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Basic Senior Year Financial Questions

The cost of capital and the tax rate are 12% and 30% respectively. Required: The net present value (NPV) of the investment Solution: (a) Project appraisal $ ‘000’ Year 0 1 2 3 4 5 Inflows - 800 750 900 1,200 1,100 Outflows - (65) (80) (50) (55) (70) Depreciation - (280) (280) (280) (280) (280) Inflow before tax - 455 390 670 865 750 Less tax @ 30% - (136.5) (117) (201) (259.5) (225) + dep. Back - 280 280 280 280 280 Cash flows - 598.5 553 749 885.5 805 I0 (1,400) - - - - - (1,400 598.5 553 749 885.5 805 PVIF 12%n 1.000 0.893 0.797 0.712 0.636 0.567 P.V (1,400) 534.5 440.7 533.3 563.2 456.4 Overall NPV = 1,128.1 The decision rule for NPV for accepting the project Under this method, a company should accept an investment venture if N.P.V. is positive i.e. if the present value of cash outflows exceeds that of cash inflows or at least is equal to zero (NPV ?0). This will rank project ventures giving the uppermost rank to that particular venture with highest NPV because this will give the maximum cash inflow or capital gain to the company. Net present value recognizes time value of money and such appreciates that a shilling now is more valuable than a shilling tomorrow and the two can only be compared if they are at their present value. Internal rate of return (IRR) This is another modern method of discounting cash flow because the technique uses the principle of NPV. It is defined as the rate which the present value of cash outflows of an investment equates the initial capital invested. IRR = Pv (cash inflows) = Pv (cash outflows) or IRR is the cost of capital when NPV = 0. It is also called internal rate of return because it depends wholly on the outlay of investment and proceeds associated with the project and not a rate determined outside the venture. A = inflow for each period C = Cost of investment The value r can be found by: i) Trial and error ii) By interpolation iii) By extrapolation i) Trial and error method a) Select any rate of interest at random and use it to compute NPV of cash inflows. b) If rate chosen produces NPV lower than the cost, choose a lower rate. c) If the rate chosen in (a) above gives NPV greater than the cost, choose a higher rate. Continue the process until the NPV is equal to zero and that will be the IRR. Example A project costs 16,200/= and is expected to generate the following inflows: $ Year 1 8,000 Year 2 7,000 Year 3 6,000 Compute the IRR of this venture. Solution 1st choice 10% = 17,565.74 > cost, choose a higher rate. 2nd choice 14% = 16,453.646 3rd choice 15% = 16,194.625 IRR lies between 14% and 15%. ii) Interpolation method Difference PV at rate of 14% = 16,453.646 253.646 PV required = 16,200.000 -5.375 PV at rate of 15% = 16,194.625 Therefore, r denotes required rate of return Therefore, r = 14% + (15% - 14%) x = 14% + 0.98% = 14.98% The acceptance rule of Internal Rate of Return (IRR) IRR will accept a venture if its IRR is higher than or equal to the minimum required rate of return which is usually the cost of finance also known as the cut off rate or hurdle rate, and in this case IRR will be the highest rate of interest a firm would be ready to pay to finance a project using borrowed funds and without being financially worse off by paying back the loan (the principal and accrued interest) out of the cash flows generated by that project. Thus,
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