## What does pricing an option mean

Suppose we're discussing a call option on Microsoft stock which is sold on 8 February 2002 On this date, Microsoft's stock price is 60.65. We will look at options on this stock which have an exercise price of X 60, and which expire on July 19, 2002. Here's what you've learned so far From Chapter 21, we know what the terminology means. Chapter 21 also tells us what the payoff pattern and profit pattern of the call option looks like by itself and in combination with other assets Chapter 22 tells...

## Annual Dividend Yield SP 500

Jubak, and many other observers, would argue that today's low dividend yields are symptomatic of our overvalued markets. Well, maybe markets are overvalued. But I believe dividend yields are so low for another reason Investors are beginning to ask our childish question Why are there dividends And they're not finding good answers. So dividends are becoming less and less important. Just think about how silly it all really is. Why would a shareholder want a company to send him his own money back...

## Excel notesolving circular references

Financial statement models in Excel always involve cells that are mutually dependent. In our model, for example, the interest earned on cash depends on the profits of the firm, but the profits depend on the interest earned on cash. Another example of mutual dependence in our model involves the fixed asset accounts Fixed assets at cost are the sum of net fixed assets plus accumulated depreciation, but accumulated depreciation is a function of the fixed assets at cost. As a result of these...

## Computing a from stock prices

There are two main ways to compute the sigma We can either calculate the sigma by looking at the series of past stock prices. Alternatively, we can calculate the implied sigma by looking at options prices this calculation is often called the implied volatility. This section describes the first method, and the next section describes how to compute the implied volatility. Below we show the annual prices for Microsoft for the decade from 1991 - 2001. Column C shows the continuously compounded...

## The share price valuation Valuing a Motherboard by using current share price

The simplest way to value Motherboard is look at the value of its share. Motherboard Shoes has one million shares, which were trading on 31 December 2004 at 50 per share. Thus the market value of the firm's equity is 50 million. In addition the company's balance sheet shows that it has short-term debt of 2.5 million and long-term debt of 7.5 million John Mba uses these balance sheet values also called book values of the debt as an approximation to the debt's market value.1 Using the current...

## A simple example Using the priceearnings PE ratio for valuation

The price earnings ratio is the ratio of a firm's stock price to its earnings per share When we use the P E for valuation, we assume that similar firms should have similar P E ratios. Here's an example Shoes for Less SFL and Lesser Shoes LS are both shoe stores located in similar communities. Although SFL is bigger than LS, having double the sales and double the profits, the companies are in most relevant respects similar management, financial structure, etc. However, the market valuation of...

## A1 The Gordon model with two dividend growth rates

The Gordon model discussed in Chapter 16 and previously in Chapter 5 assumes that there equity payouts of the firm will grow at an anticipated future growth rate g. Based on this assumption we showed that the cost of equity is where Div0 is the firm's current equity payout defined as the sum of its total dividends and stock repurchases , g is the growth rate of the equity payout, and P0 is the firm's current equity value that is, number of shares times the current share price . The assumption...

## Excel note Relative versus absolute copying

The dollar signs within a formula indicate that when the formulas are copied the cell references to the model parameters should not change. The technical jargon for this in Excel is absolute copying as opposed to the relative copying when variables are indicated without dollar signs. The distinction between absolute and relative copying is critical for financial planning models if you fail to put the dollar signs correctly in the model, it will not copy correctly when you project years 2 and...

## Risk and return depend on the your unit of account

As we've shown in the examples above, risk and return depend on the kind of security you're considering. Returns can also depend on what currency you 're calculating in. Investors these days are putting their money in many stock markets around the world, and their returns are affected both by fluctuations in stock prices and in the rates of exchange. In the example below we calculate the return in Euros and in dollars from holding the Amsterdam Stock Exchange index symbol AEX . In the table...

## The efficient frontier and the minimum variance portfolio

The efficient frontier is the set of all portfolios which are on the upward-sloping part of the graph above. Upward-sloping means that portfolios on the efficient frontier involve difficult choices increasing expected portfolio return E rp has the cost of increasing portfolio standard deviation ap. If you are choosing investment portfolios that are a mix of GM and MSFT stock, then clearly the only portfolios you would be interested in are those on the efficient frontier. These portfolios are...

## Info

The discount rate is 11 and the corporate tax rate is 34 . a. Calculate the project NPV using straight-line depreciation. b. What will be the company's gain if it uses the MACRS depreciation schedule 7. A company is considering buying a new machine for one of its factories. The cost of the machine is 60,000 and its expected life span is five years. The machine will save the cost of a worker estimated at 22,500 annually. The book value of the machine at the end of year 5 is 10,000 but the...

## Some facts about covariance and correlation

Here are some facts about covariance and correlation. We state them without much attempt at elaborate explanation or proof. Fact 1. Covariance is affected by units, correlation isn't. Here's an example In the spreadsheet below, we've presented the annual returns as whole numbers instead of percentages writing GM's 1990 return as -11.54 instead of -11.54 . The covariance cell B18 is now -552.10, which is 10,000 times our previous calculation. But the correlation coefficient B19 remains the same...

## The risk characteristics of financial assetssome introductory blather

In the course of your life you'll be exposed to many financial assets. You've already been exposed to them, even if you didn't know that they were financial assets When you were small, your parents might have opened a savings account for you at the local bank, or your grandparents bought you a few shares of stock. Now that you're a student, you're stuck with 2 Students reading this book will generally have had a statistics course. This chapter assumes some familiarity with basic statistical...

## Current assetswhats included in the financial planning model and whats not

In financial planning models the current assets category contains only items that are related to the operations of the firm. Here are several typical items that would be included in the financial planning model definition of current assets. Accounts receivable These are payments due from customers and are generated by the operations of the firm. Since accounts receivable are generated by the firm's sales, they are included in the operating current assets of the financial planning model....

## Step 2 Project a reasonable number of FCFs

A financial planning model's predictions of future FCFs are based on the assumption that the parameters of the model will not change by too much. Most financial analysts define reasonable to mean number of periods over which this basic assumption is not too silly.6 Everyone recognizes that a firm's environment is dynamic and that the model parameters will change over time, a fact that is usually addressed by doing sensitivity analysis see section 9.4 . John has assumed that he can reasonably...

## Stock Splits and the Cumulative Adjustment Factor

On 31 January 2002, you bought one share of XYZ stock for 50. One year minus one day later, on 30 January 2003, your share of XYZ stock is trading at 80. At the end of the day the stock splits For every share you own, you now have two shares. In a logical world, this would mean that the price of the share should fall by 50 , so that on 31 January 2003, it XYZ trades at 40.3 Now suppose you're trying to calculate your return on the stock. Is it--1 -20 or is the return 50--1 60 The latter, of...

## Initial accounting statements for a financial planning model

Financial planning models are predictions of what a firm's future financial statements will look like. To build such a model we start with the present the firm's current financial statements. To illustrate the process by which financial planning models are constructed, in the next section we will project five years of financial statements for Whimsical Toenails, a company which runs a chain of toenail-painting parlors. Whimsical's management and bankers want to project the firm's future...

## The models parametersthe value drivers

The sales growth parameter is usually the most important parameter of the financial planning model. In our example Whimsical Toenails current year 0 level of sales is 1,000. Over the five-year horizon of the financial planning model, the firm expects its sales to grow at a rate of 10 percent per year. Other model parameters are derived from the following financial statement relations.1 Current assets We assume that Whimsical's end-year current assets on the balance sheet will be 15 percent of...

## The models financial policy assumptions

The second component of a financial planning model is the model's financial policy assumptions. In this initial financial planning model we make the following assumptions Debt Whimsical currently has debt of 320 on its balance sheet. The company's agreement with the bank specifies that it will repay 80 of this debt in each of the next four years. Once the debt is fully repaid, the company intends to stay debt-free. Stock Company management does not intend to either issue new stock nor...

## The IRR rule for judging investments

An alternative to using the NPV criterion for capital budgeting is to use the internal rate of return IRR . Recall from Chapter 1 that the IRR is defined as the discount rate for which the NPV equals zero. It is the compound rate of return which you get from a series of cash flows. Here are the two decision rules for using the IRR in capital budgeting The IRR rule for deciding whether a specific investment is worthwhile Suppose we are considering a proj ect that has cash flows CF0 , CF1 , CF2 ,...

## Building a financial planning model

Now that we have our terminology straight, we can build our financial planning model for Whimsical Toenails. A typical financial planning model has three major components The model parameters. Also called the value drivers, a financial planning model's parameters include the major assumptions of the model. For example, we might assume that the sales growth parameter is 10 per year. Or we might assume that the current assets to sales parameter is 15 meaning that an increase of 1,000 in sales...

## Capital budgeting principle Ignore sunk costs and consider only marginal cash flows

This is an important principle of capital budgeting and project evaluation Ignore the cash flows you can't control and look only at the marginal cash flows the outcomes of financial decisions you can still make. In the jargon of finance Ignore sunk costs, costs that have already been incurred and are thus not affected by future capital budgeting decisions. Here's an example You recently bought a plot of land and built a house on it. Your intention was to sell the house immediately, but it turns...

## Why do NPV and IRR give different rankings

Below we build a table and graph that show the NPV for each project as a function of the From the graph you can see why contradictory rankings occur Project B has a higher IRR 27.38 than project A 19.77 . Remember that the IRR is the point at which the NPV curve cuts the x-axis. When the discount rate is low, Project A has a higher NPV than project B, but when the discount rate is high, project B has a higher NPV. There is a crossover point in the next subsection you will see that this point is...

## N

But when r 0, the denominator in this expression becomes 0. On the other hand, when r 0 it . Use Excel's If function to modify the formula in the Section 1.8 spreadsheet. 10. If you deposit 25,000 today, Union Bank offers to pay you 50,000 at the end of 10 years. What is the interest rate 11. Assuming that the interest rate is 5 , which of the following is more valuable 11 .d. 300 a year in perpetuity meaning forever , with the first payment at the end of this year 12. You receive a 15,000...

## Inhouse copying or outsourcing A minicase illustrating foregone opportunity costs

Your company is trying to decide whether to outsource its photocopying or continue to do it in-house. The current photocopier won't do anymore it either has to be sold or thoroughly fixed up. Here are some details about the two alternatives The company's tax rate is 40 . Doing the copying in-house requires an investment of 17,000 to fix up the existing photocopy machine. Your accountant estimates that this 17,000 can be immediately booked as an expense, so that its after-tax cost is l - 40...

## Is Sally and Daves condo investment profitableincorporating terminal value into the calculations

A little thought about the previous spreadsheet reveals that we've left out an important factor The value of the condo at the end of the 10-year horizon. In finance an asset's value at the end of the investment horizon is called the asset's salvage value or terminal value. In the above spreadsheet we've assumed that the terminal value of the condo is zero, but this assumption implausible. To make a better calculation about their investment, Sally and Dave will have to make an assumption about...

## What does IRR mean Loan tables and investment amortization

In the previous section we gave a simple illustration of what we meant when we said that the internal rate of return IRR is the compound interest rate that you earn on an asset. This simple sentence which is not easy to understand underlies a slew of finance applications When finance professionals discuss the rate of return on an investment or the effective interest rate on a loan, they are almost always refering to the IRR. In this section we explore some meanings of the IRR. Almost the whole...