Calculations in Finance: IRR, ARR, Payback and NPV - Essay Example

Topic:  Calculations in finance and an essay. Please see to the questions and on the the Instructions box. Instructions Press plchas identified that it could make operating cost savings in production by buying a new piece of machinery. There are two suitable pieces of machinery on the market, the Excel and the Super. The discount rate is 12%. The cash flows relating to Excel and Super are as follows: Excel Super £ £ Year 0 -20,000 -25,000 Year 1 4,000 8,000 Year 2 6,000 6,000 Year 3 6,000 5,000 Year 4 7,000 6,000 Year 5 6,000 8,000 Required: (i) Calculate the Net Present Value (NPV) of Excel and Super; Excel: £(380.51) Super: £(2,086.21) (ii) Which, if either, of these machines should be purchased? Why? Neither, at this discount rate, as both lose money. What is not included is the salvage value, which may push the equation to the positive. 2. The company also diversifies its operations in other areas but is unable to invest more than £470,000 in the current year and has the following projects available to it: Project Initial Investment NPV £ £ A 100,000 15,000 B 150,000 29,000 C 140,000 31,000 D 210,000 22,000 E 180,000 36,000 Required: (i) Which projects should the firm choose to invest in? Why? By analyzing the ROI, which is total investment/NPV, the projects are ranked from low to high as follows, with the last column being total investment from the highest ROI (project c) to the lowest (project d): Given that there is only 470K available, the highest-ROI projects should be chosen, i.e. project C, E and B in that order. 3. The company has the right to receive £180,000 in 5 years’ time. The market discount rate is 12%. Required: (i) It has also been offered £100,000 if he sells the right to cash now. Is this a fair price and if not why not? This is a fair price, because at the end of 5 years with a discount factor of 12%, the NPV is 94,991.75 (ii) Suppose the company invested the fair price received from the sale of the right in an account with a stated annual interest rate of 12% compounded continuously. What will be its value in 10 years’ time? 310,585 (iii) How much would Press’s investment be worth at the end of 10 years if he invested the fair price received from the right in an account returning 12% per year simple interest? 220,000 4. Essay. Discuss the relationship between the Net Present Value (NPV), Internal Rate of Return (IRR), Accounting Rate of Return (ARR) and Payback Method as methods of project appraisal. Why are these methods used by managers, even when some lag behind in terms of effectiveness? Which one do you prefer and why, give example. IRR, ARR, Payback and NPV All four methods of evaluating investments offer the notion of an investment and a return. The Accounting Rate of Return and Payback method do not offer a time value of money. That is, there is no comparing the opportunity cost, or discount rate, offered by either of the latter systems of evaluation. The first two (NPV and IRR), on the other hand, offer an indication of the time value of money with a notional discount rate, which implies and opportunity cost, or the ability to make alternative investments. The simplest of the four is the Payback Method. Its key benefit is that it is easy to calculate, and lends itself well to cash flow accounting (using the assumption that there is no bank financing). The ease of use comes from the calculation: How much is one investing Divided by How quickly that investment will be paid back (in absolute terms) Thus, under the payback method, if I am investing 100 thousand pounds, and my investment pays me 25 thousand pounds in 4 years, my payback period is 4 years. If, on the other hand, I am paid only 20 thousand pounds per year, I would receive my payback in 5 years. Everything else being held constant, I would clearly prefer the payback in 4 years rather than 5. What this payback method doesn’t do is indicate what happens after the payback. If, for example, I were to receive a lump-sum repayment of my principal (100 thousand pounds) in year 6, then the 5-year payback calculation may be more attractive. The payback method does not offer me a way to evaluate this post-payback element. To use another example, two payback methods could both return my 100 thousand pounds in 4 years: 1 with a payment of 100 thousand pounds in year 4, the other with 99 thousand pounds in year 0 and 1 thousand pounds in year 4. I would clearly prefer the latter, as I would have the use of the 99 thousand pounds for that period of time (and could earn more money through alternative investments). The Accounting Rate of Return calculates as follows: Average profit (not necessarily cash flow) Divided by Average investment This method is easy to calculate, once the profit is known. It does have the advantage of comparing averages—which may be useful in looking at varying investment and return amounts. This formula has two main problems: There is not a direct tie between profit and investment, and cash in and cash out. That means that profit may be higher or lower than actual cash, depending on a series of assumptions. Since, in the end, cash-on-cash is of greatest interest, this makes comparing investments difficult. As with the previous method, when the cash is invested or received is not part of the calculation—therefore, there is no recognition of the time value of money. Cash flow should equal profits over the long term, but the time differences in the receipt of money can make a significant difference in the preferences for the investor. If an investor is counting on receiving cash for retirement, for example, he or she may have less interest in tying up their funds in a profitable company which has poor cash flow. In addition, some businesses have high cash needs, and therefore can show high profits and low cash flow for a long time. This is generally true, for example, with companies quoted on the NYSE or NASDAQ that don’t pay dividends. These companies would argue that they would rather keep the cash in-house in order to reinvest in the business. The accounting rate of return on these businesses may look excellent, but the actual cash back to the investor (not counting equity gains) can be quite poor. The NPV (net present value) method has the advantage of recognizing the time value of money. That is, it recognizes that one pound earned in a year is worth less than one pound in my hand today. The way I calculate the difference is by comparing to other opportunities I have to invest the money. Thus, if I can easily show that I can earn 6 percent in a fairly risk-free investment, that may become my discount rate. Another way to use NPV is to establish a hurdle rate—that is, a rate below which I (arbitrarily) determine that other investments can return better—and therefore will categorically not invest if the NPV-calculated rate (investment at time x, returns at times y) is negative. The issue with NPV is that it relies on a fairly arbitrary rate of return. A fairer way to determine NPV discount rates would be to find a true “opportunity rate,” which is not always easy to do. Also, the discount rate chosen may need to change depending on extraneous circumstances. To take an extreme example, one investment can be in Zimbabwe dollars, while another can be in Swiss Francs. It is not a fair assessment of both investments to use the same discount rate: the discount rate should rather reflect the different risks related to inflation or default. The same is true when looking at stocks with different “betas,” or volatility. The discount rate should be adjusted to reflect those differences; exactly how the discount rate is calculated can be a mystery. The IRR is the most difficult to calculate of the four methods covered here, but it may best reflect the time value of money when comparing alternative investments. IRR assumes both the cost of investment, and the time in which the profits or cash flow comes back. There is an estimate of a discount rate in calculating IRR, which makes it more complex to calculate. IRR is particularly helpful where there is a relatively short time horizon on the investment capital. That is why IRR is used by Venture Capitalists and Hedge Fund managers alike. IRR allows limited partners to evaluate performance across VC and HF sectors with an easy number (Campbell 2003). One of the issues in evaluating IRR in the venture industry is that the final number cannot be calculated until all investment returns are in; on the other hand, the highly progressive nature of the IRR calculation means that beyond years 5 or 6, further returns are relatively negligible in the IRR rankings. IRR also has the problem that it does not respond to the amount of capital invested. This can be a particular problem, for example, at a large venture firm which may have had several relatively small investments pay off well, with high IRR’s. Since venture firms call down capital as needed to fund their next investments, the IRR on invested capital can therefore be very high. To take an extreme example: a $1 billion venture fund has called down $100 million, invested $50 million, and had two liquidity events within 1 year which returned a total of $100 million. The IRR on capital invested is therefore 200%, while the IRR on capital called is 100%. This does not mean, however, that the entire fund has enjoyed a 200% or 100% IRR; this just means that the immediate amount of capital invested has made those returns. The problem is that venture capitalists raise capital before they’ve fully invested their previous commitments, and well before the liquidity events have or have not taken place. The net result is that, if the venture fund wants to play games, they can make a few, small late-stage investments in firms close to IPO or sale, and realize a high nominal IRR without necessarily realizing a high actual IRR over the lifetime of the Fund. Bibliography Campbell, HF, Brown, RP. Benefit-Cost Analysis: Financial and Economic Appraisal Using Spreadsheets. Cambridge: Cambridge University Press, 2003. Appendix: From Excel Worksheet Read More