INDIAN ACADEMY SCHOOL OF MANAGEMENT STUDIES HENNUR CROSS, KALYAN NAGAR POST, BANAGLORE 1. ABC Limited is evaluating two proposals A1 and A2, both having cash flows of Rs. 30,000 each. However, these alternatives may result in different cash inflows depending upon different economic conditions, i.e., Good, Average and Bad. The following information is available. Particulars Alternati ve 1 10 years Alternati ve 2 15 years Economic Life Cash inflows : (Annual) Good Economic 8,000 6,000 condition Average Economic 6,000 5,500 condition Poor Economic 4,500 4,500 condition Evaluate the proposals and advise the firm given that the minimum required rate of return of the firm is 10%. 2 The following forecasts are made about a proposal which is being evaluated by a firm. Initial cash outlay = Rs. 12,000 Life = 4 years Cash inflows = Rs. 4,500 (annual) Cost of capital = 14% Present Value Annuity Factor for 4 years at 14% = 2.9137 Present Value Annuity Factor for 3 years at 14% = 2.3216 Analyse the sensitivity of different variables with respect to NPV. 3.X Limited has to decide between rental of two types of machine manufacturing the same product. Machine A, an expensive economy model, rents for Rs. 1000 per month, but the variable production cost is Rs. 0.25 per unit. Machine B rents for Rs. 3,000 per month, but the variable production cost is only Rs 0.10 per unit. Monthly demand varies between 10,000 and 19,000 units to the following probabilities. Demand Probabili (Units) ties 10,000 0.12 12,000 0.17 15,000 0.41 17,000 0.24 19,000 0.06 Make a comparison of the two machines. Which machine has to be rented ? If the demand is definitely known to be 10,000 units, would the decision reverse ? 4.A company considering the purchase of a new machine for Rs. 3,50,000. It feels quite confident that it can sell the goods produced by the machine so as to yield an annual cash surplus of Rs. 1,00,000. There is however, some uncertainty as to the machine’s life. A recently published Trade Association Survey shows that members of the Association have between then owned 250 of these machines and have found the lives of the machines vary as under : Number of years of Number of machines having machine life given life 3 20 4 50 5 100 6 70 7 10 Assuming a discount rate of 10%, the Net Present Value for each different machine life is as follows: Machine life Net Present (Years) Value (Rs) 3 -1,01,000 4 -33,000 5 29,000 6 86,000 7 1,37,000 You are required to advise whether the Company should purchase a new machine or not. 5. A company is considering two mutually exclusive projects X and Y. Project X costs Rs. 30,000 and Project Y costs Rs. 36,000. You have been given below the Net Present Value probability distribution for each project. Project X Project Y NPV (Rs) Probability NPV (Rs) Probability 3000 0.1 3000 0.2 6000 0.4 6000 0.3 12,000 0.4 12,000 0.3 15,000 0.1 15,000 0.2 a.Compute the Expected Net Present Value of Projects X and Y. b.Compute the risk attached to each project, i.e., standard deviation of each probability distribution c.Which project do you consider more risky, and why ? 6.Pioneer Projects Limited is considering accepting one of the two mutually exclusive Projects X and Y. The cash flows and probabilities are estimated as follows: Project X Project Y Probability Cash flows (Rs) Probability Cash flows (Rs.) 0.10 12,000 0.10 8,000 0.20 14,000 0.25 12,000 0.40 16,000 0.30 16,000 0.20 18,000 0.25 20,000 0.10 20,000 0.10 24,000 Advise the Pioneer Projects Limited. 7.A company is considering investing in a new product with an expected life of three years. It is estimated that if the demand for the product is favourable in the first year, then, it is certain to be favourable in the subsequent years. And, if it is low in the first year, it would remain low in the years 2 and 3. The company feels that cash flows over time are perfectly correlated. The cost of the project is Rs. 50,000 and the possible cash flows for three years are as follows: Year 1 Year 2 Year 3 Cash flow Probabilit Cash Flow Probabilit Cash Flow Probabilit (Rs) y (Rs.) y (Rs.) y NIL 0.10 5,000 0.15 NIL 0.15 10,000 0.20 20,000 0.20 7500 0.20 20,000 0.40 35,000 0.30 15,000 0.30 30,000 0.20 50,000 0.20 22,500 0.20 40,000 0.10 65,000 0.15 30,000 0.15 Assume a risk free discount rate of 5%. Calculate the Expected Value and Standard Deviation of the Probability distribution of possible Net Present Values. Assuming a normal distribution, what is the probability of the Project providing a Net Present Value of (i) zero or less (ii) of Rs. 15,000 or more ? 8. A project under evaluation is thought to involve a medium degree of risk. The risk free discount rate is 4% and the appropriate risk premium is believed to be 6%. The Project costing Rs. 1000 has the following estimated NPV and the probabilities of different economic conditions: Market NPV at 4% NPV at 10% Probability Conditions Good 1775 1487 Average 1220 989 Medium 665 492 Poor 110 -5 Bad -445 -503 Analyse the expected NPV and its variability. 0.10 0.20 0.40 0.20 0.10 9.X Limited is considering a Project with the following cash flows : (Rs.) Year Purchase of Running Cost Savings (Rs) Plant (Rs) 0 -7000 1 2,000 6,000 2 2,500 7,000 The cost of capital is 8%. Measure the sensitivity of the Project to changes in the plant value, running costs and savings (considering one factor at a time) such that NPV becomes zero. Which factor is most sensitive to affect the acceptability of the project. 10. The Management of ABC Company is considering the question of marketing a new product. The fixed cost required in the project is Rs. 4,000. Three factors are uncertain, viz., the selling price, variable cost and the annual sales volume. The product has a life of only one year. The Management has the data on these three factors as under : Selling Probabilit Variable Probabilit Sales Probabilit Price (Rs) y cost (Rs) y volume y (Rs) 3 0.20 1 0.30 2000 0.30 4 0.50 2 0.60 3000 0.30 5 0.30 3 0.10 5000 0.40 Consider the following sequence of thirty random numbers: 81, 32, 60, 04, 46, 31, 67, 25, 24, 10, 40, 02, 39, 68, 08, 59, 66, 90, 12, 64, 79, 31, 86, 68, 82, 89, 25, 11, 98, 16. Using the sequence (First 3 random numbers for the first trial etc.,), simulate the average profit for the above project on the basis of 10 trials. 11.X Limited is considering the purchase of a new plant requiring a cash outlay of Rs. 20,000. The plant is expected to have a useful life of 2 years without any salvage value. The cash flows and their associated probabilities for the two years are as follows : I year II year Year Cash flow Probability Cash Flow Probability (Rs) (Rs) 1 8000 0.3 4000 0.2 10,000 0.6 15,000 0.2 11,000 0.4 13,000 0.3 15,000 0.4 16,000 0.3 15,000 0.3 16,000 0.1 20,000 0.8 24,000 0.1 Presuming that 10% is the cost of capital, calculate the NPV of the Project under different conditions of cash flows and suggest whether the Project should be taken up or not. 12. D Limited has to choose one between two machines – Machine A has low fixed costs and high unit variable costs, whereas Machine B has high fixed cost and low unit variable costs. Consequently, Machine A is suited to low level demand while Machine B is suited to high level demand. It is assumed that there are only two possible demand levels – low and high – and the estimated probability of each of these events is 0.5. The estimated profits for each demand level are as follows: Low Demand High Demand Machine A 1,00,000 1,60,000 Machine B 10,000 2,00,000 There is a probability of employing a firm of marketing consultants who would be able to provide a perfect prediction of the actual demand. What is the maximum amount the company should be prepared to pay the consultants for the additional information ? 13. The initial outlay for a capital investment project consists of Rs. 100 lakhs for Plant and Machinery and Rs. 40 lakhs for Working Capital. Other details are summarized below: Sales 1 Lakh units of output per year for years 1 to 5 Selling price Rs. 120 per unit of output Variable cost Rs. 60 per unit of output Fixed overheads (excluding Rs. 15 lakhs per year for years 1 depreciation) to 15 Rate of depreciation on Plant and 25% on Written Down Value Machinery Method Salvage value of Plant and Equal to the Written Down Value Machinery method value at the end of 5th year Tax rate 40% Time Horizon 5 years Post tax cut-off rate 12% Required : I. Indicate the financial viability of the Project by calculating the Net Present Value. II. Determine the Sensitivity of the Project’s NPV under each of the following conditions : a. Decrease in Selling Price by 5% b. Increase in Selling Price by 10% c. Increase in cost of Plant and Machinery by 10% 14. MN Integrated Limited is considering a proposal for which the following relevant information is provided. Cost of the Project : Rs. 30,000 Life of the Project : 5 years Annual sales at Rs. 30 each : 1400 units Variable cost per unit : Rs. 20 Fixed cost : Rs. 3000 Depreciation : Rs. 2000 It is estimated that the following variables may take the values given here under for different economic situations : Particulars Pessimistic Optimistic Number of units sold 800 1800 Selling price Rs. 20 Rs. 20 Variable cost per unit Rs. 15 Rs. 4 Given the tax rate 50% and cost of capital 10%, analyse the sensitivity of the NPV of the proposal with respect to (i) Number of units sold; (ii) Selling price, and (iii) Variable cost per unit 15. Santaram Limited is considering to diversity into a new line of business by acquiring a running firm by paying Rs. 20,00,000 in cash. The Finance Department of the firm has prepared the following report in support of the proposal. Annual Projection Sales 18,00,000 Less : Variable cost 12,00,000 Contribution 6,00,000 Less : Fixed Cost 1,00,000 Less : Depreciation 2,00,000 Profit Before tax 3,00,000 Less : Tax 1,00,000 Profit after tax 2,00,000 Cash flow (Profit after tax + 4,00,000 Depreciation) Present Value Annuity Factor for 5.650 10 years at 12% Present Value of Annual Cash 22,60,000 inflows (4,00,000 * 5.650) Less : Cash outflow (Initial cost) 20,00,000 Net Present Value 2,60,000 However, as a Managing Director, you feel that the profit of the project may vary widely as the variables contributing to NPV are sensitive. For this purpose, the Sales, Variable Cost, Fixed Cost and Initial Investment have been pointed out as sensitive. Under the Optimistic, Pessimistic and Expected Situations, these variable may take the following values. Particulars Optimistic Expected Pessimistic Investment 18,00,000 20,00,000 24,00,000 Sales 21,00,000 18,00,000 15,00,000 Fixed Cost 80,000 1,00,000 1,30,000 Variable Cost 65% 66.67% 70% (percentage) Analyse the Sensitivity of these variables (one variable at a time) vis a vis the NPV of the proposal. 16. A company is considering two mutually exclusinve projects, Project X and Project Y. Project X costs Rs. 30,000 Project Y Rs. 36,000. You have been given below the NPV probability distribution for each project. Project X Project Y NPV Probabil NPV Probabil estimate ity estimate ity 3000 0.1 3000 0.2 6000 0.4 6000 0.3 12,000 0.4 12,000 0.3 15,000 0.1 15,000 0.2 I. Compute the Expected NPV of Projects X and Y. II. Compute the risk attached to each project, i.e., Standard Deviation of each probability distribution. III.Which project do you consider more risky and why ? IV.Compute the profitability index of each project. 17.Galpub and company proposes to install a central air conditioning system on 1st January 2011 in their office which has been taken on lease. The lease period is going to end after 3 years when the lessor has agreed to pay Rs. 10,000 for the air conditioning system. Three options of air conditioning are available, i.e., Gas, Oil and solid Fuel. The cost of installation and running expenses of all these three options under different weather conditions are as follows: Particulars Cost Operating expenses Severe weather Mild Other costs weather Gas 1,70,000 40,000 24,000 2,500 per annum Oil 1,50,000 53,000 37,000 2,500 per annum Solid Fuel 1,40,000 45,000 36,000 10,000 (year 2012) The actual operating expenses will depend upon the weather conditions and the rate of fuel prices. The fuel prices for the years 2012 and 2013 are expected to increase wither @15% per annum (probability of 0.4) or @ 25% per annum (probability of 0.6). The price increase of 2012 will be repeated in the year 2012 also. It is estimated that chances of severe and mild weather are 70% and 30% respectively in any year. 18. Shrimps Production Limited is to select a machine out of two proposals P1 and P2. The former is a semi automatic model requiring a fixed rental of Rs. 3000 per annum and variable cost of production of Rs. 0.10 per unit. The later is an economy model requiring a field rental of Rs. 1000 per annum and variable cost of production is Re. 0.25 per unit. The market demand has been showing fluctuations and the probabilities of different demand levels have been put as follows: Demand Probability 10,000 units 0.12 12,000 units 0.17 15,000 units 0.41 17,000 units 0.24 19,000 units 0.06 Which model should be acquired ? What will be the decision, if the demand level is known with certainty at 10,000 units ? 19. A firm has an investment proposal, requiring an outlay of Rs. 40,000. The investment proposal is expected to have 2 years economic life with no salvage value. In year I, there is a 0.4 probability that cash inflow after tax will be Rs. 25,000 and 0.6 probability that cash inflow after tax will be Rs. 30,000. The probabilities assigned to cash inflows after tax for the year II are as follows : Cash inflow Rs. 25,000 for the year I Cash inflow Probability Probability for the year II Rs. 12,000 0.2 Rs. 20,000 0.4 Rs. 16,000 0.3 Rs. 25,000 0.5 Rs. 22,000 0.5 Rs. 30,000 0.1 The firm uses 10% discount rate for the type of investment. 20.ABC Limited is evaluating two proposals A1 and A2, both having cash flows of Rs. 30,000 each. However, these alternatives may result in different cash inflows depending upon different economic conditions, i.e., Good, Average and Bad. The following information is available. Particulars Alternative 1 Alternative 2 Economic Life 10 years 15 years Cash inflows : (Annual) Good Economic 8,000 6,000 condition Average Economic 6,000 5,500 condition Poor Economic 4,500 4,500 condition Evaluate the proposals and advise the firm given that the minimum required rate of return of the firm is 10%. 21. The following forecasts are made about a proposal which is being evaluated by a firm. Initial cash outlay = Rs. 12,000 Life = 4 years Cash inflows = Rs. 4,500 (annual) Cost of capital = 14% Present Value Annuity Factor for 4 years at 14% = 2.9137 Present Value Annuity Factor for 3 years at 14% = 2.3216 Analyse the sensitivity of different variables with respect to NPV. 22.ABC Company is evaluating a proposal having initial outlay of Rs. 1,40,000 and economic life of 2 years. The cash inflows and the respective probabilities have been found to be as follows : Year 1 Year 2 Cash inflows Probability Cash inflows Probability (Rs.) (Rs) 1,00,000 0.3 1,40,000 0.5 80,000 0.5 70,000 0.3 10,000 0.2 60,000 0.2 Evaluate the proposals given that the firm has minimum required rate of return of 10%. 23.The following data in respect of proposal having an outlay of Rs. 6,000 has been submitted before PSR company. Year Cash Probabilit Year Cash Probabilit inflows y inflows y 1 1000 0.1 3 1500 0.1 1500 0.2 2200 0.1 2000 0.4 2800 0.7 2500 0.2 3500 0.1 3000 0.1 2 2000 0.2 2500 0.3 2700 0.2 2800 0.3 Evaluate the proposal given that the discount rate is 15%. 24.XYZ is evaluating two equal size mutually exclusive proposals A and B for which the respective cash flows together with associated probabilities are as follows: Cash inflows Probabilities Cash inflows Probabilities (Rs.) (Rs) 2000 0.3 1000 0.1 4000 0.4 3000 0.1 6000 0.3 5000 0.4 7000 0.3 9000 0.1 Find out the risks of the proposals in terms of the standard deviation. 25. RST company is engaged in evaluating the following two mutually exclusive proposals, P1 and P2, for which the relevant information is as follows : Proposal 1 Proposal 2 Cash inflows Probability Cash inflows Probability (Rs) (Rs.) 1,50,000 0.3 -4,00,000 0.2 2,00,000 0.3 3,00,000 0.6 2,50,000 0.4 4,00,000 0.1 8,00,000 0.1 Evaluate the proposals in terms of the standard deviation and coefficient of variation. 26. ABC company is evaluating a project which requires an outlay of Rs.20,000 and is expected to produce cash inflow for 3 years as follows: Year 1 Year 2 Year 3 Cash Probabilit Cash Probabilit Cash Probabilit inflow y inflow y (Rs) (Rs) 6000 0.3 4000 0.2 10,000 0.4 8000 0.6 14,000 0.3 12,000 0.2 Evaluate the proposal given data, the risk free inflow y (Rs) 6,000 0.3 10,000 0.4 14,000 0.3 rate of return 6%. 27.ABC company is considering a proposal having an initial outlay of Rs. 1,50,000 and a life of 2 years. The firm’s required rate of return is 10%. It is expected that the cash flow for the year 2 is affected by the cash flow of the year 1. Other details of the cash inflows are as follows: Year 1 Year 2 Cash inflows Probability Cash inflows Probability (Rs) (Rs) 1,00,000 0.4 1,40,000 0.5 60,000 0.3 70,000 0.2 60,000 0.6 2,00,000 0.6 1,20,000 0.3 80,000 0.1 Evaluate the proposal. 28. Simulation Model : PQR company is evaluating the installation of a new automatic machine in order to reduce the labour costs. The new machine can also meet the demand for greater capacity needed to meet increase in demand for the product and hence resulting in increase in profits for atleast 3 years. However, due to uncertainty in the expected demand for the product, the cash flows can not be accurately estimated. The following probabilities have been assigned in this reference. Year 1 Year 2 Year 3 Cash Probabilit Cash Probabilit Cash Probabiliti inflows ies inflows ies inflows es (Rs.) (Rs.) (Rs) 10,000 0.3 10,000 0.1 10,000 0.3 15,000 0.4 20,000 0.2 20,000 0.5 20,000 0.3 30,000 0.4 30,000 0.2 40,000 0.3 The new machine is having a cost of Rs. 70,000 and the scrap value of the old machine is estimated to be Rs. 28,000. Evaluate the proposal given that the discount factor is 15%. Also analyse the risk inherent in this situation by simulating the NPV values. Random numbers for 5 sets of cash flows are given here under. On the basis of simulation exercise, also find out the expected NPV of proposal will be less than 0. Year Set 1 Set 2 Set 3 Set 4 Set 5 1 4 7 6 5 0 2 2 4 8 0 1 3 7 9 4 0 3 29. ABC Company has the funds of Rs.2,00,000 which expectedly are not required for next few years and hence can be deposited in a bank @ 15% interest payable annually. Alternatively, the funds can be used to install a new machine for the production of a new item. For this, the company has two options before it. Machine 1 costing Rs. 1,80,000 which is expected to give annual cash inflows of Rs. 1,00,000, Rs. 1,20,000 and Rs. 40,000 respectively for next three years. Machine 2 costing Rs. 1,90,000 which is expected to give annual cash inflows of Rs. 1,00,000, Rs. 1,00,000 and Rs. 50,000 respectively for the next 3 years. Present the decision situation in a decision tree and evaluate the options. 30. Decision Trees : A firm of investment consultants has been asked by one of its clients with respect to investmet of a sum of Rs. 1,00,000 for a period of 2 years. After a thorough analysis of different opportunities, option A and B have been short listed. Option A will lead to a return of 8%, 10% or 12% in the first year, but due to the nature of the option, there is a correlation between the returns of the year 1 and year 2. The returns of the year 1 and the probabilities of the different returns in year 2 are as follows: Year 1 Year 2 Return 8% 10% 12% 8% 0.6 0.3 0.1 10% 0.2 0.5 0.3 12% 0.1 0.2 0.7 At this stage, the three different returns in year 1 are considered to be equally likely. Option B has a certain return of 9.5% per annum. Evaluate the options and draw a decision tree to represent the alternative courses of action and outcome. On the basis of the expected value of returns which option is preferable ? 31. PQR Company whose major product is X, is facing problems as the product X, is facing problems as the product X deteriorates rapidly, it can be produced on a monthly basis only and cannot be stored from 1 month to the next. At the start of each month, a production figure for the month is decided and necessary raw materials are procured. Unfortunately, the demand for the product X varies randomly and if the demand is more than the monthly budgeted production, then the sales are lost. If on the other hand, production is more than the actual sales, then the sales are lost. If on the other hand, production is more than the actual sale, then the goods unsold have no value. The selling price per unit is Rs. 2,400 and the variable cost is Rs. 1,500 per unit. On the basis of sales experienced, it is found that the monthly demand for the product X is between 10 and 20 units. It may be assumed that the demand of 10 units is considered as low demand, demand of 15 units s medium demand and demand of 20 units as high demand. These demand levels have the probabilities of 0.3, 0.6 and 0.1 respectively. Present the above information in the form of decision tree and also evaluate the production level given that the demand pattern does not change. 32. An investor has two alternative proposals for evaluation on the basis of the following formation: Project A Project B Cash inflows Probability Cash inflows Probability (Rs.) (Rs) 75,000 0.6 52,500 1 25,000 0.4 His utility function states that he will get utilities of 6, 4 and 1 from the first Rs. 25,000, second Rs. 25,000, third Rs. 25,000 and the fourth Rs. 25,000 respectively. Evaluate the proposals with and without utility function. 33. ABC Company is evaluating a proposal costing Rs. 3,00,000 and an economic life of 2 years over which the expected cash flows together with the probabilities have been estimated as follows: Year 1 Year 2 Cash inflows Probabilities Cash inflows Probabilities (Rs. ‘000) (Rs. ‘000) 200 0.3 100 0.3 200 0.5 300 0.2 300 0.4 200 0.3 300 0.5 400 0.2 400 0.3 300 0.3 400 0.4 500 0.3 Evaluate the project given that the abandonment value of the proposal at the end of each year 1 is Rs. 2,50,000 and the rate of discount is 12%. 34. ABC Company is considering two mutually exclusive machines X and Y. The company uses a Certainty Equivalent approach to evaluate the proposals. The estimated cash flow and certainty equivalents are both machines are as follows : Machine Machine Y X Year Cash Certainty Cash flow Certainty flows equivalent Equivalent 0 -30,000 100 -40,000 1.00 1 15,000 0.95 25,000 0.90 2 15,000 0.85 20,000 0.80 3 10,000 0.70 15,000 0.70 4 10,000 0.65 10,000 0.60 Which machine should be accepted, if the risk free rate of discount is 5%. 35. Determine the Risk Adjusted Net Present Value of the following projects : Particulars A B C Net cash Rs. 1,00,000 Rs. 1,20,00 Rs.2,10,000 outlays Project life 5 years 5 years 5 years Annual cash Rs. 30,000 Rs. 42,000 Rs. 70,000 inflow Co-efficient of 0.4 0.8 1.2 variation The company selects the risk adjusted rate of discount on the basis of co-efficient of variation. Co-efficient Risk Adjusted Present value factor 1 to 5 years of variation Rate of discount at Risk Adjusted Rate of Discount 0.0 10% 3.791 0.4 12% 3.605 0.8 14% 3.433 1.2 16% 3.274 1.6 18% 3.127 2.0 22% 2.864 More than 2.0 25% 2.689 INDIAN ACADEMY SCHOOL OF MANAGEMENT STUDIES HENNUR CROSS, KALYAN NAGAR POST, BANAGLORE IMPORTANT SUMS ON PROJECT ANALYSIS AND IMPLEMENTATION – SELF STUDY SUMS PROBABILITY ANALYSIS : 1.PQR Limited is considering the introduction of a new product. The anticipated demand, probabilities of demand and profits for each products are given below. Choice is to be made between Product X and Product Y. Product X Product Y Product Probability Profit Product Probability Profit Demand of demand (Rs. in Demand of Demand (Rs in (units) (%) crores) (units) (%) crores) 50,000 20 -8000 30,000 15 -12,000 60,000 10 -5000 40,000 15 -10,000 70,000 30 11,000 50,000 40 14,000 80,000 20 14,000 60,000 20 16,000 90,000 20 17,000 70,000 10 18,000 100 100 2.X Limited has to decide between rental of two types of machines manufacturing the same product. Machine A, an inexpensive economy model, rents for R. 1000 per month, but the variable production cost is Re.0.25 per unit. Machine B rents for Rs. 3,000 per month, but the variable production cost is only Re. 0.25 per unit. Machine B rents for Rs. 3,000 per month, but the variable production cost is only Re.0.10 per unit. Monthly demand varies between 10,000 and 19, 000 to the following probabilities: Demand 10,0 12,0 15,0 17,0 19,0 (units) 00 00 00 00 00 Probability 0.12 0.17 0.41 0.24 0.06 Make a comparison of the two machines. Which machine X Limited should rent ? If the demand is definitely known to be 10,000 units, would the decision reverse ? 3.A firm wants to avoid risk and choose between either of two alternative products. Both the products have the same contributory margin of Rs. 4 per unit, the same increment in annual fixed costs (Rs.4 lakhs) and require similar amounts of processing facilities. Both the product will have the same break even volume of one lakh units and for any levels of sales will yield the same profit contributions. Given the probability distribution of sales for Products 1 and 2, as under, which product the firm will prefer ? Units Product Product sold 1 50,000 0.1 75,000 0.2 1,00,00 0.3 0 1,25,00 0.3 0 1,50,00 0.1 0 2,25,00 0 0 2 0.2 0.3 0.2 0.1 0.1 0.1 4.The following table presents the proposed cash flows for the projects M and N with their associated probabilities. Which project has a higher preference for acceptance ? Possibilit Project M Project N ies Cash flow (Rs. in Probabilit Cash Flow (Rs. in Probabilit lakhs) ies lakhs) ies 1 7,000 0.10 12,000 0.10 2 8,000 0.20 8,000 0.10 3 9000 0.30 6,000 0.10 4 10,000 0.20 4,000 0.20 5 11,000 0.20 2,000 0.50 5.A Company has estimated the following demand level of the products : Sales volume 10,0 12,0 14,0 16,0 18,0 (units) 00 00 00 00 00 Probability 0.10 0.15 0.25 0.30 0.20 It has assumed that the sales price of Rs. 6 per unit, marginal cost Rs. 3.50 per unit, and fixed cost Rs. 34,000. What is the probability that : (a) the company will break even in the period ? (b) the company will make a profit of atleast Rs. 10,000 ? 6.A company has estimated the unit variable cost a product to be Rs. 10 and the selling price is Rs. 15 per unit. Budgeted sales for the year are 20,000 units. Estimated fixed costs are as follows : Fixed costs 50,0 60,0 70,0 80,0 90,0 (Rs) 00 00 00 00 00 Probability 0.10 0.3 0.3 0.2 0.1 What is the probability that the company will equal or exceed its target profit of Rs. 25,000 for the year. 7.X Limited produces a range of products with an average contribution / sale ratio of 30% on current prices. Currently, fixed costs are Rs. 1,50,000 per annum and estimates are being prepared for the next budget period for which the forecasts have been selected : Sales at current 4,00,0 7,00,0 9,00,0 price 00 00 00 Probability 0.2 0.7 0.1 For the next budget period : Inflation 12 6 2 rate % % % Probabilit 0.3 0. 0. y 5 2 The inflation rate is expected to affect all the variable costs and 60% of the fixed costs. The company anticipates being able to raise selling price in line with inflation without losing sales. The probabilities shown are independent. You are required to prepare a table of all positive results and calculate the probability of atleast breaking even; Also calculate the probability of making at least Rs. 70,000 profit. 8.Unique Products Limited is considering a proposal of whether to invest in a project which would need an immediate expenditure on capital equipment of Rs. 40,000. The Projected sales from the project has been estimated as follows : Sales volume 2,0 6,0 8,0 10,0 14,0 (units) 00 00 00 00 00 Probability 0.1 0.3 0.3 0.20 0.10 0 0 0 Once the sales are established at a certain volume in the first year, they will continue at that same volume in subsequent years. The unit selling prices will be Rs. 12, the unit variable cost will be Rs. 8. There will be additional fixed cost of Rs. 20,000 (all cash items). The project will have a life of 6 years after which equipment could be sold for scrap at a price of Rs. 3,000. You are required to find out (a) the expected value of NPV of the project and (b) the minimum volume of sales per annum required to justify the project. The cost of capital of the company is 10%. Discount factor of Re.1 per annum for 6 years at 10% is 4.355 and the discount factor of Re.1 at the end of six years at 10% is 0.5645. Ignore taxation. BEST AND WORST POSSIBLE ESTIMATES : 9. Forward Looking Limited is preparing their budget for 2009. In the preparation of the budget, they would like to take no chances, but would like to envisage all sorts of possibilities and incorporate them in the budget. Their estimates are as under : (a) If the worst possible happens, sales will be 8,000 units at a price of Rs. 19 per unit. The material cost will be Rs. 9 per unit, the Direct Labour will be Rs. 2 per unit and the variable overheads will be Rs. 1.50 per unit. The fixed cost will be Rs. 60,000 per annum. (b) If the best possible happens, sales will be 15,000 units at price of Rs. 20 per unit. The material cost will be Rs. 7 per unit, direct labour Rs. 3 per unit and the variable overheads will be Re.1 per unit. The fixed cost will be Rs. 48,000 per annum. (c) It is most likely however that the sales will be 2,000 units above the worst possible level at a price of Rs. 20 per unit. The material cost Rs. 8, Direct Labour Rs. 3, Variable overheads Re. 1 per unit. The fixed cost will be Rs. 50,000 per annum. (d) There is a 20% probability that the worst will happen, a 10% probability that the best will happen and a 70% possibility that the most likely outcome will occur. What will be the expected value of profit as per the budget 2009? 10.Venkatesh Limited is always discarding old lines and introducing new lines of products and is considering at present three alternative promotional plans for ushering in new products. Various combination of prices, development expenditure and promotional outlays are involved in these plans. High, medium and low forecast of revenues under each plan have been formulated and their respective probabilities of occurrence have been estimated. Their budgeted revenues and probabilities along with other relevant data are summarized below : Particulars Plan I Plan Plan II III Budgeted revenue with probability : High 30 24 50 (0.3) (0.2) (0.2) Medium 20 20 25 (0.3) (0.7) (0.5) Low 5 15 0 (0.4) (0.1) (0.3) Variable cost as percentage 60% 75% 70% of revenue Initial Investment 25 20 24 Life in years 8 8 8 The company’s cost of capital is 12% and the income tax rate is 40%. Investments in promotional programs will be amortised by the Straight Line Method. The company will have net taxable income each year, regardless of the success or failure of the new products. (a)Substantiating with figures, make a detailed analysis and find out which of the promotional plans is expected to be the most profitable ? (b) In the worst event, which of the plans would result in maximizing the profits. 11. Y Limited is reviewing the price that it charges for a major product line. Over the past three years, the product has sales averaging 48,000 units per annum at a standard selling price of Rs. 5.25. Costs have been raising steadily over the past year and the company is considering raising this price to Rs. 5.75 or Rs. 6.25. The sales manager has produced the following schedule to assist with the decision. Price Rs. Rs. 5.75 6.25 Estimates of Demand : Pessimistic Demand 35,00 10,00 (Probability 0.25) 0 0 Most likely Demand 40,00 20,00 (Probability 0.60) 0 0 Optimistic Demand 50,00 40,00 (Probability 0.15) 0 0 Currently the unit cost is estimated at Rs. 5 as follows: Variable costs Rs. : Direct 2.5 Materials 0 Direct Labour 1.0 0 Direct 1.0 Overheads 0 4.5 0 Fixed 0.5 Overheads 0 Total 5.0 0 The company considers that the most likely value per unit variable cost over the next year is Rs. 4.90 (probability 0.75), but it could be as high as Rs. 5.20 (probability 0.15) and it might even be as low as 4.75 (probability 0.10). Total fixed costs currently are Rs. 24,000 per annum, but it is estimated that the corresponding total for the coming year will be d: Rs. 25,000 with a probability of 0.2; Rs. 27,000 with a probability of 0.6; Rs. 30,000 with a probability of 0.2. (Demand quantities, unit costs and fixed costs can be assumed to be statistically independent. Analyse the foregoing information in a way which you consider will assist management with the problem, give your views on the situation and advise on the new selling price. Calculate the expected level of profit that would follow from the selling price that you recommend. VALUE OF PERFECT INFORMATION : 12. A Limited has a choice between three projects X, Y and Z. The following information has been estimated: Projects Market Demand Profit (Rs. ‘000) D1 D2 D3 190 50 15 110 200 160 150 140 110 0.6 0.2 0.2 X Y Z Probabilit ies Which projects should be undertaken if the decision is made by Expected Value Approach ? Calculate the Expected Value of Perfect Information. 13. Toys for Tiny Tots Limited manufactures high quality toys for children, which are sold by mail order and through departmental stores. Kiddy Products is prepared to sell the design and manufacturing rights for three products. However, it will only sell the rights to one product, not to two or three. The costs of the rights are : Pussy cat – Rs. 62,500; Teddy Bear – Rs. 75,000; Jack in Box – Rs. 52,500. Toys for tiny tots Limited feel that any of these products would make an attractive addition to its range through the products would have sales life of only one year and wish to select the best of the three products. The following information has been made available : Particulars Pussy Teddy Jack in Cat Bear Box Selling price per 199 140 115 unit Variable cost per 98 75 65 unit Fixed production 70,000 95,000 60,000 cost Advertisement 55,000 40,000 20,000 These figures have been worked out with great care and circumspection. But, when it comes to sales volumes, the Sales Manager could provide only the following analysis of possibilities. Pussy Cat Teddy Bear Jack in Box Volume in Probabil Volume in Probabil Volume in Probabili units ity units ity units ty 2000 0.7 Nil 0.1 2500 0.1 3000 0.2 3000 0.4 3000 0.3 4000 0.1 6000 0.5 4000 0.4 5000 0.2 You are required to advice the company of the best course of action based on the above information . In the case of Teddy bear, it is felt that the company should launch a market research study costing Rs. 20,000 which would be able to determine precisely whether the sales would be NIL, 3000 or 600 units. Is it worthwhile to undertake the study ? Assume all the costs are avoidable. STANDARD DEVIATION : 14.Pioneer Projects Limited is considering accepting one of the two mutually exclusive projects X and Y. The cash flow and probabilities are estimated as follows : Project X Project Y Probabil Cash flow Probabil Cash Flow ity (Rs) ity (Rs.) 0.10 12,000 0.10 8,000 0.20 14,000 0.25 12,000 0.40 16,000 0.30 16,000 0.20 18,000 0.25 20,000 0.10 20,000 0.10 24,000 Advice the Pioneer Projects Limited. 15. Based on the data given below, ascertain which of the following two projects would be more risky based on the criteria of co-efficient of variation ? Project A Project B Cash flow Probabil Cash flow Probabili (Rs) ity (Rs.) ty 3000 0.10 2000 0.10 3500 0.20 3000 0.25 4000 0.40 4000 0.30 4500 0.20 5000 0.25 5000 0.10 6000 0.10 16. A company is trying to choose between two investment proposals A and B. Project A has a standard deviation of Rs. 6500 while project B has a standard deviation of Rs. 7,200. The Finance Manager wishes to know which investment to choose, given each of the following combinations of the expected values : (a) Project A and Project B both have expected net present value of Rs. 15,000 (b) Project A has Expected NPV of Rs. 18,000 while Project B has Rs. 22,000. 17. Given the following information, find out which project is more risky, either A or B. State of the Probability of Actual cash flow Market occurrence (Rs) Project Project A B High 0.2 1000 1200 Normal 0.6 800 800 Low 0.2 600 400 SENSITIVITY ANALYSIS 18. From the following project details, calculate the sensitivity of the (a) Project Cost, (b) Annual Cash Flow and (c) Cost of Capital. Which variable is the most sensitive ? Project Cost Rs. 12,000; Annual Cash flow Rs. 4,500; Life of the Project 4 years; Cost of capital 14%. The annuity factor at 14% for 4 years is 2.9137 and at 18% for 4 years is 2.6667. 19. X Limited is considering a project with the following cash flows: Yea Purchase of the Running cost Savings r Plant (Rs) (Rs) 0 70,000 Nil Nil 1 Nil 20,000 60,000 2 Nil 25,000 70,000 The cost of capital is 8%. Measure the sensitivity of the project to changes in the level of running cost, savings and plant cost. Which factor is the most sensitive ? The present values of Re.1 at 8% for the year 1 = 0.9259 and for the year 2 = 0.8573. 20. VERY VERY IMPORTANT SUM ON SENSITIVITY ANALYSIS : The initial investment outlay for a capital investment project consists of Rs. 100 lakhs for plant and machinery and Rs. 40 lakhs for working capital. Other details are summarized as follows: Sales : 1 lakh units of output per year for years 1 to 5. Selling price : Rs. 120 per unit of output Variable cost : Rs. 60 per unit of output Fixed overheads (excluding depreciation) : Rs. 15 lakhs per year for years 1 to 5 Rate of depreciation on plant and machinery : 25% on WDV method Salvage value of plant and machinery : Equal to WDV method Applicable tax rate ; 40% Time Horizon : 5 years Post tax cut off rate : 12% Required ; (a)Indicate the financial viability of the project by calculating the NPV. (b) Determine the sensitivity of the project’s NPV under each of the following conditions : (i) Decrease in selling price by 5%; (ii) Increase ion variable cost by 10%; (iii) increase in cost of plant and machinery by 10%. SIMULATION MODELLING : 21. The Everalert Limited which has a satisfactory preventive maintenance system in its plant, has installed a new Hot Air Generator based on electricity, instead of fuel oil for drying its finished products. The Hot Air generator requires periodicity shutdown maintenance. If the shutdown is scheduled annually, the cost of maintenance will be as under : Maintenance cost 15,0 20,0 25,0 (Rs.) 00 00 00 Probability 0.3 0.4 0.3 The costs are expected to be almost linear, i.e., if the shutdown is scheduled twice a year the maintenance cost will be double. There is no previous experience regarding the time taken between breakdowns. Costs associated with break down will vary depending upon the periodicity of maintenance. The probability distribution of break down cost is estimated as under : Break down costs ( Rs per Shutdown once a Shutdown twice a annum) year year 75,000 0.2 0.5 80,000 0.5 0.3 1,00,000 0.3 0.2 Simulate the total costs (maintenance costs and break down costs) and recommend whether shutdown overhauling should be restored to once a year or twice a year. Random numbers for Alternative I : For Maintenance cost : 27, 44, 22, 32, 97 For Breakdown cost : 03, 50, 73, 87, 59 Random numbers for Alternative II : For Maintenance cost : 42, 04, 82, 38, 91 For Breakdown cost : 54, 65, 49, 03, 56 22. For a Washing Powder manufacturing company, frequency of contribution (i.e., sale price – variable cost) per unit, annual demand and requirement of investment were found as follows: Contribution per unit 3 5 7 9 1 (Rs.) 0 Relative frequency 0. 0. 0. 0. 0. 1 2 4 2 1 Annual Demand (‘000 units) Relative frequency 20 25 30 35 40 45 50 0.0 0.1 0.2 0.3 0.2 0.1 0.0 5 0 0 0 0 0 5 Required investment (Rs in ‘000) Relative frequency 1.7 2.0 2.5 50 00 00 0.2 0.5 0.2 5 0 5 Consider the random numbers 93, 03, 51, 59, 77, 61, 71, 623, 99, 15 for using Monte Carlo simulation for 10 runs, to estimate the percentage of return on investment (ROI) defined as : ROI (%) = (Cash inflow / investment) * 100 for each run, Recommend an optimum investment strategy based on model value dof ROI. 23. An investment company wants to study the investment projects based on market demand, profit and the investment required, which are independent of each other. Following probability distributions are estimated for each of these three factors: Annual Demand (‘000 25 30 35 40 45 50 55 units) Probability 0.0 0.1 0.2 0.3 0.2 0.1 0.0 5 0 0 0 0 0 5 Profit per unit 3 5 7 9 10 Probability 0.1 0.2 0.4 0.2 0.1 0 0 0 0 0 Investment required (Rs. 275 300 350 in ‘000) 0 0 0 Probability 0.2 0.5 0.2 5 0 5 Using Simulation process, repeat the trial 10 times, compute the investment on each trial taking these factors into trial. What is the most likely return ? Use the following random numbers (30, 12, 16) (59, 09, 69), (63, 94, 26) (27, 08, 74), (64, 60, 61), (28, 28, 72), (31, 23, 57), (54, 85, 20), (64, 68, 18), (32, 31, 87). In the bracket above, the first random number is for annual demand, the second one is for profit and the last one is for the investment required. CERTAINTY EQUIVALENT AND RISK ADJUSTED DISCOUNT RATE : 24. Delta Corporation is considering an investment in one of the two mutually exclusive proposals. Project A : It involves initial outlay of Rs. 1,70,000 Project B : It involves initial outlay of Rs. 1,50,000. The Certainty Equivalent approach is employed in evaluating risky investments. The current yield on treasury bills is 5% and the company uses this as riskless rate. Expected values of net cash inflow which their respective certainty equivalents are as follows : Yea Project A Project B r Cash inflow Certainty Cash inflow Certainty (Rs.) Equivalent (Rs.) Equivalent 1 90,000 0.8 90,000 0.9 2 1,00,000 0.7 90,000 0.8 3 1,10,000 0.5 1,00,000 0.6 Answer the following with reasons : (a)Which of the Project should be acceptable to the company ? (b) Which Project is riskier and why ? Explain. (c) If the company wants to use the risk adjusted discount rate method, which project would be analysed with higher rate ? 25. Fast run Automobiles Spares Limited is considering the investment in one of the three mutually exclusive projects Zeta 10, Meta 10, and Neta 10. The company’s cost of capital is 15% and the risk free rate of return is 10%. The income tax rate for the company is 40%. FASL has gathered the following basic cash flow and risk index data for each project. Projects Zeta Meta Neta 10 10 10 Initial investment 15,00, 11,00, 19,00,0 000 000 00 Cash inflows after tax for the year : 1 6,00,0 6,00,0 4,00,00 00 00 0 2 6,00,0 4,00,0 6,00,00 00 00 0 3 6,00,0 5,00,0 8,00,00 00 00 0 4 6,00,0 2,00,0 12,00,0 00 00 00 Risk index 1,80 1.00 0.60 Using the Risk Adjusted Discount Rate, Determine the Risk Adjusted NPV for each of the project. Which project should be accepted by the company ? Give reasons. 26. The projected cash flows and the Expected net abandonment values for a project are given below: Yea Cash Abandonment r inflows Values 0 (1,00,000 NIL ) 1 35,000 65,000 2 30,000 45,000 3 25,000 20,000 4 20,000 NIL Should the project be abandoned and if so, when ? (Cost of capital may be taken as 10%).