Capital Investment The amount of cash or cash equivalents paid or the fair value of the other consideration given to acquire the asset. Fair value is the amount for which an asset could be exchanged between knowledgeable willing partners in an arm’s-length transaction. Expenditure that increases an asset’s capacity or efficiency or extend its useful life are called Capital Expenditure . Example: the costs of installation of factory machinery. Expenditures that do not extend an asset’s capacity but merely maintain the asset in its working order are classified as Revenue Expense . These costs are expenses and are immediately matched against revenue. Example: the costs of replacing a flat tyre of a company car. Determining which costs to include in the asset account and which costs not to include is very important. If a cost is not included in an asset account, then it must be expensed immediately. This distinction is important because it has immediate implication for the profit.
Capital Investment Appraisal Example: Proctor Hedges Limited This company has 2 machines with the purchase price (capital outlay) and depreciation schedule as follows.
However, these 2 machines have maximum capacity: Machine A – 40 000 units per year Machine B – 60 000 units per year Also, the company forecasts the market demand over the future 5 years. The forecasted production schedule hence is as follows. Forecasted production
Forecasted sales With the forecasted production figures, we then can estimate the profit projections.
Forecasted profits However, we must deduct depreciation from each of the annual profit figures calculated earlier, before calculating the average profit.
Average Expected Return The accounting rate of return (ARR) method uses projections of accounting profit to calculate the expected rate of return on capital invested into an asset or project.
Average Capital Employed Next, we calculate average capital employed . We take initial capital employed (at Time 0) and capital employed by the end of the final year of operation (Time 5) and average the two figures, as follows:
Accounting Rate of Return We now have both elements necessary for the calculation (average accounting profit and average capital employed) of ARR. The ARR calculation shows Machine A as the better of the two options. Although Machine B is estimated to produce more profit, the average investment is considerably higher.
The Time Value of Money The principle of the time value of money rests on the observation that, because of interest. At a constant rate of 10%, $1 invested now (at Time 0) is the equivalent of $1.61 = 1*(1+0.1) 5 by the end of year 5. Conversely, we could say that $1.61 at the end of year 5 is the equivalent of $1 now. In order to have $1.61 at the end of year 5 we would need to invest $1 now. How can this be expressed in a formula?
Net Present Value NPV is a method of investment appraisal that uses the technique of discounting in order to express all future estimated cash flows in the same terms. It takes into account the time value of money and ensures that the appraisal compares like with like. Machine A
Net Present Value Machine B NPV>0 indicates a project is acceptable. However, if we must choose between projects, we should invest in the project with the largest NPV. In this case, Machine B is preferable to Machine A.
Internal Rate of Return The IRR of an investment or project is the expected yield (expressed as a percentage). IRR is the discount rate, which, applied to expected cash flows, produces an NPV of Zero . Machine A: calculate NPV at various rates The internal rate of return lies somewhere between 18% and 20%.
Internal Rate of Return
Internal Rate of Return Linear Interpolation IRR of Machine A is 18% + 1.54% = 19.54% Note: IRR for Machine B is 17.68%
Comparison of the Investment Appraisal Techniques ARR is calculated on accounting profits. This methods is straightforward and popular method. However, it takes no account of the time value of money. NPV and IRR are calculated cash flow. These methods are supposedly more accurate as it takes the time value of money into calculations. However, it is challenging in determining an appropriate discount rate. It might be less intuitive and difficult to explain to non-financial managers
Expected Return and Volatility When there are S possible scenarios, the expected return is and volatility of stock, estimated as the standard deviation of return is , where Example: Suppose a company’s stock performance depends on economy state. What are the expected return and standard deviation of return of this company’s stock? E(r) = 0.3*0.15+0.5*0.1+0.2*0.05 = 10.5%. SD(r) = [0.3*(0.15-0.105)^2+0.5*(0.1-0.105)^2+0.2*(0.05-0.105)^2]^0.5 = 3.5%. Economy State (s) Probability (p(s)) Return (r(s)) Boom 30% 15% Normal 50% 10% Recession 20% 5%
Frequency distributions of annual HPRs, 1926-2008
Use CAPM: where E(R i ) is the cost of equity . We may find estimates for the following parameters: R f : Australia cash rate (one-year short rate) E(R m ) : Annual return of ASX200 index in previous year : Available in DatAnalysis via MQ Library or Yahoo Finance Estimate Cost of Equity 19
WACC The weighted average cost of capital (WACC) is the rate that a company is expected to pay on average to all its security holders to finance its assets. The WACC is commonly referred to as the firm's cost of capital , i.e. the discount rate used in NPV. The formula of WACC is: where D is total debt, r D is the cost of debt, E is total equity, and r E is the cost of equity. Estimate r D : One can find the average bond yield of the bonds having the same credit rating.