1. P4 Advanced Investment Appraisal

2. 2 2 Section C: Advanced Investment Appraisal C1. Discounted cash flow techniques and the use of free cash flows. C2. Application of option pricing theory in investment decisions. C3. Impact of financing on investment decisions and adjusted present values. Designed to give you the knowledge and application of:

3. 3  Capital Investment Appraisal using NPV  Capital Investment Appraisal using IRR & MIRR  Forecast a company’s free cash flow and its free cash flow to equity (pre and post capital reinvestment).  Specified capital investment programme, on a firm's current and projected dividend capacity. [3]  Value of a firm using its free cash flow and free cash flow to equity under alternative horizon and growth assumptions. [3]  Application of Monte Carlo simulation to investment appraisal. Demonstrate an understanding of: i. simple model design ii. types of distribution controlling the key variables within the simulation iii. simulation output and assessment of the likelihood of project success iv. measurement and interpretation of project value at risk C1: Discounted cash flow technique and the use of free cash flows Learning Outcomes

4. 4 Cash flow (CF) analysis & free cash flow concept Important in investment analysis Estimation of CF Profitability of investment projects determined by evaluating CF Free cash flows of firm (FCFF)  FCFF are the cash inflows, net of capital expenditure  CF available to service shareholders and lenders  CF should be discounted to ascertain a project’s NPV Free cash flow = Revenues – Operating – Taxation – Capital + Depreciation and +/- Changes in of Firm (FCFF) expenditure expenditure Amortisation working capital

5. 5 Accept / Reject criteria for a project NPV > Zero Accept Investment NPV = Zero May Accept Investment NPV < Zero Reject Investment NPV = Present value of cash inflows less Present value of cash outflows Net present value (NPV) A positive NPV would indicate a potential increase in the value added to the firm if a specified project or portfolio of projects is undertaken.

6. 6 The local tax laws define the period the tax flows relate to 3. Timing Taxation effects of the relevant cash flows Capital allowances tax relief on disposal Disposal of assets loss on disposal allowable against profits resulting in tax savings shown as cash inflows profit on disposal tax payment Balancing allowance / charge 2. Capital cash flows reduce profits, resulting in tax savings shown as cash inflows Revenues (inflows) Expenses (outflows) Refers to revenue expenditure or income affecting operating profit increase profits, resulting in tax increases shown as cash outflows 1. Operating cash flows

7. 7 Linear programming approach to multi- period capital rationing Linear programming (LP) is a mathematical technique used to arrive at the optimal production plan & optimal resource allocation with an objective of cost minimisation and profit maximisation. Multi-period capital rationing arises when there is more than one cash outflow and these cash outflows arise in different time periods for different projects.  Firm objective is to choose that package of projects which gives the maximum total NPV subject to the capital constraints.  As the number of alternatives and constraints increase, the decision-making process becomes more complex.  Use of a mathematical programming method is recommended.

8. 8 Internal rate of return (IRR) Situations for the calculation of IRR When the project cash inflows are identical When the project cash inflows are not identical Internal Rate of Return (IRR) It is the required rate of return or cost of capital which produces an NPV of zero when used to discount the project’s cash flows. Present value of cash inflows = present value of cash outflows Continued …

9. 9 Calculation of IRR when the project cash inflows are identical Criteria: IRR ≥ minimum desired rate of return, the investment project should be accepted. IRR < desired rate of return, the project should be rejected. Factor / Payback = cash outflow. annual cash inflow Go across the row of the year (equivalent to the life of the project) of the table of cumulative present values and find the closest figure to the factor as calculated above The corresponding rate of that figure is the IRR Continued …

10. 10 Calculation of IRR when the project cash inflows are not identical  In such a situation, the interpolation method is to be used.  The NPV at two discount rates will be required (preferably a positive and negative NPV). Where a is lower of the two rates of return used b is higher of the two rates used A is NPV obtained using rate a B is NPV obtained using rate b Calculation of IRR when the project cash inflows are not identical

11. 11 Modified internal rate of return (MIRR) Modified Internal Rate of Return (IRR) Discount rate that equates present value of the terminal cash inflow to the initial investment in year zero n Terminal Value = ∑ CF t (1+r) n-t T=0 n Terminal value of cash flows MIRR = ---------------------------------------------------- 1 Present value of investment outlay 1 2 Calculate terminal value of project cash flows using reinvestment rate / cost of capital Find discount rate that equates terminal value to initial investment outlay 3 Discount rate is IRR

12. 12 Free cash flow of equity (FCFE) Free cash flows of equity (FCFE) Cash surplus generated by a firm which is available for reinvestment or redistribution FCFE Net income after taxationX Less: Capital expenditure(X) Add: Depreciation & amortisationX Add: New debts issuedX Less: Debt repayments(X) Add / (Less): Changes in working capitalX Less: Preference dividends paid(X) FCFEX FCFF RevenuesX Less: Operating expenditure(X) Less: TaxationX Less: Capital expenditureX Add: Depreciation & amortisation(X) Add / (Less): Changes in working capitalX FCFFX Refer to Example (page 195)

13. 13 Advise on a specified capital investment programme a firm’s current & projected dividend capacity Excess cash flow after all positive NPV can be:  Distributed in large cash dividends to shareholders  Share purchase schemes; or  Higher level of gearing which increases interest payments and reduces discretionary cash flow Dividends + Equity repurchase Cash to shareholders: FCFE ratio = FCFE Formula Dividends Function of free cash flow to equity (FCFE) Other than FCFE, reasons: future investment requirements, stability requirements, taxation, etc.

14. 14 Valuation of a firm using free cash flow FCFF at constant rate FCFF 0 (1 + g) V o = ------------------------- R e – g Where V o = Value of the firm R e = Expected rate of return g = Expected growth rate Terminal values- FCFF growing at a rate higher than the growth rate of economy Value of a firm is the discounted value of future cash flow available for payment as dividend / for investment n FCFF t Terminal value of business V 0 = ∑ ---------- + ---------------------------------------- T=1 (1 + R e ) t (R e - g) Where R e is the cost of capital (1 + g)

15. 15 Valuation of a firm using free cash flow to equity FCFE at constant rate  Formulae remains same as value of firm.  Use FCFE in place of FCFF Terminal values- FCFE growing at a rate higher than the growth rate Value of equity is the discounted value of future cash flow available for payment as dividend / for investment  Formulae remains same as value of firm.  Use FCFE in place of FCFF Refer to Example (page 197)

16. 16 Monte Carlo simulation Technique of spread sheet simulation Monte Carlo simulation Used to calculate the NPV from a combination of economic variables which affect the NPV calculation Assessment of risk is important & must be incorporated in the investment appraisal process. Cash flows can vary due to risks. Statistical tool of simulation can be applied to measure such risk. Simulation - quantitative procedure used to describe a process by developing a model of that process, and then conducting a series of organised experiments to predict the probable outcome of that process.

17. 17 Steps for adjustments 1. Select on observation from each factor 2. Assign probability values to factors 3. Generate random numbers for each factor 4. Calculate NPV by electing value of each factor corresponding with random number 5. Repeat process several times (process is called iteration) 6. Will generate probability distribution (PD) of NPV 7. Plot PD of NPV on a graph Market factors Operating & fixed cost factors Investment cost factors Continued …

18. 18 Standard deviation Significance of simulation output Expected net present value (ENPV) Used to measure risk of projects Weighted average of returns where probabilities of possible outcomes are used as weights  Process of iterations gives range of outputs.  If number of iterations is large, outputs follow a normal probability distribution.  Normal probability distribution can be used to further analyse the risk in the investment appraisal process.  Normal probability distribution is a symmetric, continuous bell-shaped curve Continued …

19. 19 Project value at risk (project VaR) Project VaR measures the potential loss in the value of a project over a defined period for a given confidence level signifies maximum amount by which the actual NPV of a project will be lower than its expected NPV Used by management in decision making Project VaR = Z x  x T Where: Z is the standard normal variable  is the standard deviation T is the time period over which the value at risk will be calculated. Project VaR can be used by the management of a company to decide whether to accept or reject a particular investment project taking into account the expected NPV and the risk. Usefulness of VaR

20. 20 Recap  Capital Investment Appraisal using NPV  Capital Investment Appraisal using IRR & MIRR  Forecast a company’s free cash flow and its free cash flow to equity (pre and post capital reinvestment).  Specified capital investment programme, on a firm's current and projected dividend capacity. [3]  Value of a firm using its free cash flow and free cash flow to equity under alternative horizon and growth assumptions. [3]  Application of Monte Carlo simulation to investment appraisal. Demonstrate an understanding of: i. simple model design ii. types of distribution controlling the key variables within the simulation iii. simulation output and assessment of the likelihood of project success iv. measurement and interpretation of project value at risk

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