1. F9 Financial Management

2. 2 Designed to give you the knowledge and application of: Section D: Investment appraisal D3. Discounted cash flow (DCF) techniques D4. Allowing for inflation and taxation in DCF

3. 3 Learning Outcomes D3. Discounted cash flow (DCF) techniques  Concepts relating to interest and discounting [2] : i. the relationship between interest rates and inflation, and between real and nominal interest rates ii. the calculation of future values and the application of the annuity formula iii. the calculation of present values, including the present value of an annuity and perpetuity, and the use of discount and annuity tables iv. the time value of money and the role of cost of capital in appraising investments  Calculate net present value and discuss its usefulness as an investment appraisal method. [2]  Calculate internal rate of return and discuss its usefulness as an investment appraisal method. [2]  Discuss the superiority of DCF methods over non-DCF methods. [2]  Discuss the relative merits of NPV and IRR. [2]

4. 4 Compensates the lender for the risk that the borrower may not return the money Nature of interest Money charged by a lender to a borrower Relationship between interest rates and inflation If inflation is prevalent, rates charged on loans increase in order to compensate lenders for this additional factor Concepts relating to interest and discounting Example: Item Wye was priced at $1 on 1 January 20X8 and Peter could have purchased 100,000 Wyes with the given principal amount. Assuming inflation of 5%, the price of the item Wye became $1.05. On 1 January 20X9, he can purchase only 100,000/1.05= 95,238 units with the same amount. In other words, the purchasing power of the amount has been reduced by 100,000 - 95,238 = 4,762 units i. e. around 5%. If Peter wants to retain the purchasing power of the principal amount, he will demand a higher rate of interest to compensate for losses incurred due to inflation (1+ Nominal rate or money rate) = (1+ Real rate) x (1+ Inflation rate)

5. 5 rate of interest charged which does not take inflation into account rate of interest which incorporates the real rate and the inflation rate Real rateNominal / money rate (1 + i) = (1+r) (1+h) Relationship Example Peter lends $100,000 to Robert on 1 January 2008 who is to return this after 1 year with 8% interest. After one year, Robert returns $100,000 + interest of $8,000. If Peter wants to retain the purchasing power of the principal amount, he will demand a higher rate of interest to compensate for losses incurred due to inflation. (1+i) = (1 + 0.08) (1+0.05) Thus, i = (1.08)(1.05) – 1 I = 13.4% Real & Nominal interest rate

6. 6 value at a future date, of an amount invested today at a particular simple or compound interest rate Future value Simple interest interest will be earned only on the principal amount and no interest is paid on accrued interest Example $100,000 is lent for 4 years at simple interest of 10%. Interest is equal to 100,000 x 10% =10,000 per year. The total interest is equal to 10,000 x 4 = 40,000. The future value of the initial investment of $100,000 is $140,000 Compound interest interest is paid on the original principal amount plus accrued interest; interest earns interest FV=PV (1+r) n Calculated using  Simple interest  Compound interest  Frequent compounding  Annuity Future Value Continued …

7. 7 146,41013,310133,1004 12,100121,0003 11,000110,0002 10,000100,0001 Closing balance 10% interest for the year Opening balance Year No. Example $100,000 is lent for 4 years at compound interest of 10%. The future value after 4 years will be $146,410. Note that this is higher than the future value, based on simple interest calculated earlier, which was $140,000. This is because interest compounds upon interest earned. Continued …

8. 8 Annuity if a fixed amount is invested annually, at a fixed interest rate a constant flow of cash that occurs annually Example An amount of $100,000 is invested at the beginning of each year for 3 years @10% interest. Find out the value of the total investments at the end of the third year. FV = 100,000 x ( (1+ 0.10) 3+1 -1) -100,0000 0.10 = 100,000 x (1.4641-1) -100,000 0.10 = 100,000 x 4.641- 100,000 = 464,100 - 100,000 = 364,100 Annuity Continued …

9. 9 Example $100,000 is lent for 4 years at a yearly compound interest of 10%. The compounding of interest is done semi-annually. With half yearly compounding, the future value will be calculated as follows: Interest rate for half year is 10/2 = 5% Number of periods in half years = 4 x 2 =8 FV = $100,000 x (1+ 0.05) 8 = $100,000 x (1.05) 8 = $100,000 x 1.477455 = $147,745.5 Frequent compounding If compounding is done more frequently, then the future value will be higher r FV () 2 + 1 PV= 2×n Continue …

10. 10 Year 0 Year 5 (PV) (FV) $100 $161 Discounting Year 0 Year 5 (PV) (FV) $100 $161 Compounding $100 invested today at a rate of 10% for 5 years PV = $100 FV = $100 x (1.1) 5 = $161 161 to be received in 5 years. Rate of interest is 10%. FV = $161 $161 = $161 x 0.621 = $99.9 (approx $100) First present value is calculated and found out the future value by adding on or compounding interest Compounding Interest is deducted from the future value in order to ascertain the present value Discounting vs Calculation of present values

11. 11 Perpetuity the annuity that is to be received or paid indefinitely into the future Present value of perpetuity = A/r Where, A = amount of perpetuity r = rate of discounting (expressed as a decimal) Time value of money amount of money will have different values at different times value of money depends on the time of transaction amount to be received today is considered better than the same amount to be received after 1 year Reasons for preference of time value of money Inflation: reduces the purchasing power of money Risk: amount may not be received in full or not received at all Time: the amount can be invested to earn income Perpetuity & Time value of money

12. 12 Cost of capital Cost associated with source of capital It may be actual interest paid or an opportunity cost Discussed in Section F Role of cost of capital in appraising investments a company expects returns higher than or equal to the cost of capital Example Wellpack Co’s average cost of capital is 8%. It receives two alternative investment proposals. One gives a return of 10% and the other 6%. The company will accept the first and reject the second proposal. The company cannot afford to pay a cost of capital of 8% if it earns only 6% by investing the same amount in the business. Cost of Capital

13. 13 Inflows Outflows - = NPV Present value of cash outflows Present value of cash inflows Either +’ve or –’ve or zero depending on what is greater (inflow or outflow) Net Present Value (NPV) difference between the amount of initial investment and the sum of the discounted cash flows which the investment is predicted to generate. NPV = Present value of cash inflows - Present value of cash outflows Calculate net present value (NPV) and discuss its usefulness as an investment appraisal method.

14. 14 Steps for calculation of NPV 1 Determine the total cash outflow of the project & the time periods in which outflows & inflows occur 2 Compute the total discounted cash outflow (cash outflow x present value factor) 3 Determine the total discounted cash inflow of the project and the time periods in which outflows & inflows occur 4 Compute the total discounted cash inflow (cash inflow x present value factor) 5 Compute NPV by subtracting the discounted cash inflows (step 4) from the discounted cash outflows (step 2) Accept / reject criterion NPV > Zero ACCEPT the investment proposal NPV = Zero Investment proposal may be accepted NPV < Zero REJECT the investment proposal

15. 15 Example A cash payment of $60,000 on 1 January 2008 will be occurred in 2007, for the purpose of cash flow discounting. Timing assumptions or conventions  Initial cash outlay is incurred at the beginning of the first period.  Any transaction during a period is assumed to occur at the end of the period.  Cash flows occurring at the beginning of a year are assumed to have occurred in the previous year for discounting purposes only. Rate of discount Depends on the targeted rate of return that is more than or equal to the cost of capital Re-investment rate assumption Cash flows generated during the life of the project can be reinvested elsewhere at a rate equal to the cost of capital. Cash Flow Continued …

16. 16 25,470NPV 25,470 32,0400.71245,0003 39,8500.79750,0002 53,5800.89360,0001 (100,000)1.000(100,000)0 Present value ($)Discounting factorCash flow ($)Year Example The financial manager of Fairloss Ltd is considering the purchase of equipment costing $100,000. The equipment is expected to result in an annual cash inflow of $60,000, $50,000 and $45,000 in years 1, 2, and 3 respectively. Using the NPV method, advise the financial manager whether the equipment is worth buying. Assume the cost of capital as 12%. Since the project’s NPV is positive $25,470 it should be accepted. The positive NPV equates to a net cash inflow which would add to shareholder wealth. Continued …

17. 17 Internal Rate of Return (IRR) It is the required rate of return or cost of capital which produces a NPV of zero when used to discount the project’s cash flows. Situations for the calculation of IRR When the project cash inflows are identical When the project cash inflows are not identical Calculate internal rate of return (IRR) and discuss its usefulness as an investment appraisal method.

18. 18 Calculation of IRR when the project cash inflows are identical  Divide the cash outflow by the annual cash inflow. The result is called ‘factor’ or ‘payback’.  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.  If the IRR is greater than or equal to the minimum desired rate of return, the investment project should be accepted. If the IRR is less than the desired rate of return, the project should be rejected. Example Strilco is considering an investment proposal with an initial investment outlay of $6,000. It expects the annual cash inflow to be $1,450 in the next 6 years. Calculate the IRR for the project. Continued …

19. 19 Answer Strilco has an identical cash inflow of $1,450 for six years consecutively. It uses the cumulative present value factors table to calculate the IRR. In this case, the inflows are identical. Therefore, we can use the cumulative present value factors table. As we know, IRR represents the rate where NPV is nil. Therefore, ($1,450 x CPVFr,6) - $6,000 = 0 Where CPVFr,6 is the cumulative present value factor for 6 years, and r is IRR. CPVFr,6 = 6,000/1,450 = 4.137931 Looking at the cumulative present value factors table and checking the row for 6 years, we find that the value of 4.111 which is the nearest to 4.137, appears in the column of 12%. Therefore, we can conclude that the internal rate of return is approximately 12%. Continued …

20. 20 Where a is lower of two rates of return used b is higher of 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  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).

21. 21 Answer When we take the discounting factor as 20%, we get a negative NPV of $1,011. Hence we reduce the discounting factor to 15% resulting in a positive NPV of $209. 209 (1,011) NPV 3,9510.6593,4680.5786,0003 5,2980.7574,8570.6947,0002 6,9600.8706,6640.8338,0001 (16,000)1 1 0 Present value15% PV factorsPresent value20% PV factorsCash flowPeriod The following table gives the details of a project proposed by Perk Co, project M. Calculate the internal rate of return for project M of Perk Co. 6,0003 7,0002 8,0001 (16,000)0 Cash flowPeriod Example Continued …

22. 22 Where. a is lower of two rates of return used b is higher of two rates used A is NPV obtained using rate a B is NPV obtained using rate b IRR: 209 = 15 + ----------------- x (20 -15) % 209 - (-1011) 209 = 15 + -------------------- x 5% 1,220 = 15 + 0.1713 x 5% = 15.01% Continued …

23. 23 Decision Rule Rule is to accept all the independent projects with positive NPV or competing projects with highest NPV NPVIRR Accept all independent projects where IRR is greater than the company’s cost of capital or target rate of return DCF techniques are considered superior to Non-DCF techniques because they account for Time value of money Uncertainty factor Timing of cash flows Superiority of Discounted Cash Flow methods over non-discounted Cash Flow methods DCF & Non- DCF Techniques

24. 24 Merits depending upon the kind of project Both methods can be used for single project with conventional cash flows NPV is more suitable for non- conventional cash flows For mutually exclusive projects preference should be given to NPV NPV accommodate the changes in discount rates that occurs during the life of a projects Relative merits of NPV and IRR  IRR method uses percentage terms hence ignores the relative size of the project  IRR is easier to understand, especially for non-financial managers  NPV assumes that cash flow generated during the life of a project can be reinvested elsewhere at a rate equal to the cost of capital where as in case of IRR the rate of return should be equal to IRR General Refer to Example (page 183)

25. 25 Recap  Concepts relating to interest and discounting [2] : i. the relationship between interest rates and inflation, and between real and nominal interest rates ii. the calculation of future values and the application of the annuity formula iii. the calculation of present values, including the present value of an annuity and perpetuity, and the use of discount and annuity tables iv. the time value of money and the role of cost of capital in appraising investments  Calculate net present value and discuss its usefulness as an investment appraisal method. [2]  Calculate internal rate of return and discuss its usefulness as an investment appraisal method. [2]  Discuss the superiority of DCF methods over non-DCF methods. [2]  Discuss the relative merits of NPV and IRR. [2]

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