%,9)[EOY9] +50,000(F/P,5%,9)(P/F,8.62%,10)[EOY10]}(A/P 8.62%,10) = $60,841 where (for example) 50,000(F/P,5%,1)(P/F,8.62%,2)CEOY2] is the value at EOYO (i.e., Present Worth) of the inflation-adjusted operating cost at EOY2 AED= {400,000(0.5)(0.25)(P/F, iaf,1)+(0.25)BV[EOY1](P/F,iaf,2) +(0.25)BV[EOY2](P/F,iaf,3)+(0.25)BV[EOY3](P/F iaf,4) +(0.25)BVLEOY4](P/F,iaf,5)+(0.25)BVLEOY5](P/F,iaf,6) +(0.25)BV[EOY6](P/F,iaf,7)+(0.25)BVLEOY7](P/F,iaf,8) +(0.25)BV[EOY8](P/F iaf,9) +(0.25)BV[EOY9](P/F,iaf,10)}(A/P iaf,10) = $42,457 where BVLEOY13= Book Value at end-of-year 1 AEI AED BV EOY 0 1 50,000 14.720 50,000 350,000 2 52,500 13,248 87,500 262,500 3 55,125 11.776 65,625 196,875 4 57,881 10,304 49,219 147,656 5 60.775 8,832 36,914 110,742 6 63,814 7,360 27,686 83,057 7 67,005 5,888 20,764 62,292 8 70,355 4,416 15,573 46,719 9 73,873 2,944 11,680 35,040 10 77,566 1,472 26,280 PEOC- 397,076 PEI = 59,317 PED = 277,092 AEOCO 60,841 AEI 9,089 AED 42.457 PEOC=Present Worth of Annual Operating Expenses; AEOC=Annual Equivalent Operating Expenses AEl-Annual Equivalent Interest Expense (on debt); AED=Annual Equivalent Depreciation 8,760 In the above Table, annual operating expenses are FULLY SENSITIVE to (grow exactly at the) inflation rate. 51 Page Cash Flow Approach to AER NSV= SV-t(SV-BV)=100,000-0.5(100,000-26,280)=$63,140 Section B: Annual Equivalent Revenue Requirement (Questions 14 to 19) Your decision to purchase a small business depends on the annual equivalent revenue (AER) required to meet all expenses (operating, taxes, return on capital, repayment of debt) given the values of parameters such as the inflation rate, the debt ratio, the return anticipated on your investment as shown in the following Table iafridf)(1-t)+(1-1){(1+ie)(1+if)-1] where 1. iaf inflation-adjusted after-tax cost of debt and owner-provided capital 2. id = inflation-free before-tax cost of debt capital 3. idf = inflation-adjusted before-tax cost of debt capital 4. io cost of equity (owner) capital 5. If = inflation rate 6. debt ratio 7. to tax rate 8. SV-Gross salvage value (ie., SV before taxes) 9. NSV-SV adjusted for taxes on recaptured depreciation and NSV-SV-taxes on recaptured depreciation-taxes on capital capital gains (as required) where gains (as required) Use the following equation: AER -AEOC+[P(A/P iaf,N)-NSV(A/F iaf,N)-t(AED)/(1-t) AEOC-annual equivalent operating expenses AED Annual Equivalent Depreciation AER - pre-tax annual revenues required meet annual expenses Reminder: The net salvage value (NSV) is the after-tax salvage value (SV) for relevant income taxes (if any) due to capital gains, recaptured depreciation or terminal loss. 500,000 1. Initial Cost or Purchase Price (8) 2. Projected Salvage Value (5) 3. Useful life (years) 4. Annual Operating Cost (5) at EOY1 50.000 5 60.000 14. Inflation rate (1)-0%; r0%; tw0%; le-B%. MARR (=lat) for this business environment is 15 Inflation rate (if)=0%; w0%; t-0%; le=8%. The annual equivalent revenue (AER) for this business environment is Inflation rate (if)0%; t-0%;re50%; ide12%; le=8%. If you needed to borrow 50% of the required capital (le, 50% of $500,000). MARR (-ial) for this business environment 16 3/4 17. Inflation rate (if)=0%; t=40%; r=50%;id=12%; le=8%. If you borrowed 50% of the required capital, the AER (see formula above) would be 18. Inflation rate (if)=10%; t=40%; r=50%; id=12%; le=8%; annual operating costs are fully responsive to the inflation rate. MARR (=iaf) for this business environment would be 19. Inflation rate (if)=10%; t=40%; r=50%;id=12%; ie=8%; annual operating costs are fully responsive to the inflation rate. AER for this business environment would be

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