这是一份anu澳大利亚国立大学ECON2014/ECON6014作业代写的成功案例

In this calculation, $\pi_{i}$ is the profit or return associated with the $i$ th outcome; $p_{i}$ is the probability that the $i$ th outcome will occur; and $E(\pi)$, the expected value, is a weighted average of the various possible outcomes, each weighted by the probability of its occurrence.
The deviation of possible outcomes from the expected value must then be derived:
$$
\text { Deviation }{i}=\pi{i}-E(\pi)
$$
The squared value of each deviation is then multiplied by the relevant probability and summed. This arithmetic mean of the squared deviations is the variance of the probability distribution:$$
\text { Variance }=\sigma^{2}=\sum_{i=1}^{n}\left[\pi_{i}-E(\pi)\right]^{2} p_{i}
$$
The standard deviation is found by obtaining the square root of the variance:
$$
\text { Standard Deviation }=\sigma=1 \sqrt{\sum_{i=1}^{n}\left[\pi_{i}-E(\pi)\right]^{2} p_{i}}
$$
The standard deviation of profit for project $A$ can be calculated to illustrate this procedure:

ECON2014/ECON6014COURSE NOTES ：

A variant of NPV analysis that is often used in complex capital budgeting situations is called the profitability index (PI), or the benefit/cost ratio method. The profitability index is calculated as follows:
$$
P I=\frac{\text { PV of Cash Inflows }}{\text { PV of Cash Outflows }}=\frac{\sum_{t=1}^{n}\left[E\left(C F_{i t}\right) /\left(1+k_{i}\right)^{t}\right]}{\sum_{t=1}^{n}\left[C_{i t} /\left(1+k_{i}\right)^{t}\right]}
$$
The PI shows the relative profitability of any project, or the present value of benefits per dollar of cost.

In the SVCC example described in Table 15.4, NPV >0 implies a desirable investment project and $P I>1$. To see that this is indeed the case, we can use the profitability index formula, given in Equation 15.5, and the present value of cash inflows and outflows from the project, given in Equation 15.4. The profitability index for the SVCC project is
$$
\begin{aligned}
P I &=\frac{P V \text { of Cash Inflows }}{P V \text { of Outflows }} \
&=\frac{\$ 27,987,141}{\$ 20,254,820} \
&=1.38
\end{aligned}
$$