Tutor profile: Jason G.
Subject: Applied Mathematics
Hypothesis Testing Example: The amount of time airplanes spend in maintenance is a critical factor in airline profitability. A particular airline has records that show for a sample of 49 planes, the average downtime is 12 hours. However, the industry average is 11 hours with a standard deviation of 3.5 hours. At the 10% significance level, should the airline company conclude that its downtime differs significantly from the industry average?
Let's first establish our parameters to work with: Xbar = 12 hours *Xbar is the numerical average in our dataset Mu (μ) = 11 hours * Our observed average Sigma = 3.5 hours n = 49 *n is our number of observations, so in this case, we have 49 planes a = 10% *significance level - we will usually test at 5 or 10 percent Our null hypothesis (H0) is the one we can accept without strong evidence that points to our alternative hypothesis (Ha). We assume our null hypothesis is true and determine whether the sample data is consistent with the null hypothesis. H0: μ = 11 hours Ha: μ ≠ 11 hours Let's calculate our standard error. Sigma/sqrt of n = 3.5/sqrt49 = .5 Let's calculate our Z obs. (Xbar - μ)/standard error = (12 hours - 11 hours)/.5 = 2 *T test vs. Z test to indicate how many standard deviations an observation in a data is above or below the mean. Generally speaking, if we know the whole population we use a Z score. In this example, we don't have information on EVERY airplane, but 49 is a fairly high example. Let's calculate our probability value or P-value. The question states, "significantly different from" which indicates a 2 tailed test. You can either use a standard normal table from a textbook or easier, let's plug the excel formula for Norm.S.Dist which returns the standard normal distribution. In excel: 1 - Norm.S.Dist(2, true) = .0228 2 is our Z obs and True for cumulative. This gives us our right tail test. So if the question stated "significantly greater than" the industry average we could stop here. But because we need to know both distribution tails, we will multiply by 2. In either case, we want to know the statistical significance of our data, i.e. is 12 hours statistically more than 11 hours given the industry average. 2* .0228 = .0455 .0455 < 10%, so we reject the null and know that our airline's downtime significantly different from the industry average. If we wanted to be more precise, we could have tested at the 5% level. But as we observe, 4.55% is still smaller than 5%.
Subject: Corporate Finance
What are the three fundamental principles of valuation?
1) Evaluate free cash flow on a pre-financing basis. What does this mean? We focus on cash flows generated from operations. This is much different than using accounting terms and evaluating the balance sheet. The balance sheet takes into account how projects and the firm are financed, i.e. creditors vs. shareholders. *When projecting cash flows, we ignore capital raising and focus on operations. 2) Only cash flows matter! Cash in from operation - Cash out from operations = Free Cash Flows 3) Marginal cash flow is estimating the cash flow on an incremental basis, which means how much will we make taking on a new project vs. not taking on a new project. For instance, it costs $10 for a kid to set up a lemonade stand. After 4 hours of hard work, the kid has made a profit of $5. One way of looking at this scenario is that the kid made money; the other way of looking at it is the kid's opportunity cost of time. Were 4 hours of work worth $5 bucks.... or could the kid have been mowing lawns in that same period of time and made $20 bucks. This example is what we mean by "marginal" cash flow.
What is the purpose of business strategy?
Strategy refers to the combined tactics used to create market advantages for your respective company - simply put, to win and beat competitors. "Value Creation" is a necessary condition for strategy, but alone is not sufficient; thus, "Capturing Value" is the necessary second part of the equation. So we have to first create value, i.e. product innovation, lowering costs, and then we have to capture the value that we just created. The two key drivers that shape a firm's strategy are: 1) the external environment; and 2) our firm's resources. Of the two drivers, we have much less control over the external environment. Then, there are generally three key strategies employed: 1) Strategy as a position 2) Strategy as leverage 3) Strategy as opportunity
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