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Problem No. 1 A(N,I) FACTOR = (1+i)^n – 1 / i Here, (1.1)^4 – 1 / 0.1 = 4.641 FVA = A * A(N,i) = 4000 * 4.641 = 18,564/- Problem No.2 10000(1+i)^4 = 12625 i = 6% hly or 12% pa

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If compounded qly, then Maturity = 10000(1.03)^8 = 12668/- Problem No.3 (i) 2000(1.08)^2 = 2332.80 (ii) 2000 (1.04)^4 = 2339.80 (iii) 2000 (1.02)^8 = 2343.40

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Problem No.4 3P = P (1+i)^7 (1+i)^7 = 3 or (1+i) = 3^(1/7) 1+ i = 1.169931 or i = 16.99%

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Problem No.5 P(n,i) factor = [(1.03)^12-1]/[0.03 * (1.03)^12] = 9.95399 Instalment = Loan / P(n,i) = 500000 / 9.95399 = 50231.11

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Problem No.6 Value of Pepetuity = Interest / rate of interest = 5000 / 0.833% = ` 6,00,240 Add: First Month Pension = ` 6,05,240/-

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Problem No.7 PV of Money outflow under Outright purchase = ` 500,000 PV of Money Outflow under instalment option = 102500 * 4.111 = 4,21,378 Note: Instalment : 615000 / 6 = 102500 Conclusion: Instalment Option is better.

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Problem No.8 Maturity = 75000 (1.08)^5 = 111108 Interest = ` 36108 Problem No. 9 Effective ROI = [(1.03)^4 -1] * 100 = 12.55%

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Problem No.10 PV of ` 50000 = 50000 / 1.7234 = `29012/=

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Problem No. 1 YearCFAT (`) PVF @ 10%DCFAT (` )( ` ) 1300,0000.9091272,730 2360,0000.8264297,504570,234 3300,0000.7513225,390795,624 4264,0000.6830180,312975,936 5240,0000.6209149,0161,124,952 Initial investment of ` 10 lakhs is exceeded in Year 5.Hence the payback period on time proportion basis as follows:- DCAFT earned during the Year 4 = ` 1, 49,016( ` 11, 24,952 - ` 9, 75,936), for a period of 12 months. Hence, time period for earning ` 24,064 in order to recover the initial investment would be : - Payback period = ` 24,064 / ` 1,49,016 * 12 months = 2 months (approx.) Hence, Payback period = 4 years, 2 months

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Accept / Reject Criteria for NPV (Net Present Value): If the NPV of the Project is +, then the project may be accepted else rejected. NPV = Cum. PVCIF – Initial Cash Out Flow (ICOF) Points to be noted: Cum. PVCIF = Sum of Discounted Cash Flows (Cash Flow * PVF) of all the years. When Working Capital Requirement is given, remember to take the same in Initial Cash Outflow and also in Terminal (Last Year) Cash Inflow. Remember to take the salvage value of Plant in the last year if given. Cash Inflow = PAT + Depreciation If the cash flows are uniform Cum. PVCIF = Cash Flow * Cum. PVF In case of Capital Rationing, If the projects are divisible the Allocation of Funds should be based on Ranking of PI. Else Allocation should be considered for various alternatives (mix of Projects). We should ensure that maximum funds are utilized and maximum NPV achieved.

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Accept/Reject Rule for PI: PI = Cum. PVCIF / ICOF. IF PI > 1 then Accept the Project, else Reject. Please note that if PI > 1 then NPV is +. Accept/Reject Rule for IRR: IF IRR > Cost of Capital, then Accept the Project, else Reject. Three Important Points about IRR: Internal Rate of Return is the Rate of Return from the Project. It is the maximum rate upto which funds can be borrowed to finance the project. When IRR = COC then PI = 1, NPV = 0. That is when we take the IRR as the Cost of capital of the Project (for Discounting Purpose) then NPV is NIL.

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Problem No. 2 Computation of NPV for Project X ( `. Lacs) YearPBDTDepnPBTTax @ 50% PAT CFAT (PAT+DEPN) DF @15%PV 125151055200.87017.40 235152010 250.75618.90 345153015 300.65819.74 465155025 400.57222.88 565155025 400.49719.88 655154020 350.43215.12 735152010 250.3769.40 815 --- 0.3274.91 Present Value of Cash Inflows 128.23 Less: Initial Investment120.00 Net Present Value 8.22

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Problem No. 2 Computation of NPV for Project Y ( `. Lacs) Conclusion: As project Y has a higher NPV, hence it is suggested to take up Project Y. YearPBDTDepnPBTTax @ 50% PAT CFAT (PAT+DEPN) DF @15%PV 14020 10 300.87026.10 260204020 400.75630.24 380206030 500.65832.90 450203015 350.57220.02 530201055250.49712.43 620 000 0.4328.64 Present Value of Cash Inflows 130.33 Less: Initial Investment120.00 Net Present Value 10.33

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Problem No. 3 Initial investment + Working Capital = 120 + 15 = `. 135 Lakhs Additional Equipment required ( beginning of Year 3 = end of Year 2) = `. 10 Lakhs Total Cash Outflows (135 + 10 ) = `. 145 Lakhs

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Problem No. 3 Cont… Note: Depreciation = ( Original Cost – Scrap Value) / Useful Life First Equipment = `. 120 Lakhs / 8 years = Rs. 15 Lakhs p.a. Second Equipment = ( `. 10 Lakhs – ` 1 Lakhs) / 6 years = `. 1.50 Lakhs p.a. In the 8th year, there will be additional cash flows to the extent of scrap value of additional equipment `. 1 Lakhs and recovery of working capital `. 15 Lakhs

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Problem No. 3 Cont… Sl. no. ParticularsYear 1Year 2Year 3-5Year 6-8 1Sales Quantity ( Capacity x 400000) in units 80,000120,000300,000200,000 2Sales Value Rs. 100 per unit (Rs. Lacs)80.00120.00300.00200.00 3Variable Cost @ 40% of Sales32.0048.00120.0080.00 4Contribution (2-3)48.0072.00180.00120.00 5Fixed Cost Production16.00 Selling (Advertisement)30.0015.0010.004.00 Depreciation ( See note)15.00 16.50 Total Fixed Cost 61.0046.0042.5036.50 6PBT (4-5)(13.00)26.00137.5083.50 7Tax @ 50%-13.0068.7541.75 8PAT (6-7)(13.00)13.0068.7541.75 9Depreciation15.00 16.50 10 CFAT (8+9)2.0028.0085.2558.25

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Problem No. 3 Cont… Computation of NPV YearCFAT (Rs. Lacs)PVF @ 12%DCFAT (Rs. Lacs) 12.000.89291.7858 228.00-10.00 = 18.000.797214.3496 385.250.711860.6810 485.250.635554.1764 585.250.567448.3709 658.250.506629.5095 758.250.452326.3465 874.25( 58.25+15.00+1.00)0.403929.9896 TotalDiscounted Cash Inflows265.3839 Initial Investment135.0000 Net Present Value130.3939

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Problem No. 4 Sales40000 Less: Operating cost + Depn16750 Profit Before Tax 23250 Less: Tax – 30% Assumed6975 Profit After Tax16275 Net cash inflow (PAT + Depn – Loss of Commission Income)14025 In 8th year : New cash inflow after tax14,025 Add: Salvage value of machine6,000 Net cash inflow in year 8 :20,025

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Problem No. 4 Calculation of Net present value (NPV) Profitability Index = Cum. Disc CIF / ICOF = 77612/80000 =0.97 Advise: Since the net present value is negative and profitability index is < 1, the hospital should not purchase the diagnostic machine. YearCFATPV factor @ 10% Present value of cash inflows 1 to 714,0254.86768260 820,0250.4679352 77612 Less: Cash Outflows80,000 NPV-2388

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Problem No. 5 YearCFATPVF at 10%DCFATPVF at 12%DCFAT 130,000.000.909127,273.000.892926,787 240,000.000.826433,056.000.797231,888 360,000.000.751345,078.000.711842,708 430,000.000.683020,490.000.635519,065 520,000.000.620912,418.000.567411,348 Total DCFAT138,315.00131,796 Less: Initial Investment136,000.00136000 Net Present Value2,315.00(4,204)

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Problem No. 5 From the above i.e. with one positive NPV and negative NPV, IRR is estimated using the interpolation method as under:- NPV @ 10% = 2315 (Positive NPV) NPV @ 12% = 4204 (Negative NPV) Diff 2% = 6519 2315 / 6519 * 2 = 0.71% IRR (from the +ve side)= 10% + 0.71% =10.71% 4204 / 6519 * 2 = 1.21% IRR (from the –ve side) = 12% - 1.29% =10.71%

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Problem No. 6 Year012345 Initial Cost (680)---(Rs. ‘ 000)- Before tax Cash Flows -240275210180160 Tax @ 35% -8496.2573.563 After Tax cash flows -156178.75136.5117104 Tax Saving on Depn. ( Depreciation * Tc ) -42 Working Capital Released -000080 Net Cash Flow -198220.75178.5159226 PVF @ 12% 10.89290.79720.71180.63350.5674 -PV (680)176.79175.98127.06101.04128.24 -NPV 29.12 PVF @ 15% 10.86960.75610.65750.57180.4972 -PV (680)172.18166.91117.3690.92112.37 -NPV (20.26)

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Problem No. 6 Internal Rate of return IRR = 12% + (29.12/49.38) * 3% = 13.77% Discounted Payback Period Discounted Cash Flows at K = 12% considered = 176.79 + 175.98 + 127.06 + 101.04 + 12 * 99.13/128.24 = 4 years and 9.28 months Payback Period (Net Cash flows are considered) = 198 + 220.75 + 178.5 + 12 * 82.75/159 = 3 years and 6.25 months

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Problem No. 7 Calculation of Annualised CF for Machine A Annualized cash Outflow = 8,98,416 / 2.4868 = Rs. 3,61,274 YearCash OutflowDep. Factor @ 10%Dep. Factor 06,00,0000 11,20,0000.9091 1,09,092 21,20,0000.8264 99,168 31,20,0000.7513 90,156 2.4868 8,98,416

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Problem No. 7 Calculation of Annualised CF for Machine B Annualized cash Outflow = 7,12,400 / 1.7355 = Rs. 4,10,486 Conclusion: Machine ‘A’s Annualized cash out flow is lower than machine ‘B’. Therefore machine ‘A’ should be purchased. YearCash OutflowDep. Factor @ 10%Dep. Factor 04,00,0000 11,80,0000.9091 1,63,638 21,80,0000.8264 1,48,762 1.73557,12,400

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Problem No. 8 Sl.no.ProjectABCDE 1Initial Investment (Rs. in Lakhs) 1.003.000.502.001.00 2NPV0.200.350.160.250.30 3PI1.2001.1171.3201.1251.300 4Rank based on PI IIIVIIVII

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Problem No. 8 If the Projects are Divisible then If the projects are divisible, then allocation should be based on Rank. RankProjectInvestment (Rs. In Lacs) Cum. Investment (Rs. In Lacs) NPV (Rs. In Lacs) 1 C 0.50 0.16 2 E 1.001.500.30 3 A 1.002.500.20 4 D (1/4) 0.503.000.06 Total0.72

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Problem No.8 If the Projects are Indivisible then If the projects are indivisible, then various combination of investsments should be considered. Combination with maximum NPV should be chosen. OptionCombination of ProjectsTotal Investment (Rs. In Lacs) NPV (Rs. In Lacs) 1A,D3.000.45 2B3.000.35 3D,E3.000.55 4A,C,E2.500.66 5 C,D 2.50 0.41

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Problem No.1 Cost of Equity Ke = (1 / 20) * 100 + 5 = 10% Cost of Pref. Share Kp = [ 5 + (100 – 108)/10]/ [(100+108)/2] = 4.04% Cost of Debenture Kd = [10 (1 – 0.5) + (100 – 101)/10] / [ (100+101)/2] = 4.88%

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Problem No.1 COMPUTATION OF WACC – BV WEIGHTS WACC = [ 10 * 2 + 4.04*1 + 4.88*1] / 4 = 7.23% CAPITALCOSTAMOUNT IN RS.WEIGHT EQUITY 10.00 1,000,000.002 PREFERENCE 4.04 500,000.001 DEBENTURE 4.88 500,000.001

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Problem No.1 COMPUTATION OF WACC – MV WEIGHTS WACC = [ 10 * 96 + 4.04*22 + 4.88*21] / 139 = 8.28% CAPITALCOSTAMOUNT IN RS.WEIGHT EQUITY 10.00 24,00,00096 PREFERENCE 4.04 5,50,00022 DEBENTURE 4.88 5,25,00021

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Problem No.2 I = 16, t = 35% Kd = I ( 1 – t) / NP * 100 % (a) If issued at par: Kd = 16(.65) / 100 = 10.4% (b) If issued at 10% Discount Kd = 16(.65) / 90 = 11.56% (c) If issued at 10% Premium Kd = 16(.65) / 110 = 9.45%

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Problem No.3 D 0 = 2; G = 10%, D 1 = 2*(1.10) = 2.20 P 0 = 40 Ke = (2.2 / 40) * 100% + 5% = 15.50% (ii) Ke = 15.50%, D 0 = 2, G = 11%, then D1 = 2 * 1.11 = 2.22 P 0 = D1 / (Ke – g) = 2.22 / 4.5% = Rs.49.33 (iii) Ke = 16%, G – 10%, D = 2, then P = ? P = 2 / (16% - 10%) = Rs.33.33

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Let the Equity Capital be 10x Debt Funds = 6x Total Capital Employed = 16x Given ROCE = 20%, Hence EBIT = 3.20x Less: Interest 6x * 10%= 0.60x Profit Before Tax= 2.60x Less: Tax 40%= 1.04x Profit after tax= 1.56x Equity Capital = 10x Return on Equity = 1.56x / 10x = 15.60% Problem No. 1

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Problem No. 2 Net Sales: Rs. 30 crores EBIT Rs. 3.6 crores @ 12% on sales ROI = EBIT Capital Employed = {3.6 (10+2+6) 100} = 20% 2. Degree of Financial Leverage= EBIT / EBIT- Interest = {3.6 (3.6-0.9)} = 1.3333 Degree of Combined Leverage= DFL DOL 3 = 1.3333 DOL DOL= 3 1.3333 Degree of Operating Leverage = 2.25

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Rs.( In Crores) EBIT3.6 Add: Interest on Debt0.9 EBT2.7 Less: Tax @ 40%1.08 EAT1.62 Less: Preference dividend0.26 Earnings available for Equity Shareholders1.36 Problem No. 2 ROE = 1.36 / 10 = 13.6%

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Problem No. 3 (i) Financial leverage: Combined Leverage= Operating Leverage (OL) x Financial Leverage (FL) 2.8 = 1.4 x FL FL = 2 Financial Leverage = 2

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Sales = 30,00,000 Less: Variable Cost = 22,86,000 Contribution = 7,14,000 Less: Fixed Cost = 2,04,000 EBIT = 5,10,000 Less: Interest = 2,55,000 EBT =2,55,000 Less: Tax = 76,500 EAT = 1,78,500 PV Ratio = 23.8% EPS = 1,78,500 / 170000 = Rs.1.05 Problem No.3 OL = 1.40 C / C – 204000 = 1.40 C = 714000

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Problem No. 3 (iii)

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To Find, Sales Value at which EBIT = NIL Contribution = EBIT + Interest + Fixed Cost = 2.55+2.04 = 4.59 Sales = Contribution / PVR = 4.59/23.8% = Rs.19.29 Lacs Problem No.3

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SALES LESS: VARIABLE COST CONTRIBUTION LESS: FIXED COST EBIT LESS: INTEREST EBT LESS: TAX EAT Problem No.4 COMPANY A 91000 56000 35000 20000 15000 12000 3000 900 2100 COMPANY B 105000 63000 42000 31500 10500 9000 1500 450 1050

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NET INCOME APPROACH NET OPERATING APPROACH MODIGLIANI – MILLER APPROACH TRADITIONAL APPROACH

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CAPITAL STRUCTURE IS NOT RELEVANT TO THE VALUE OF THE FIRM S = V - D V = VALUE OF THE FIRM S = VALUE OF EQUITY D = VALUE OF DEBT

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CAPITAL STRUCTURE IS RELEVANT TO THE VALUE OF THE FIRM V = S + D V = VALUE OF THE FIRM S = VALUE OF EQUITY D = VALUE OF DEBT

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NOI / EBIT5,00,000 Less: Interest on Deb 10% on Rs.15 Lacs1,50,000 Earnings available to ESH3,50,000 Overall cost of capital15% Value of the Firm = 500000 / 0.1533,33,333 Market Value of Debt15,00,000 Total Value of the Firm (V = S + D)18,33,333 Cost of Equity = 350000 / 18,33,33319.09% Problem No. 5

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NOI / EBIT5,00,000 Less: Interest on Deb 10% on Rs.20 Lacs2,00,000 Earnings available to ESH3,00,000 Equity Capitalisation Rate16% Market Value of Equity (350000/16%)18,75,000 Market Value of Debt20,00,000 Total Value of the Firm (V = S + D)38,75,000 Overall Cost of Capital = EBIT / Value of Firm = 500000/3875000 12.90% Problem No. 6

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Problem No. 7 EBIT – EPS INDIFF. (PLAN 1 & PLAN 2) [(E-0)*.6 – 0] / 325000 = [(E-125000)*.6 – 0] / 156250 SOLVING THIS E = 250000/=

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Problem No. 7 EBIT – EPS INDIFF. (PLAN 1 & PLAN 3) [(E-0)*.6 – 0] / 325000 = [(E-0)*.6 – 125000] / 156250 SOLVING THIS E = 416,667/=

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Problem No. 8 PLAN 1: NO. EQUITY SHARES = 60000 INT. ON DEB = 48000 PLAN 2: NO. EQUITY SHARES = 40000 INT. ON DEB = 48000 PREF. DIVIDEND = RS.28000 EBIT – EPS INDIFF. (PLAN 1 & PLAN 2) [(E-48000)*.65 – 0] / 60000 = [(E-48000)*.65 – 28000] / 40000 SOLVING THIS E = 1,77,231/=

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Problem No. 9

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Indifference Point Between Plan P & Q [(EBIT – I 1 )(1 – t) – Preference Dividend] / N1 = [(EBIT – I 2 ) (1 – t) – Pref. Dividend] / N2 (EBIT – NIL) (1 – 0.50) –NIL/ 2, 00,000 = (EBIT – 2, 00,000) (1 – 0.50) – NIL / 1, 00,000 0.50 EBIT / 2= 0.50 EBIT – 1, 00,000 0.50 EBIT= EBIT – 2, 00,000 EBIT= 2, 00,000 / 0.50 EBIT= Rs. 4, 00,000

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Problem No. 9 Between Plan P & R (EBIT – NIL) (1 – 0.50) – NIL / 2, 00,000 = (EBIT – NIL) (1 – 0.50) – 2, 00,000 / 1, 00,000 0.50 EBIT / 2= 0.50 EBIT – 2, 00,000 0.50 EBIT= EBIT – 4, 00,000 EBIT= 4, 00,000 / 0.50 EBIT= Rs. 8, 00,000

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Problem No. 9 Between Plan Q & R (EBIT –2, 00,000)(1 – 0.50) –NIL/1, 00,000 = (EBIT–NIL) (1 – 0.50) – 2, 00,000/ 1, 00,000 0.50EBIT – 1, 00,000 = 0.50EBIT – 2, 00,000 Indifference point is not possible for this plan. Plan Q is best among others because EPS is Maximum in this case.

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Working Capital Days =Day CA - Day CL Days Raw Material -50000 *360=30 600000 Work in Progress -30000 *360=22 500000 Finished goods -40000 *360=18 800000 Debtors -45 115 Less: Creditors Period -30 No. of Cycles 85 No. of Operating Cycles = 360 /85= 4.24 times

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Cash Cost Current AssetsAmount (inRs.) Raw materials ( 9,00,000 * 1/12 ) 75,000 Debtors ( Refer WN ) 4,90,000 Finished goods ( Refer WN ) 2,35,000 Cash 1,00,000 Sales promotion expenses ( 120000 * 1/4 ) 30,000 CA 9,30,000 Less: Current Liabilities Creditors ( 9,00,000 * 2/12 ) 1,50,000 Wages ( 7,20,000 * 1/12 ) 60,000 Mfg. Overheads 80,000 Admn. Overheads ( 2,40,000 * 1/12 ) 20,000 CL 3,10,000 Working Capital ( CA - CL ) 6,20,000 Add:Safety Margin 20% 1,24,000 Working Capital Requirement 7,44,000

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WN – 1 Debtors (Cash Cost) Sales = 36,00,000 Less: GP = 9,00,000 Fact. Cost = 27,00,000 Less: Mat, Lab, Manu. Exp Depn = Rs.1,20,000 Fact. Cash Cost = 27,00,000 – 1,20,000 = 25,80,000 Add: Admn. Exp = 2,40,000 Add: Selling Exp = 1,20,000 Cash Cost of Sales = 29,40,000 Debtors = 29,40,000 * 60/360 = 4,90,000

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WN – 2 Finished Goods (Cash Cost) Fact. Cash Cost = 27,00,000 – 1,20,000 = 25,80,000 Add: Admn. Exp = 2,40,000 Cash Production = 28,20,000 Finished Goods = 28,20,000 * 30/360 = 2,35,000

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Current Delay in Invoicing: 3*20% + 4*10% + 5*40% + 6*30% = 4.8 Days Delay on Account of Outsourcing: 0*40% + 1 * 40% + 3 * 20% = 1.0 Day Saving in Delay by outsourcing = 3.8 Days Debtors Equivalent = 730 * 3.8 / 365 = 7.6 Lacs Saving in ROI @ 20% = 7.6 * 20% = ` 1,52,000 Saving in Postage = 4000 * 12 = ` 48,000 Total Saving on Account of O/s = ` 2,00,000

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Current Collection Period: 36 Days Collection Period Account of Outsourcing: 30 Saving in Colln Period by O/s = 6 Days Debtors Equivalent = 730 * 6 / 365 = 12 Lacs Saving in ROI @ 20% = 12 * 20% = `.2,40,000

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ParticularsCost ` Benefit ` Net Benefit ` Remarks Invoicing2,00,000 0 Indifferent Monitoring Collections 2,50,0002,40,000(10,000) Reject Both4,00,000 (after discount of Rs.50000) 4,40,00040,000 Accept

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