Net Working Capital Current Assets Current Liabilities (Equ. 1–3) The amount of net working capital is a measure of whether a company can pay its bills when they become due. By "wiping out" the effect of financing, the results become more comparable from year to year for a given company and more comparable between companies in the same industry. Think of the present value formula as sandpaper, removing the earnings value.
The par value of the bond is its future value under most circumstances. When calculating yield to maturity, this is the par value of the bond. The interest rate that balances the present value of the inflows and outflows with the amount financed is the imputed interest rate for the lease.
Generally, the cost of capital is discussed in terms of the weighted average cost of capital, WACC. The cost of capital for preferred stock is simply the dividend divided by the par value of the stock. Ks is the cost of existing common equity Pn is the price of the security.
Suppose a $31 share was being issued; flotation costs as a percentage of share price were 9.6%; the cost of retained earnings according to CAPM methods and bond yield was 14.1% and 16%, respectively. Equation 9–10 is the most general form of the weighted average cost of capital equation.
Since test1 and test2 are cash outflow brackets, we can conclude that we have bracketed the "actual" IRR. If the NPV is zero, we know our IRR is correct because IRR is, by definition, the discount rate that makes the NPV zero. Since there are no tables for 20.247%, it would be impossible to do this proof without the present value formula discussed in Chapter 5 and given in Eq.
The accuracy of the calculation of the internal rate of return can be further improved if necessary by (1) using the present value formula for the calculation of test1 and test2 and increasing the number of decimal places in the calculation above the number in the tables; (2) choosing IRR1 and IRR2 closer to the "real" value of the internal rate of return, which we have already estimated fairly accurately. Recall that interpolation is based on a computational trick that says that the slopes of the lines between them are almost exactly the same if the points on the curve are quite close. Calculations of the internal rate of return can be made from the spreadsheet, as well as an analysis of variance to determine whether the chosen IRR1 and IRR2 were close enough to the actual IRR to converge to the answer with the required degree of accuracy.
Projects with the highest internal rate of return rank higher than projects with a lower IRR. Projects with an IRR greater than the cost of capital should be considered for financing. The advantage of internal rate of return is that it is directly comparable to competing uses of funds.
The IRR can be compared with the yield of stocks and bonds, and with the yield of other projects. It can also be used to determine the optimal capital budget by ranking projects in terms of their IRR and comparing them to the marginal cost of capital. MODIFIED INTERNAL RATE OF RETURN (MIRR) In certain circumstances, when there is more than one cash outflow (investment), IRR can provide multiple solutions.
The IRR is used to find the discount rate that will make the present value of the cash inflows equal to the present value of the cash outflows. The MIRR is the discount rate that, when applied to all cash flows other than the initial investment, makes the net present value zero. What is the future value of all cash inflows and outflows at the end of the project in year 3 (not including the initial investment).
The calculus trick is to say that the slope of the line between our two test inputs and outputs is almost equal to the slope of the line between the point defined by one test input and its output on the one hand, and the point that between a known value, for example the market value of a bond or the amount of an investment, and the input we are trying to determine. Our interpolation trick can be used for almost any function with the following conditions: the function is continuous, and the selected test input is reasonably close to the actual input we are trying to determine. The quality of the solution can be determined by subtracting the output of the proof from the known value and dividing the difference by the known value.
If the resulting variance is unacceptably large, use the solution of the interpolation as a test input and repeat the algorithm. If it is zero or negative, it will not increase shareholder wealth and should be rejected. This discount rate is also the return on a project and can be directly compared to the cost of capital and alternative investments.
Interpolation can be used to estimate IRR and MIRR to any degree of accuracy desired. The degree of precision in an estimate can be determined by using the IRR or MIRR estimate in the NPV equation to determine whether the result is zero. If this is not the case, the variance, or relative degree of error, can be measured by dividing the calculated NPV by the investment.
If the variance is too large, other test IRRs and MIRRs can be used to calculate new, more precise estimates of IRR and MIRR, respectively. It is a forward-looking process, and little weight is given to anything that happened before the date on which budget decisions are made. Cash that will flow into or out of the company whether or not the project is undertaken is irrelevant.
Sunk Costs: Expenses incurred prior to the capital budget decision, known as sunk costs, never are. For example, if a project can be built on a foundation that already exists, it will indirectly influence the capital budget decision by reducing future costs. For example, if a truck already owned by the company can be sold for $20,000 or used in an investment project, the market value of the truck should be charged to the project.
