# Project Appraisal And Risk

PROJECT APPRAISAL AND RISK
Q1. Risk & Uncertainty is an important part to be considered before any projects investment appraisal. Select the appropriate option which relates to either Risk or Uncertainty. (HA)It is Quantifiable RISK UNCERTAINTYIncreases as the projects life increases RISK UNCERTAINTYIt is difficult to assign probabilities RISK UNCERTAINTYIncreases as the variability of returns increases RISK UNCERTAINTY(2 marks)
Q2. Cipher Co. plans to buy a new machine which will produce expected sales of 110,000 units per year. Each unit can be sold for \$15 per unit. The project is expected to last for five years. The project NPV is \$1780. The company profit tax one year in arrears at an annual rate of 30% per year. Calculate the sensitivity of the new machine to a change in selling price using the cost of capital of 11%.4%4.4%4.7%5%(2 marks)

Q3. Calculate the sensitivity of selling price? The following information to be used:Investment in Year 0 \$30,000, Sales volume 200 units per annum each costing \$200, Variable cost \$50/unit & Total Fixed cost \$6000 per annum. The project life is estimated to be three years with the cost of capital of 10%. (MCQ)30.5%29.8%25%15%(2 marks)
Q4. Select the appropriate strength & weaknesses for sensitivity analysis according to the statements. (HA)It identifies crucial areas for the success of the project STRENGTH WEAKNESSIt provides information which allows management to make subjective judgments STRENGTH WEAKNESSIt is not an optimizing technique STRENGTH WEAKNESSIt assumes that changes to variables can be made independently STRENGTH WEAKNESS(2 marks)
Q5. Calculate the sensitivity of contribution? The following information to be used:Investment in Year 0 \$60,000, Sales volume 600 units per annum each costing \$125, Variable cost \$10/unit & Total Fixed cost \$4000 per annum, the Tax rate is 20% will only be applicable on taxable cash flows & capital allowances are to be ignored. The project life is estimated to be two years with the cost of capital of 8%. (MCQ)45.4%41.8%33.2%30.6%(2 marks)
Q6. Dmitri is contemplating purchasing a machine for \$275,000 which he will use to produce 50,000 units per year for five years. These products selling price is \$10/unit and variable costs are expected to be \$6/unit. Incremental fixed costs will be \$70,000 every year for production & \$25,000 every year for selling and distribution. Petra has a required rate of return of 10% per annum. By how many units must the estimate of production and sale volume fall for the project to be regarded as not worthwhile? (MCQ)2,8756,4658,11512,315(2 marks)
Q7. Zulu Co. is considering to invest in a project costing \$20,000, the amount is payable at the start of the first year of operation. The estimated future cash flows & its probabilities are given below: Year 1 The present value of cash flow (\$) Probabilities17,500 0.7211,700 0.2(5,000) 0.08Year 2The present value of cash flow (\$) Probabilities23,000 0.65(3,500) 0.35Calculate the total expected value? (MCQ) \$23,700\$14,540\$13,725\$8,265(2 marks)
Q8. An individual uses expected value on the assumption to (MCQ)Reduce risk for a given level of returnMaximize return for a given level of riskReduce risk irrespective of the level of returnMaximize return irrespective of the level of risk(2 marks)
Q9. Which of the following TWO are disadvantages of Expected value? (MRQ)Relatively simple calculationIgnores variability of payoffsDeals with multiple outcomesThe answer is only a long-run average (2 marks)
Q10. “Using mathematical models, it produces a distribution of the possible outcomes from the project using multiple uncertain variables.” Choose the appropriate Technique. (MCQ)SimulationRisk-adjusted discount ratesAdjusted paybackExpected value(2 marks)
Q1. It is Quantifiable RISK Increases as the projects life increases UNCERTAINTYIt is difficult to assign probabilities UNCERTAINTYIncreases as the variability of returns increases RISK
Q2. ASelling Price = 110,000 × \$15 = \$165, 0000Annuity Factor 11% (1 – 5 years) = 3.696Annuity Factor 11% (1 – 6 years) = 4.231Discount Factor 11% (Year 1) = 0.901Annuity Factor 11% (2 – 6 years) = 4.231 – 0.901 = 3.33Year 1-5 Tax rate Year 2-6 Cash flow 1650,000 × 30% 495,000 × × Annuity 3.696 3.33 Selling Price after tax 6098,400 – 164,8350 445,0050Sensitivity = (1,780 ÷ 445, 50050) × 100 = 4%
Q3. Years Cash flow (\$) Discount Factor (10%) Present value (\$)Investment 0 (30,000) 1 (30,000)Sales Revenue 1-3 40,000 2.487 99,480Variable Cost 1-3 (10,000) 2.487 (24,870)Fixed Cost 1-3 (6,000) 2.487 (14,922)NPV 29,688Selling Price = (29,688 ÷ 99,480) × 100 = 29.8%
Q4. It identifies crucial areas for the success of the project STRENGTH It provides information which allows management to make subjective judgments STRENGTH It is not an optimizing technique WEAKNESSIt assumes that changes to variables can be made independently WEAKNESSInformation will be presented to management in a form which facilitates subjective judgment to decide the likelihood of the various possible outcomes considered.It is not an optimizing technique. It does not point directly to the correct decision.It assumes that changes to variables can be made independently, e.g. raw material costs will change independently of other variables. This is highly unlikely.
Q5. CYears Cash flow (\$) Discount Factor (8%) Present value (\$) After Tax Present value (\$) Investment 0 (60,000) 1 (60,000) (60,000)Sales Revenue 1-2 75,000 1.783 133,725 106,980Variable Cost 1-2 (6,000) 1.783 (10,698) (8,558)Fixed Cost 1-2 (4,000) 1.783 (7,132) (5,706)NPV 55,895 32,716Contribution = (32,716 ÷ [106,980 – 8,558]) × 100 = 33.2%
Q6. CYear Cash flow (\$) Discount factor (10%) Present Value (\$)Machine 0 (275,000) 1 (275,000)Contribution 1-5 200,000 3.791 758,200Fixed cost 1-5 (95,000) 3.791 (360,145)NPV 123,055PV of contribution must fall by \$123,055 Sales volume must fall by \$123,055 ÷ 758,200 = 16.23% Fall in sales volume = 0.1623 × 50,000 = 8,115
Q7. DYear 1 Present value of cash flow (\$) Probabilities Expected value (\$)17,500 0.72 12,60011,700 0.2 2,340(5,000) 0.08 (400)14,540Year 2The present value of cash flow (\$) Probabilities Expected value (\$)23,000 0.65 14,950(3,500) 0.35 (1,225)13,725(14,540 + 13,725) – 20,000 = 8,265
Q8. DThe Expected Value is the weighted average of all the possible outcomes, with the weightings based on the probability estimates. This is specifically used to maximize the shareholder’s wealth exclusive of any risk assumptions.
Q10. AThe simulation uses a mathematical model, it produces a distribution of the possible outcomes from the project using multiple uncertain variables.

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