MASTER MINDS No. for CA/CWA & MEC/CEC. CAPITAL BUDGETING SOLUTIONS TO ASSIGNMENT PROBLEMS Problem No. Calculation of ARR for machine A and B: Machine A Step : Average Profit After Tax 5,, 5,, 5, Total Profit No. of Years 5,, 5,, 5, 5 5 5, Step : Average investment in the project (Initial Investment Salvage Value) + Salvage Value + Additional Working Capital Machine B 5,. (5,,) +, (5,,) + + 4, 3, + 4, 4,. Step 3: Average PAT ARR Average Investment in the Pr oject 5, 5% 3, 5, 37.5% 4, Problem No. Problem No.3 Payback reciprocal 4, X %, IPCC_34.5e_F.M_ Capital Budgeting_Assignment Solutions
Ph: 9885 55/6 www.gntmasterminds.com The above payback reciprocal provides a reasonable approximation of the internal rate of return, i.e. 9%. Problem No.4 Problem No.5 IPCC_34.5e_F.M_ Capital Budgeting Assignment Solutions
MASTER MINDS No. for CA/CWA & MEC/CEC Problem No.6 Step : P.V. of Cash outflows (Rs. in. Lakhs) Amount (Rs.) Amount (Rs.) Cost of New Equipment 75 Less: Subsidy from State Govt. 5 Add: Investment in W.C Add: Investment in additional equipment.5 P.V. thereof.5 x PVF (%, 3 yr).5 x.7 8.9 P.V of Cash Outflows 78.9 Step : P.V of Operating Cash inflows Given that selling price per unit Variable Cost ratio Therefore, Contribution ratio Contribution per unit Rs. 6% Variable Cost ratio 6% 4% x 4% Rs.48 Year Year Year 3 Year 45 Year 68 a. Sales Volume (Lakhs of Units).7.8.6.7.8 b. Contribution per Unit ( x 4%) (Rs.) Rs.48 Rs.48 Rs.48 Rs.48 Rs.48 34.56 5.84 4.8 9.6 86.4 c. Total contribution (a x b) d. Fixed Cost 8 8 8 8 8 e. PBDT (cd) 6.56 33.84 6.8.6 68.4 f. Depreciation (WN ).875.875.875 4.5 4.5 IPCC_34.5e_F.M_ Capital Budgeting_Assignment Solutions 3
Ph: 9885 55/6 g. PBT / (Loss) (e f) h. www.gntmasterminds.com (5.35).965 84.95 87.475 44.75 Brought forward of Loss (5.35) i. Profit after set off (g h) (5.35) 6.65 84.95 87.475 44.75 j. Tax @ 3% (i x 3%).995 5.4775 6.45 3.85 k. PAT (5.35) 4.655 59.4475 6.35 3.995 l. CFAT (k + f) 6.56 6.53 8.35 85.3575 55.75 m. PVF @ %.89.797.7.5.36 n. Present Value (l x m) 4.77.44 57.8.64 75. P.V of Operating Cash Inflows 7.384 Lakhs Step 3: P.V. of Terminal Cash inflows Amount (Lakhs) th GSP / NSP on sale of initial equipment at the end of 8 year th GSP / NSP on sale of additional equipment at the end of 8 year.5 Add: Recovery of Working Capital Terminal Cash Inflows.5 Present value there of.5 x PVF (%, 8).5 x.44 8.585 Lakhs Step 4: Calculation of NPV NPV P.V. of Cash Inflows P.V of Cash Outflows P.V of Operating Cash Inflows + P.V of Terminal Cash Inflows P.V of Cash Outflows Step + Step 3 Step 7.384 + 8.585 78.9.69 Lakhs WN: Calculation of Depreciation per annum Depreciation p.a. cost scrap Life Depreciation on Original Equipment 75 8.875 Depreciation on Additional Equipment.5.5 5.5 Problem No.7 (Rs. In Lakhs) Step : Calculation of Present Value of Cash Outflows Amount Cost of windmill Cost of land 3. 5. 35. st Less: Subsidy from Govt. receivable at the end of year Present value thereof [5 x PVF (5%, y)] 5 x.87 5 3.5 Present Value of Net Cash Outflows 3.95 Step : Calculation of Present Value of Operating Cash Inflows a. Lakhs of generated (Note) units Y Y Y3 Y4 Y5 Y6 Y7 Y8 Y9 Y 4 4 4 4 4 4 4 4 4 4 IPCC_34.5e_F.M_ Capital Budgeting Assignment Solutions 4
MASTER MINDS No. for CA/CWA & MEC/CEC b. Cost per unit (in Rs.).5.5.75 3. 3.5 3.5 3.75 4.5 4.75 5.5 c. Savings in Electricity Cost (a x b) (in Lakhs) 54 6 66 7 78 84 9 4 6 d. Maintenance Cost 4 6 8 4 6 8 3 e. Depreciation f. (5) 54 58 6 66 7 74 84 94 4 g. Tax (Tax Shield) @ (5) 5% PBT (cde) (Loss) 7 9 3 33 35 37 4 47 5 h. PAT / (Loss) (fg) (5) 7 9 3 33 35 37 4 47 5 7 9 3 33 35 37 4 47 5 i. CFAT (h + e) 75 j. PVF @ 5%.87 k. Present Value (i x j).756.658.57.497.43.376.37.84.47 5.5.4 9.8 7.73 6.4 5. 3.9 3.73 3.35.84 Therefore, Present Value of Operating Cash Inflows 94.8 Lakhs Step 3: Calculation of Present Value of Terminal Cash Inflows (At the end of the project) Land Wind Mill a. Gross Sale Proceeds 6 b. WDV / Book Value 5 c. Capital Gains (a b) 45 d. Capital Gains tax @ 5% (Note 3) e. Net Sale Proceeds (NSP) (a d) 6 Terminal Cash Inflows 6 Lakhs Net Sale Proceeds on Sale of Assets 6 Lakhs Present value there of 6 x PVF (5%, y) 6 x.47 4.8 Lakhs Step 4: Calculation of NPV NPV PV of cash inflows PV of cash outflows PV of Operating Cash Inflows + PV of Terminal Cash Inflows PV of cash outflows. 94.8 + 4.8 3.95 7.69 Lakhs Conclusion: Since NPV is positive it is beneficial for the company to accept the proposal. Note : No. of units of electricity generated 5,, Less: Electricity freely supplied to State Govt. @ 4%,, No. of units of Electricity that can be utilised 4,, units Note : It is given in the problem that cost of windmill has to be written off % in the first year for income tax purposes. Note 3: It is given that tax on capital profit should be ignored. Therefore, Gross Sale Proceeds will be equal to Net Sale Proceeds. Assumptions: Cash flows are assumed to accrue at the end of each year. Interim cash inflows at the end of each year are assumed to be reinvested at the rate of cost of capital. Cash flows given in the problem are assumed to be certain. Problem No.8 Computation of initial cash outlay Equipment Cost () Working Capital () (Rs. in lakhs) 5 35 IPCC_34.5e_F.M_ Capital Budgeting_Assignment Solutions 5
Ph: 9885 55/6 www.gntmasterminds.com Calculation of Cash Inflows: Years Sales in units Contribution @ Rs. 6 p.u. Fixed cost Advertisement Depreciation Profit /(loss) Tax @ 5% Profit/(Loss) after tax Add: Depreciation Cash inflow 8, (Rs.) 48,, 6,, 3,, 5,, (3,,) NIL (3,,) 5,,,,,, (Rs.) 7,, 6,, 5,, 5,, 6,, 3,, 3,, 5,, 8,, 3 5 3,, (Rs.),8,, 6,,,, 6,5,,37,5, 68,75, 68,75, 6,5, 85,5, 6 8,, (Rs.),,, 6,, 4,, 6,5, 83,5, 4,75, 4,75, 6,5, 58,5, Computation of PV of CIF Year CIF (Rs.) PV Factor @ % Rs.,,.893,78,6 8,,.797,3,6 3 85,5,.7 6,69,8 4 85,5,.636 54,,9 5 85,5,.567 48,33,675 6 58,5,.57 9,53,75 7 58,5,.45 6,3,9 8 58,5,.44 9,99,7 WC 5,, SV,,,73,,45 PV of COF Additional investment,35,, Rs.,,.797 7,97, NPV,4,97,,3,4,45 Recommendation: Accept the project in view of positive NPV. Problem No.9 IPCC_34.5e_F.M_ Capital Budgeting Assignment Solutions 6
No. for CA/CWA & MEC/CEC MASTER MINDS IPCC_34.5e_F.M_ Capital Budgeting_Assignment Solutions 7
Ph: 9885 55/6 www.gntmasterminds.com IPCC_34.5e_F.M_ Capital Budgeting Assignment Solutions 8
MASTER MINDS No. for CA/CWA & MEC/CEC 693 Problem No. Calculation of Net Cash flows Contribution (3..75) 5, Rs. 6,5 Fixed costs 4, (,5, 3,)/5 Rs., Year Capital (Rs.) Contribution (Rs.) Fixed costs (Rs.) (,,) (5,) 6,5 (,) 6,5 (,) 3 6,5 (,) 4 6,5 (,) 5 3, 6,5 (,) Calculation of Net Present Value Year Net cash flow (Rs.) (,,) 6,5 % discount factor..99 Adverts (Rs.) (,) (5,) Net cash flow (Rs.) (,,) 6,5 6,5 4,5 4,5 7,5 Present value (Rs.) (,,) 5,99 IPCC_34.5e_F.M_ Capital Budgeting_Assignment Solutions 9
Ph: 9885 55/6 3 4 5 www.gntmasterminds.com 6,5 4,5 4,5 7,5.86 75.683.6,889 3,67 8,345 44,4 3,7 The net present value of the project is Rs. 3,7. Problem No. Step : Calculation of Present value of Net Cash outflows. Machine A: Year 3 Purchasing Cost Running Cost p.a. Cash flow 7,5,,, PVF @ 4%.533 PV 7,5, 5,6,6 (PVAF@9%, 3y) PV of Net cash outflows,56,6 Machine B: Year 3 Purchasing Cost Running Cost p.a. Cash flow 5,, 3,, PVF @ 4% PV 6,,.759 5,7,73 (PVAF@9%, y) PV of Net cash outflows,7,73 Step : Calculation of Equivalent Present Value of Annual Net Cash outflows.. Machine A,56,6,56,6 PVAF(9%,3y ).533 4,96,9. MachineB,7,73,7,73 PVAF(9%,y ).759 5,84,36 Conclusion: Since Equivalent Present Value of Net Cash Outflow is less, it is beneficial to purchase Machine A. Problem No. Statement showing the Evaluation of Two Machines A B,5, 3,, Running cost of machine per year (Rs.): (ii) 4, Cumulative present value factor for 3 years @ %: (iii).486 6, Machines Purchase cost (Rs.): (i) Life of machines (years).735 99,44 [(ii) (iii)],4, [(ii) (iv)],49,44,4,,,338 [(vi) (iii)],7,637 [(vi) (iv)] Cumulative present value factor for years @ %: (iv) Present value of running cost of machines (Rs.): (v) Cash outflow of machines (Rs.): (vi)(i) +(v) Equivalent present value of annual cash outflow Decision: Company X should buy machine A since its equivalent cash outflow is less than machine B. Problem No.3 First of all we shall find an approximation of the payback period:,, 4 5, Now we shall this figure in the PVAF table corresponding to 6 year row. The value 4 lies between values 4. and 3.998 correspondingly discounting rates % and 3% respectively. NPV @ % NPV% (,,) + 4. x 5,,775 IPCC_34.5e_F.M_ Capital Budgeting Assignment Solutions
MASTER MINDS No. for CA/CWA & MEC/CEC NPV3% (,,) + 3.998 x 5, (5) The internal rate of return is, thus, more than % but less than 3%. The exact rate can be obtained by interpolation:,775x X(3% %) IRR %,775 (5) IRR.98% Problem No.4 Problem No.5 IPCC_34.5e_F.M_ Capital Budgeting_Assignment Solutions
Ph: 9885 55/6 www.gntmasterminds.com Problem No.6 Working notes: Cost Scrap Value,5, Rs.3, 5 Life Cost Scrap Value,4, Depreciation on machine. Y Rs.4, 6 Life Depreciation on machine. X Annual savings: Wages Scrap Total savings(a) Annual estimated cash cost: Indirect material Supervision Maintenance Total cash cost(b) Annual cash savings(ab) Less: depreciation Annual savings before tax Less: tax @ 3 % Annual profit after tax Add: depreciation Annual cash in flows Machine X Machine Y 9,,,,,, 5,,35, 6,, 7, 5, 8, 6,, 35, 75, 3,,, 4, 45, 3,5 6, 8, 3,5 3, 4, 4, 6,5 8, Evaluation of alternatives: (i) ARR average annual net savings Average investment 3,5 x 4% Machine X 75, 4, x 35% Machine Y,, Decision: Machine X is better. IPCC_34.5e_F.M_ Capital Budgeting Assignment Solutions
MASTER MINDS No. for CA/CWA & MEC/CEC [Note: ARR can be computed alternatively taking initial investment as the basis for computation (ARR Average Annual Net Income/Initial Investment). The value of ARR for Machines X and Y would then change accordingly as % and 7.5%respectively] (ii) Present Value Index Method Present Value of Cash Inflow Annual Cash Inflow x P.V. Factor @ % Machine X 6,5 x 3.79 Rs.,33,85 Machine Y 8, x 4.354 Rs.3,57,8 P.V index present value of cash inflow Investment Machine X,33,85.5539,5, Machine Y 3,57,8.4876,4, Decision: Machine X is better. Problem No.7 NPV IRR Project C 4,39 (I) 6.5% () Project D 3,83 (II) 37.6% () From the above figures, NPV supports Project C and IRR supports Project D. Therefore there is a conflict in ranking of projects between NPV & IRR. Reasons for conflict in rankings:. The projects are mutually exclusive. Cash flow disparity/ Time disparity 3. NPV assumes that interim cash inflows are reinvested @ cost of capital where as IRR assumes that the interim cash inflows are reinvested @ IRR Decision: The objective of Financial Management is to maximize shareholders wealth. NPV ranks the proposals in accordance with this objective. Therefore it is beneficial to select the project being preferred by NPV i.e., Project C. Problem No. 8 IPCC_34.5e_F.M_ Capital Budgeting_Assignment Solutions 3
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MASTER MINDS No. for CA/CWA & MEC/CEC Problem No.9 Problem No. (i) Cost of Project At 5% internal rate of return (IRR), the sum of total cash inflows cost of the project i.e initial cash outlay Annual cost savings Rs. 96, Useful life 5 years Considering the discount factor table @ 5%, cumulative present value of cash inflows for 5 years is 3.353 Hence, Total Cash inflows for 5 years for the Project is 96, x 3.353 Rs. 3,,888 IPCC_34.5e_F.M_ Capital Budgeting_Assignment Solutions 5
Ph: 9885 55/6 www.gntmasterminds.com Hence, Cost of the Project Rs. 3,,888 (ii) Payback Period Payback period Cost of the Project / Annual Cost Savings Rs. 3,,888 / 96, Payback Period 3.353 years (iii) Net Present Value (NPV) NPV Sum of Present Values of Cash inflows Cost of the Project Rs. 3,37,98.4 3,,888 Rs. 6,94.4 Net Present Value Rs. 6,94.4 (iv) Cost of Capital Profitability index Sum of Discounted Cash inflows / Cost of the Project.5 Sum of Discounted Cash inflows / 3,,888 Sum of Discounted Cash inflows Rs. 3,37,98.4 Since, Annual Cost Saving Rs. 96, Hence, cumulative discount factor for 5 years Rs. 3,37,98.4 / 96, From the discount factor table, at discount rate of 3%, the cumulative discount factor for 5 years is 3.5 Hence, Cost of Capital 3% Problem No. (a) Payback Period Method: A 5 + (5/9) 5.5 years B 5 + (5/) 5.4 years C + (/).5 years Net Present Value: NPVA ( 5) + (9 6.45) (5) + 553.5 Rs.53.5 NPVB is calculated as follows: Year 3 4 5 6 7 8 9 Cash flow (Rs.) (5,) 7 8 9,,,,3,4,5,6 % discount factor..99.86.75.683.6.564.53.467.44.386 Present value (Rs.) (5,) 636 66 676 683 683 677 667 654 636 68 59 IPCC_34.5e_F.M_ Capital Budgeting Assignment Solutions 6
MASTER MINDS No. for CA/CWA & MEC/CEC NPVC (5) + (.487) + (.683) Rs.657 Internal Rate of Return If NPVA, present value factor of IRR over years 5/9 5.556 From tables, IRR A per cent. IRRB Year Cash flow (Rs.) % discount factor Present value (Rs.) 3 4 5 6 7 8 9 (5,) 7 8 9,,,,3,4,5,6..99.86.75.683.6.564.53.467.44.386 (5,) 636 66 676 683 683 677 667 654 636 68,59 Interpolating: IRRB % discount factor..833.694.579.48.4.335.79.33.94.6 Present value (Rs.) (5,) 583 555 5 48 44 4 363 36 9 59 (776),59x +6.7 6.7 per cent (,59 776) IRRC Year Cash flow (Rs.) 3 4 (5,),,,, 5% discount factor..87.756.658.57 Present value (Rs.) (5,),74,5,36 57 4 8% discount factor..847.78.69.56 Present value (Rs.) (5,),694,436,8 56 36 4 x3 5.5 6.5 per cent (4 36) Accounting Rate of Return 5, ARRA: Average capital employed Rs.,5 (9, 5, ) Average accounting profit Rs.4 ( 4x) ARRA 6 per cent,5 (,5 5, ) ARRB: Average accounting profit Rs.65 (65 x) ARRB 6 per cent,5 (7, 5, ) ARRC Average accounting profit Rs.5 4 (5 x) ARRC per cent,5 Interpolating: IRRC 5 IPCC_34.5e_F.M_ Capital Budgeting_Assignment Solutions 7
Ph: 9885 55/6 www.gntmasterminds.com (b) Summary of Results Project A 5.5 6.4 53.5 Payback (years) ARR (%) IRR (%) NPV (Rs.) B 5.4 6 6.7,59 C.5 6.5 657 Comparison of Rankings Method 3 Payback C B A ARR B C A IRR B C A NPV B C A PROBLEM NO. Although from NPV point of view Project A appears to be better but from IRR point of view Project B appears to be better. Since, both projects have unequal lives selection on the basis of these two methods shall not be proper. In such situation we shall use any of the following method: (i) Replacement Chain (Common Life) Method: Since the life of the Project A is 6 years and Project B is 3 years to equalize lives we can have second opportunity of investing in project B after one time investing. The position of cash flows in such situation shall be as follows: NPV of extended life of 6 years of Project B shall be 8,8,43 and IRR of 5.%. Accordingly, with extended life NPV of Project B it appears to be more attractive. (ii) Equivalent Annualized Criterion: Method discussed above has one drawback when we have to compare two projects one has a life of 3 years and other has 5 years. In such case the above method shall require analysis of a period of 5 years i.e. common multiple of these two values. The simple solution to this problem is use of Equivalent Annualised Criterion involving following steps: a) Compute NPV using the WACC or discounting rate. b) Compute Present Value Annuity Factor (PVAF) of discounting factor used above for the period of each project. c) Divide NPV computed under step (a) by PVAF as computed under step (b) and compare the values. Accordingly, for proposal under consideration: Project A Project B NPV @ % 6,49,94 5,5,488 PVAF @% 4..4 Equivalent Annualized Criterion,57,854,4,68 Thus, Project B should be selected. PROBLEM NO. 3 Company has options Option Purchase Machinery and Service the Part at the end of year Option Purchase Machinery and replace the Part at the end of year IPCC_34.5e_F.M_ Capital Budgeting Assignment Solutions 8
MASTER MINDS No. for CA/CWA & MEC/CEC Option : Purchase the machinery and service the part at the end of year. Year 3 3 Cost of machine Cost of service Operating Net cash inflows Salvage value Cash flow (5,) (,) 8,,5 PVF @ %.99.487.75 NPV PV (5,) (9,9) 44,766 9,388 (4,936) Option : Purchase machinery and replace the part at the end of Year Year 3 4 4 Cost of machine Net cash inflows Cost of replacement Operating Cash inflows Salvage value Cash flow (5,) 8, (5,4) 8, 9, PVF @ %.487.86.683.683 NPV PV (5,) 44,766 (,7),94 6,47 487 Conclusion: Since NPV is positive in case of option, it is beneficial for the company to purchase the machinery and replace the part at the end of year. If the Supplier gives a discount of Rs. 5,/In such a case revised NPV will be as follows: Option : NPV (4,936) + 5, + 64 Option : NPV 487 + 5, 5,487 Conclusion: Since supplier is providing discount for both the options decision making will remain same. PROBLEM NO. 4 IPCC_34.5e_F.M_ Capital Budgeting_Assignment Solutions 9
Ph: 9885 55/6 www.gntmasterminds.com THE END IPCC_34.5e_F.M_ Capital Budgeting Assignment Solutions