# 会计代写|财务管理代写Financial Management代考|Three Techniques for Estimating Investment Risk

## 会计代写|财务管理代写Financial Management代考|Three Techniques for Estimating Investment Risk

Three previously mentioned techniques – sensitivity analysis, scenario analysis, and simulation-are useful for making subjective estimates of investment risk. Although none of the techniques provides an objective measure of investment risk, they all help the executive to think systematically about the sources of risk and their effect on project return. Reviewing briefly, an investment’s IRR or NPV depends on a number of uncertain economic factors, such as selling price, quantity sold, useful life, and so on. Sensitivity analysis involves an estimation of how the investment’s figure of merit varies with changes in one of these uncertain factors. One commonly used approach is to calculate three returns corresponding to an optimistic, a pessimistic, and a most likely forecast of the uncertain variables. This provides some indication of the range of possible outcomes. Scenario analysis is a modest extension that changes several of the uncertain variables in a mutually consistent way to describe a particular event.

We looked at simulation in some detail in Chapter 3 as a tool for financial planning. Recall that simulation is an extension of sensitivity and scenario analysis in which the analyst assigns a probability distribution to each uncertain factor, specifies any interdependence among the factors, and asks a computer repeatedly to select values for the factors according to their probability of occurring. For each set of values chosen, the computer calculates a particular outcome. The result is a graph, similar to Figure 3.1, plotting project return against frequency of occurrence. The chief benefits of sensitivity analysis, scenario analysis, and simulation are that they force the analyst to think systematically about the individual economic determinants of investment risk, indicate the sensitivity of the investment’s return to each of these determinants, and provide information about the range of possible returns.

The most common way to do this is to add an increment to the discount rate; that is, discount the expected value of the risky cash flows at a discount rate that includes a premium for risk. Alternatively, you can compare an investment’s IRR, based on expected cash flows, to a required rate of return that again includes a risk premium. The size of the premium naturally increases with the perceived risk of the investment.

To illustrate the use of such risk-adjusted discount rates, consider a $\$ 10$million investment promising risky cash flows with an expected value of$\$2$ million annually for 10 years. What is the investment’s NPV when the risk-free interest rate is 5 percent and management has decided to use a 7 percent risk premium to compensate for the uncertainty of the cash flows?

A little figure work reveals that at a 12 percent, risk-adjusted discount rate, the investment’s NPV is $\$ 1.3$million ($\$11.3$ million present value of future cash flows, less $\$ 10$million initial cost). The positive NPV indicates that the investment is attractive even after adjusting for risk. An equivalent approach is to calculate the investment’s IRR of 15.1 percent and note that it exceeds the 12 percent risk-adjusted rate, again signaling the investment’s merit. Note how the risk-adjusted discount rate reduces the investment’s appeal. If the investment were riskless, its NPV at a 5 percent discount rate would be$\$5.4$ million, but because a higher risk-adjusted rate is deemed appropriate, NPV falls by over $\$ 4$million. In essence, management requires an inducement of at least this amount before it is willing to make the investment. A virtue of risk-adjusted discount rates is that most executives have at least a rough idea of how an investment’s required rate of return should vary with risk. Stated differently, they have a basic idea of the position of the market line in Figure 8.1. For instance, they know from the historical data in Table 5.1 of Chapter 5 that over many years, common stocks have yielded an average annual return about 6.4 percentage points higher than the return on government bonds. If the present return on government bonds is 2 percent, it is plausible to expect an investment that is about as risky as common stocks to yield a return of about 8.4 percent. Similarly, executives know that an investment promising a return of 40 percent is attractive unless its risk is extraordinarily high. Granted, such reasoning is imprecise; nonetheless, it does lend some objectivity to risk assessment. # 财务管理代考 ## 会计代写|财务管理代写Financial Management代考|Three Techniques for Estimating Investment Risk 前面提到的三种技术——敏感性分析、情景分析和模拟——对投资风险的主观估计很有用。尽管没有一种技术可以客观地衡量投资风险，但它们都可以帮助管理人员系统地思考风险来源及其对项目回报的影响。简单回顾一下，一项投资的 IRR 或 NPV 取决于许多不确定的经济因素，例如售价、销售数量、使用寿命等。敏感性分析涉及估计投资的品质因数如何随这些不确定因素之一的变化而变化。一种常用的方法是计算对应于不确定变量的乐观、悲观和最可能预测的三种回报。这提供了可能结果范围的一些指示。情景分析是一种适度的扩展，它以相互一致的方式改变几个不确定变量来描述特定事件。 我们在第 3 章中详细讨论了模拟作为财务规划的工具。回想一下，模拟是敏感性和情景分析的扩展，其中分析师为每个不确定因素分配概率分布，指定因素之间的任何相互依赖性，并要求计算机根据其发生概率反复选择因素的值。对于选择的每组值，计算机都会计算出一个特定的结果。结果是一个类似于图 3.1 的图表，绘制了项目回报与发生频率的关系。敏感性分析、情景分析和模拟的主要好处是它们迫使分析师系统地思考投资风险的各个经济决定因素， ## 会计代写|财务管理代写Financial Management代考|Risk-Adjusted Discount Rates 最常见的方法是增加贴现率；也就是说，以包含风险溢价的贴现率对风险现金流量的预期值进行贴现。或者，您可以将基于预期现金流的投资 IRR 与再次包含风险溢价的要求回报率进行比较。溢价的大小自然会随着投资的感知风险而增加。 为了说明这种风险调整贴现率的使用，考虑$10万投资承诺有风险的现金流，预期价值为$2每年 10 万美元，为期 10 年。当无风险利率为 5% 并且管理层决定使用 7% 的风险溢价来补偿现金流量的不确定性时，投资的 NPV 是多少？ 一个小数字工作表明，在 12% 的风险调整贴现率下，投资的 NPV 是$1.3百万 （$11.3百万 未来现金流量的现值，减去$10万初始成本）。正 NPV 表明即使在调整风险后投资也具有吸引力。一种等效的方法是计算投资的 15.1% 的内部收益率，并注意到它超过了 12% 的风险调整后利率，这再次表明了投资的价值。

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