Project Risk Project Risk Project risk is the average risk for the firm. The higher the perceived risk, the more investors will demand as a rate of return (cost of financing). Since the firm is the sum of all projects, the marginal cost of capital (MCC) appropriately captures the risk of the average project. Financing weights do not change due to financing the project. If financing mix for a project is different, it may alter the risk of the firm and thus change financing costs. Specifically, increasing the amount of debt financing should increase the risk of the firm while increasing the amount of equity financing should lower the risk of the firm. Probabilistic Models identify the uncertainty in the project outcomes Marginal Investment Marginal investment opportunity curve A curve representing the internal rate of return on successive inputs of investment Marginal cost of capital cost of capital required for each additional project, (project costs rise after the capital budget of a certain size is reached) Marginal Cost of Capital Cost of another unit of capital. Marginal cost of capital is the cost of adding one additional unit value of fund requirement. Marginal cost of capital (MCC) is defined as the cost of the last monetary value of new capital the firm raises, and the marginal cost rises as more and more capital is raised during a given period. Cost of Capital (Example) Tax rate: 40% Dividend per share: 1.15, Growth rate: 8%, Share price: 23. Cost of Equity = [(1.15 x 1.08)/23] + .08 =13.35% Capital Value Percentage Cost WACC Long term debt 754000000 44.62% 10.00% 6.00% Preferred stock 40000000 2.37% 10.30% 10.30% Equity 896000000 53.02% 13.35% 13.35% Total capital 1690000000 100.00% 10.00% Capital Structure Schedule The firm wants to raise 1 million in new capital, it should obtain 450,000 of debt, 20,000 of preferred stock, and 530,000 of common equity. The debt will have an interest rate of 10% and an after-tax cost of 6%, and the preferred stock will have a cost of 10.3%. The cost of common equity will be 13.35% if retained earnings are used, but it will increase to 14% if it issues new equity. Dividend per share: 1.15, Growth rate: 8%, Share price: 20.5. Change in Cost of Capital Tax rate: 40% Dividend per share: 1.15, Growth rate: 8%, Share price: 20.5. Cost of Equity = [(1.15 x 1.08)/20.5] + .08 =14% Marginal cost of capital (MCC) = 0.34% Capital Value Percentage Cost WACC Long term debt 754000000 44.62% 10.00% 6.00% Preferred stock 40000000 2.37% 10.30% 10.30% Equity 896000000 53.02% 14.00% 14.00% Total capital 1690000000 100.00% 10.34% Marginal Cost of Capital Investment Opportunity Schedule Optimal Investment Capital Budgeting Model Optimal investment budget is where the marginal investment opportunity curve intersects the marginal cost of capital curve Project Risk A situation in which possible future events can have reasonable probabilities assigned. Probabilities can be: a priori obtained by repetition or based on general mathematical principles statistical empirical, based on past events Risk Estimation Project A is expected to generate a continuous compounded return (Average 10% standard deviation 30%). Return is expected to exhibit a normal distribution The probability that the return is more than 15% is 43%** Probability of the return being less than 5% is 31%* **: 1-NORMDIST(0.15,0.10,0.30, TURE) *: NORMDIST(-0.05,0.10,0.30,TRUE) Expected value as a measure of risk Expected value: the average of all possible outcomes weighted by their respective probabilities R = expected value pi = probability of case i n = number of possible outcomes Ri = value in case i i n i R Ri p = = 1 Standard deviation as a measure of risk Risk Adjusted Discount Rates Risk adjustment is made in the denominator of the present-value calculation K = rf + RP K = rf + x (rm rf ) K = risk adjusted discount rate rf = risk-free rate (short-term Treasury securities) RP = risk premium Example rf = 6% rm = 10% = 2.5 K = 6% + [2.5 x (10% - 6%)] = 16% Cost of equity = 16% Economic risk premium RP = 4% Market and Economic risk adjusted cost = 20% Sources of Business Risk Economic conditions Fluctuations in specific industries Competition and technological change Changes in consumer preferences Costs and expense changes (materials, services, labor) Qualitative Risk Assessment Project A: Investment 668,000; 13.7% Project Risk Grade Risk Components Low Medium High Total 1 2 3 4 5 Initial cash outflow 3 Business Recession 5 Project Failure 1 Project Cost Uncertainty 3 Market Risk 3 Environmental Risk 4 Workplace Risk 1 Operational Safety and Security 2 Total 2 2 9 4 5 22 Risk Assessment 2.75 Risk Assessment: Total Grade / Number of items (22/8) Medium: Risk Grade=3 Qualitative Risk Assessment Project B: Investment 458,000; 13.7% Project Risk Grade Risk Components Low Medium High Total 1 2 3 4 5 Initial cash outflow 2 Business Recession 3 Project Failure 3 Project Cost Uncertainty 2 Market Risk 2 Environmental Risk 3 Workplace Risk 1 Operational Safety and Security 2 Total 1 8 9 0 0 18 Risk Assessment 2.25 Risk Assessment: Total Grade / Number of items (18/8) Medium: Risk Grade = 2 Qualitative Risk Assessment (Example) For each risk grade a 10% risk reward Project A Adjusted cost of capital = 16.44% Project B Adjusted Cost of capital = 15.07% Risk Grade 1 2 3 4 5 Risk Reward 1 1.1 1.2 1.3 1.4 Adjusted Cost of Capital 13.70% 15.07% 16.44% 17.81% 19.18% Certainty Equivalent A certain (risk-free) cash flow that would be acceptable as opposed to the expected value of a risky cash flow In the certainty equivalent method, the risk adjustment is made in the numerator of the present-value calculation Political Risk Analysis International projects need to consider political risk. Political risk incorporated in the NPV by adjusting expected project cash flows. Expropriation: States have a sovereign right under international law to take property held by nationals or aliens through nationalization or expropriation for economic, political, social or other reasons. The protection of foreign investors from uncompensated expropriations traditionally has been one of the main guarantees found in international investment agreements (IIAs). Blocked funds: Cash flows generated by foreign projects cannot be immediately repatriated to the parent firm due to capital flow restrictions of the government. Incur transfer pricing that incurs higher expenses for the subsidiary or shift the subsidiary funds to research and development expenditure to generate future revenues. Project Simulation Simulation model of a project to evaluate project outcome Monte Carlo analysis Simulates a models outcome many times to provide a statistical distribution of the calculated results Predict the probability of project completion by a specified date or the probability that the cost will be equal to or less than a certain value Different types of distribution functions applicable for specific projects Steps in Project Simulation Collect the most likely, optimistic, and pessimistic estimates for the variables in the model Determine the probability distribution of each variable Select a random value based on the probability distribution for each variable Run a deterministic analysis based on the model Repeat selection of a random value and run the model several times to obtain the probability distribution of the models results Project Information Assumptions: Price > Cost; Average > Standard deviation Value Measure Variable Value Average Standard deviation Price per unit Price 15.50 15 2 Number Units 2200 2500 300 Production cost per unit Cost 2.50 2.6 0.25 Selling cost per unit Sales cost 1 Annual depreciation Depreciation 2000 Tax rate (%) Tax 40.00% Required rate of return Return 10.00% Cash Flow and NPV Cash flow = [ Units x (Price Cost 1 2000)] tax + Depreciation 2000 NPV =NPV (0.1, Year 1 to 5) + Year 0 Price 15.50 Unit 2200 Cost 2.5 Year tax Cash flow 0 -10000 -10000 1 24400 9760 16640 2 24400 9760 16640 3 24400 9760 16640 4 24400 9760 16640 5 24400 9760 16640 NPV 53079 Simulation NORMINV(RAND(), average, standard deviation) 0.00% 20.00% 40.00% 60.00% 80.00% 100.00% 120.00% 0 5 10 15 20 25 30 Frequency Bin Histogram Frequency Cumulative % Sensitivity Analysis Effects of changing one or more variables on an outcome Determine the impact of tax rate changes on project returns Spreadsheet soft wares perform sensitivity analysis Base Case Scenario Investment in the beginning of Year 1: -100000; Discount rate 8.5% Project sensitivity factors: Units, Sales Price per unit, Cost per unit Base Case Year 1 Year 2 Year 3 Year 4 Year 5.. ..Year 12 Year 13 Year 14 Year 15 Units 1000 1000 1100 1100 1100 1400 1400 1400 1500 Sales Price per unit 11.00 11.00 11.00 12.00 12.00 14.00 15.00 15.00 15.00 Cost per unit 0.16 0.16 0.16 0.18 0.18 0.20 0.20 0.20 0.20 Cash flow 10840 10840 11924 13001 13002 19320 20720 20720 22200 Impact on NPV 0 10000 20000 30000 40000 50000 Units Sales Pice Cost Net Present Value Scenario Sensitivity Analysis NPV Base Case Optimistic Pesimistic Impact on IRR 0.00% 5.00% 10.00% 15.00% 20.00% Units Sales Pice Cost Internal Rate of Return Scenario Sensitivity Analysis IRR Base Case Optimistic Pesimistic Decision Trees A diagram that points out graphically the order in which decisions must be made and compares the value of the various actions that can be undertaken. Decision points are designated with squares on a decision tree. Chance events are designated with circles and are assigned certain probabilities. Example Real Option An opportunity to make changes in some aspects of the project while it is in progress or to adjust even before the project is started Value of the project = NPV + option value Types of options option to vary output option to vary inputs flexibility option to abandon option to postpone option to introduce future products Expansion of Plant Excess capacity with the anticipation of increase in product demand is estimated at 200 million If demand increases, the expansion will be profitable. NPV with expansion option = 1050 million NPV without expansion option = 870 million Real option value of expansion plan = 180 million Real option value < cost of expansion; Expansion plan ought to be rejected! Benefits from software risk management Information Technology Project Management, Ninth Edition., 2019 , Cengage. Business Scenario A firm is considering acquiring a new drilling machine that is expected to be more efficient. The project is to be evaluated over four years. The initial outlay required to get the new machine operating is $675,000. Incremental cash flows associated with the machine are uncertain, hence management estimates the following probabilistic forecast of cash flows by year ($000). Assume a cost of capital at 10%. Determine the projects best and worst NPVs and their probabilities. What are the value and probability of the most likely NPV outcome? Present these results on a probability distribution. Year 1 Prob. Year 2 Prob. Year 3 Prob. Year 4 Prob. 150 0.3 200 0.35 350 0.20 300 0.25 170 0.4 210 0.45 370 0.35 360 0.35 300 0.3 250 0.20 400 0.45 370 0.40