SOLUTIONS TO ASSIGNMENT PROBLEMS. Problem No.1 10,000 5,000 15,000 20,000. Problem No.2. Problem No.3

Size: px

Start display at page:

Download "SOLUTIONS TO ASSIGNMENT PROBLEMS. Problem No.1 10,000 5,000 15,000 20,000. Problem No.2. Problem No.3"

Gerald Mosley
5 years ago
Views:

1 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

2 Ph: /6 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

3 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 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) b. Contribution per Unit ( x 4%) (Rs.) Rs.48 Rs.48 Rs.48 Rs.48 Rs c. Total contribution (a x b) d. Fixed Cost e. PBDT (cd) f. Depreciation (WN ) IPCC_34.5e_F.M_ Capital Budgeting_Assignment Solutions 3

4 Ph: /6 g. PBT / (Loss) (e f) h. (5.35) Brought forward of Loss (5.35) i. Profit after set off (g h) (5.35) j. 3% (i x 3%) k. PAT (5.35) l. CFAT (k + f) m. % n. Present Value (l x m) P.V of Operating Cash Inflows 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 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 Lakhs WN: Calculation of Depreciation per annum Depreciation p.a. cost scrap Life Depreciation on Original Equipment Depreciation on Additional Equipment Problem No.7 (Rs. In Lakhs) Step : Calculation of Present Value of Cash Outflows Amount Cost of windmill Cost of land st Less: Subsidy from Govt. receivable at the end of year Present value thereof [5 x PVF (5%, y)] 5 x 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 IPCC_34.5e_F.M_ Capital Budgeting Assignment Solutions 4

5 MASTER MINDS No. for CA/CWA & MEC/CEC b. Cost per unit (in Rs.) c. Savings in Electricity Cost (a x b) (in Lakhs) d. Maintenance Cost e. Depreciation f. (5) g. Tax (Tax (5) 5% PBT (cde) (Loss) h. PAT / (Loss) (fg) (5) i. CFAT (h + e) 75 j. 5%.87 k. Present Value (i x j) 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 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 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 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 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

6 Ph: /6 Calculation of Cash Inflows: Years Sales in units Rs. 6 p.u. Fixed cost Advertisement Depreciation Profit /(loss) 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 % Rs.,,.893,78,6 8,,.797,3,6 3 85,5,.7 6,69,8 4 85,5, ,,9 5 85,5, ,33, ,5,.57 9,53, ,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

7 No. for CA/CWA & MEC/CEC MASTER MINDS IPCC_34.5e_F.M_ Capital Budgeting_Assignment Solutions 7

8 Ph: /6 IPCC_34.5e_F.M_ Capital Budgeting Assignment Solutions 8

9 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

10 Ph: / ,5 4,5 4,5 7, ,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,,, 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,, 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 %: (iii).486 6, Machines Purchase cost (Rs.): (i) Life of machines (years) ,44 [(ii) (iii)],4, [(ii) (iv)],49,44,4,,,338 [(vi) (iii)],7,637 [(vi) (iv)] Cumulative present value factor for %: (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 correspondingly discounting rates % and 3% respectively. % 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%.

11 MASTER MINDS No. for CA/CWA & MEC/CEC NPV3% (,,) 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

12 Ph: /6 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: 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

13 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. % Machine X 6,5 x 3.79 Rs.,33,85 Machine Y 8, x Rs.3,57,8 P.V index present value of cash inflow Investment Machine X,33, ,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 cost of capital where as IRR assumes that the interim cash inflows are 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

14 Ph: /6 IPCC_34.5e_F.M_ Capital Budgeting Assignment Solutions 4

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.

15 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 5%, cumulative present value of cash inflows for 5 years is Hence, Total Cash inflows for 5 years for the Project is 96, x Rs. 3,,888 IPCC_34.5e_F.M_ Capital Budgeting_Assignment Solutions 5

16 Ph: /6 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 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) Rs.53.5 NPVB is calculated as follows: Year Cash flow (Rs.) (5,) 7 8 9,,,,3,4,5,6 % discount factor Present value (Rs.) (5,) IPCC_34.5e_F.M_ Capital Budgeting Assignment Solutions 6

17 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/ From tables, IRR A per cent. IRRB Year Cash flow (Rs.) % discount factor Present value (Rs.) (5,) 7 8 9,,,,3,4,5, (5,) ,59 Interpolating: IRRB % discount factor Present value (Rs.) (5,) (776),59x per cent (,59 776) IRRC Year Cash flow (Rs.) 3 4 (5,),,,, 5% discount factor Present value (Rs.) (5,),74,5, % discount factor Present value (Rs.) (5,),694,436, x 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

18 Ph: /6 (b) Summary of Results Project A Payback (years) ARR (%) IRR (%) NPV (Rs.) B ,59 C 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 % 6,49,94 5,5, 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

19 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 % NPV PV (5,) (9,9) 44,766 9,388 (4,936) Option : Purchase machinery and replace the part at the end of Year Year Cost of machine Net cash inflows Cost of replacement Operating Cash inflows Salvage value Cash flow (5,) 8, (5,4) 8, 9, % NPV PV (5,) 44,766 (,7),94 6, 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 , 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

20 Ph: /6 THE END IPCC_34.5e_F.M_ Capital Budgeting Assignment Solutions

SOLUTIONS TO ASSIGNMENT PROBLEMS. Problem No.1

W.N.-1: Calculation of depreciation per annum Depreciation p.a. = SOLUTIONS TO ASSIGNMENT PROBLEMS Cost -Scrap Value Life W.N.-2: Calculation of PAT p.a. Problem No.1 80,000 5 10,000 = Rs.14,000 p.a. 2.