Examination paper on a capital budgeting project


a) the projects net present value is a loss of £2,180,988. The IRR is -7%. The project does not pay back, since the viable lifespan of the project is six years. Therefore, the project as presently constituted is not viable. The initial setup cost for the facility of £12 million represents such a significant upfront cost that the project simply cannot generate sufficient revenue to render it viable.

The first assumption is that the £2 million already spent on product development is not taken into consideration. When examining a capital budgeting project, sunk costs should not be incorporated into the calculation. This is because that money has already been spent, and the decision that management is faced with concerns money that has not yet already been spent. Capital budgeting has a strong future orientation.

The second assumption is with regards to the plant space. The £80,000 of rent that the company would forgo is included in the calculation. An opportunity cost such as this should be included in the calculation. My calculations of the taxes from the project also included the opportunity cost, because that income would have been taxable. In other words, the £80,000 in revenue would have been subject to £24,000 had it been earned. Opportunity cost calculations must be on a net basis, not gross. The other opportunity cost that was included was the potential resale of the equipment. If the project goes ahead, that equipment will not be sold, but will be disposed of later for no value. Therefore that opportunity cost must also be included.

There were also a few items that did not represent cash flows. These items include the depreciation on the £12 million investment and the £50,000 in rent that head office attributed to the project. The rent charged is not a cash flow for the project, since the opportunity cost of not renting that space has already been included in the calculation. That rent, however, affects the after-tax cash flow because it increases expenses, lowering the project’s tax burden. Depreciation expense will also lower the project’s tax burden.

Not included in the calculation was the variable cost of £1.80 per unit. This is the portion of head office costs that has been attributed to the project. This is not counted as a project cash flow, because these costs are not project-specific. They would be paid by the company regardless of whether or not the project proceeded. This also means that they do not represent a project-specific tax benefit, either. The capital budgeting process should ideally incorporate cash flows that are attributable to the project itself.

It was assumed for this project that the 20% of completed goods inventory is attributed to the year in which the goods were produced, rather than sold. For example, year 1 production would be the 300,000 sold in year 1, plus the additional finished goods inventory required for year 2 of 80,000. The year 6 production would therefore be the 400,000 units sold less the 80,000 in the finished goods inventory at the beginning of the year.

The 10% materials that need to be purchased in advance of the coming year were not included in the project’s calculations. It was assumed that materials will be purchased on credit, and that the increases in liabilities will be offset by an increase in accounts receivable.

A b) the purpose of a sensitivity analysis is to test the effects on the budget calculations of changes to key variables. Sensitivity analyses are a crucial component of capital budgeting for a couple of reasons. One is that the figures used in the budgeting process are estimates, and thus subject to change. Management needs to know what the impacts of some key changes might be. A project could have a high net present value as calculated, but a minor shift in one variable may render the project unprofitable. The other reason why sensitivity analysis is important is to help management identify ways to improve a project’s profitability. For a project such as this one, management can evaluate different price points, or identify that the major impediment to profitability is the £12 million initial cost and realize that if they can cut that figure they can improve the project’s outlook dramatically.

For this project I performed a sensitivity analysis on the £12 million initial cost, the discount rate, the price, the sales estimates and the variable costs. The initial cost is a significant impediment to profitability. In order to achieve the company’s desired rate of return on this project, that initial cost would need to be reduced to £7.25 million. That represents a reduction of 39.5%. Given that this cost is in the very near-term, the £12 million figure is likely fairly accurate. What this says about the project is that since the company is unlikely to change the initial cost enough to bring the project to the desired rate of return, profitability must be found elsewhere.

A test of the sales estimates reveals that if an extra 100,000 units are produced each year, the project’s IRR increases to the 14% hurdle rate. It is unknown if the sales estimates are reasonable at this time, but these increases amount to 33% and 25%, which again points to a lack of viability for this project.

Adjusting the price shows us that an increase to £23 will put the value of the project past the hurdle rate. This represents a 28% increase over the estimated price of the product. This may be something that the market can bear, depending on the product and market conditions. This can be a starting point for further discussion as to how this product can be made profitable. For example, suppose modifications are made that would allow the product to be priced at a premium level. The materials cost may increase to £7 but the selling price goes up to £25. Such a scenario would effectively increase the contribution margin of the product, thereby bringing it into profitability.

The sensitivity analysis can also be used to identify variables that have very little bearing on the project. Reductions in the cost of capital, for example, are not sufficient to bring the project to profitability. This is in large part due to the fact that the initial capital outlay is not discounted, and represents a significant portion of the total cost.

Sensitivity analysis can also be used to measure combinations of variables. It may be feasible, for example, to cut the initial cost by £1 million, and raise the price slightly. From that analysis, even adding in a reduction in the tax rate, we see that the project does not clear the hurdle rate based on minor changes. From performing all of these different sensitivity analyses, we can identify improving the contribution margin as the best way to bring the project to profitability. However, if it requires a series of variables to fall into their best-case scenarios for this project to be viable, then it should not be considered a viable project.

2. a) a price earnings (P/E) ratio measures the value of a company’s stock vs. The amount of money that the company is actually earning. In theory, the value of a company is the net present value of its future earnings. Future earnings are calculated based on present earnings and the expected growth rate. The growth rate is applied to the earnings, and then discounted back to present value. The P/E ratio is therefore an indicator of the company’s future growth prospects, as determined by the market. The result is that if you have two companies both with earnings of fifty cents per share, the one with the higher growth prospects will have the higher stock price.

One valuation model is the dividend growth model. This is a variation of the P/E model, in that only the dividends are measured to determine stock price. This is recognition of the fact that a share of stock represents an investment, and the value of that investment is the value of the cash flows emanating from it. The underlying theory is that it is the dividends, not the earnings, that comprise the value of the investment. The earnings are related to the value of the company as a whole, and only if their capital structure is 100% equity. Therefore, the dividend discount model is a more realistic measure of the value of the stock, as an investment rather than the value of the company as a whole. The components of the dividend discount model are today’s dividend, the payout ratio, the expected dividend growth rate, and the discount rate. The P/E can be used to derive the expected growth rate, since P/E is an indicator of the expected future earnings. With these earning and the payout ratio, the future earnings growth can be extrapolated and used to calculate the NPV.

A b) the four companies I have chosen to analyze are FedEx, Yahoo, Nike and Boeing. The respective P/E ratios are 19.25 (FDX), 18.58 (YHOO), 13.38 (NKE) and 8.15 (BA). There are many explanations for the differences between the P/E ratios of these companies. One is the expected rate of growth. Each of these companies is operates mainly in one market, and is either the dominant player or in an industry with only one other major competitor. Some of the factors that contribute to the growth rate will contribute to differences in the P/E. For example, the stage of the industry life cycle is important. Nike and Yahoo are in industries that are entering maturity in western markets, but still have significant overseas growth potential. FedEx and Boeing, however, are in fuel-dependent transportation businesses that may be approaching a declining stage.

Another key potential factor is the company’s earnings. Nike, for example, as high earnings, which since earnings are the denominator will lower their P/E. FedEx, on the other hand, has struggled in the past year and has seen a decline in earnings. Their P/E would improve under such a circumstance, but their stock price has suffered of late as the expected slump in the economy has damaged their future earnings potential.

Another factor is the dividend payout. In general, dividend payout ratio is considered to be inversely proportional to a company’s growth prospects. In this case, Boeing has by far the highest payout ratio, and thus they have the lowest P/E. Nike and FedEx have small dividends, but are still viewed by the market as having growth potential. Yahoo is also seen as a growth company, and they do not pay a dividend. Given the life cycle stage of their industry, the market is not pricing much growth into Yahoo stock, and the stock value may be slightly depressed on the expectation that slower growth and a dividend is forthcoming.

3.a) the expected ex-rights price would be the price of the stock once the rights issue has taken place. In this case, the rights are issued at 11 for 18. The price at issue was 372.5p and the right was for shares at 200p. Therefore, the expected ex-rights price is calculated as follows:

18)(372.5) = 6705 and (11)(200) = 2200. The value of the stock is now 8905 for every 29 shares. This, the ex-rights price, is therefore 307p.

The value of a right at the time of the announcement would be the difference between the expected ex-rights price and the exercise price of the right. So the value of the right at the time of issue would be 307-200 = 107p.

A b) if a shareholder has 900 shares, that is going to be worth 550 rights. The value of the rights, if sold, will be (550) [HIDDEN] = 58,850p. The value of the 900 shares once the company goes ex-rights will be (900) [HIDDEN] = 276,354p. Therefore the total value will be 276,354+58,850 = 335,204.

If the shareholder retains the rights, he will have 1450 shares valued at 307.06 each, for a value of 445,237p. From this, the money paid for the discounted shares must be deducted, a figure equal to (550) [HIDDEN] = 110,000p. This leaves the investor with a value of 335,237.

A c) the rationale for having the issue underwritten is that the company is in poor financial circumstances. Rights issues are typically undertaken as a means for a struggling company to raise capital without going to the debt market. It may be that the company is already overleveraged, or that they may not have any more access to capital. At the time of the RBS rights issue, the company was in need of cash following their purchase of ABN Amro, and the economy had not performed to expectations. This left RBS in a cash crunch.

The reason RBS had the deal underwritten was to ensure that it was entirely sold. The issue was the largest such deal in UK history, which added to the risk that the issue would not sell out. Therefore, RBS used an underwriter to ensure that the deal went through. The underwriters then passed the issue along to sub-underwriters who were able to take the issue to the retail markets.

The underwriting fee for this was £210 million, based on 1.75% of £12 billion. The subunderwriters received 1%, or £120 million. The subunderwriting fee seems low, given that the subunderwriters are the group that bears most of the risk. If the issue is not popular, the subunderwriters become stuck with the rights. Generally, the issue would only become unpopular if the rights were a losing financial proposition. In this case, the rights were not, and the subunderwriters were able to move the issue.

There was some controversy regarding the underwriting fee, but a couple of factors need to be taken into account. One is that the issue was of historically large proportions. To take an issue of this size to market without an underwriter would itself by unprecedented. Furthermore, RBS was in desperate need of the money, as part of a larger restructuring program. For them, to fail to place the issue was not an option. After the first 95% of the issue had been exercised, there remained a portion that had not been. The role of the underwriters at that point would be to either absorb the stock themselves, or scramble to find a potential buyer of the rights. In this case, three of the investment banks were able to place the remainder of the issue for RBS. If anything, this case serves to illustrate the value of the underwriters’ role in the new issue process. Without underwriters, RBS would have been in a struggle to place this issue.

A d) Potter’s views are somewhat simplistic. He contends that to take up the rights issue would allow the investor to avoid dilution. This is true to the extent that the investor who does absolutely nothing will see dilution. However, no investor of sound mind would consider this a viable option. Instead, the alternatives to consider are to either sell the rights or exercise them. In this case, we can expect the rights to be fairly priced. Therefore, the benefit of the discount is a fallacy. The discount and dilution are priced into the ex-rights price. The price of the right is the different between the market price of the stock and the ex-rights price. Therefore, selling the rights has the same financial result as exercising them. The markets are efficient, so there the choice of either action is revenue-neutral. The only question is whether the investor wishes to acquire more shares in RBS or not, and Potter did not address the rights issue on those terms.

4) a) for this question, the five securities I have chosen are Alliance & Leicester, Alliance Unichem, Amvescap, Anglo American, and Antofagasta. The returns for these five securities are listed are weekly, for the year 2005. The average weekly return for the portfolio is 0.6173054%. The standard deviation of the portfolio’s returns is 0.021510327.

A b) the average weekly returns and standard deviations for the securities are as follows:

Alliance & Leicester Avg Return 0.27%; Std Dev 0.018

Alliance Unicom Avg Return 0.14%; Std Dev 0.026

AMVESCAP Avg Return 0.67%; Std Dev 0.052

Anglo American Avg Return 0.95%; Std Dev 0.032

Antofagasta Avg Return 1.04%; Std Dev 0.035

Covariances (right hand side) and correlation coefficients (left hand side) for the pairs are contained in the following table:





The average covariance is.000267469, and the average variance is.001199103. So therefore the standard deviation is:

The square root of that number is the standard deviation, so 0.021302493.

In question a, the standard deviation calculated was.00215, so the results of the two methods were very similar.

5) a) the value of options derives from the distance between the strike price and current price, plus time value. The difference between the strike price and current price is the intrinsic value of the option. The time value reflects that the longer the time frame until expiry, the greater the chance that the stock price will move into the money, or further into the money. Therefore, the longer the time until expiry, the more time value the option will have. In the case of the M&S options, when you compare options with the same strike price, the difference in intrinsic value between them in zero. Therefore, the difference in the value of the options is entirely attributable to the time value. November is further away than September; therefore the time value will be greater. This means that the option will trade at a higher price.

A b) if an investor purchases a (long) straddle, the expected payoff will be as follows: The investor will lose the 46.5p that the straddle cost if the stock sits at 210p. With movements in either direction, the investor will be able to exercise one of the options and recoup some of the investment. The investor will break even if the price either rises to 256.5p or falls to 163.5p. The appropriate time to invest in a straddle is when the investors believe that the stock will move strongly in particular direction, but does not know in which direction that movement will be. The high cost of a straddle demands that the move be strong, and the use of both a put and a call hedges against the lack of sense regarding the direction of the movement.

A c) the contention that options are a zero sum game for both the investor and the writer is fair. Wealth is neither created nor destroyed in an options contract. Each party sits on the opposite side of the transaction. Therefore, when one party wins by a certain amount, the other loses by the same amount. The net wealth is zero since the option transaction merely facilitates the movement of wealth from one party to the next. In any given options contract, one of the counterparties will win and the other will lose, and by equal amounts.

However, multiple option strategies can be used so that either the investor or the writer is involved in a series of such zero sum games.

An additional consideration, however, is that of motive. Options are sometimes as a hedge. So while the monetary value of the contract is a zero sum game, the hedge itself may have value, or allow the hedger the security required to generate value elsewhere. Therefore, in terms of utility, an options contract is not necessarily a zero sum game, despite the fact that strictly in terms of wealth, it is. Also, if the underlying stock is already owned, and this means that the degree of loss on the security when it changes hands may not be a zero sum game, just the theoretical loss.

The options market, however, is not a zero sum game for the market makers, who skim transaction costs in the form of spreads.

Works Cited

McClure, Ben. (2008). Understanding Rights Issues. Investopedia. Retrieved October 24, 2008 at http://www.investopedia.com/articles/stocks/05/062905.asp

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