Showing posts with label Finance. Show all posts
Showing posts with label Finance. Show all posts

Wednesday, May 11, 2011

Capital Budgeting

0 comments

Capital Budgeting A capital expenditure is an outlay of cash for a project that is expected to produce a cash inflow over a period of time exceeding one year. Examples of projects include investments in property, plant, and equipment, research and development projects, large advertisingcampaigns, or any other project that requires a capital expenditure and generates a future cash flow.
Because capital expenditures can be very large and have a significant impact on the financial performance of the firm, great importance is placed on project selection. This process is called capital budgeting.

Criteria for Capital Budgeting Decisions

Potentially, there is a wide array of criteria for selecting projects. Some shareholders may want the firm to select projects that will show immediate surges in cash inflow, others may want to emphasize long-term growth with little importance on short-term performance. Viewed in this way, it would be quite difficult to satisfy the differing interests of all the shareholders. Fortunately, there is a solution.
The goal of the firm is to maximize present shareholder value. This goal implies that projects should be undertaken that result in a positive net present value, that is, the present value of the expected cash inflow less the present value of the required capital expenditures. Using net present value (NPV) as a measure, capital budgeting involves selecting those projects that increase the value of the firm because they have a positive NPV. The timing and growth rate of the incoming cash flow is important only to the extent of its impact on NPV.
Using NPV as the criterion by which to select projects assumes efficient capital markets so that the firm has access to whatever capital is needed to pursue the positive NPV projects. In situations where this is not the case, there may be capital rationing and the capital budgeting process becomes more complex.
Note that it is not the responsibility of the firm to decide whether to please particular groups of shareholders who prefer longer or shorter term results. Once the firm has selected the projects to maximize its net present value, it is up to the individual shareholders to use the capital markets to borrow or lend in order to move the exact timing of their own cash inflows forward or backward. This idea is crucial in the principal-agent relationship that exists between shareholders and corporate managers. Even though each may have their own individual preferences, the common goal is that of maximizing the present value of the corporation.
Alternative Rules for Capital Budgeting

While net present value is the rule that always maximizes shareholder value, some firms use other criteria for their capital budgeting decisions, such as:
  • Internal Rate of Return (IRR)
  • Profitability Index
  • Payback Period
  • Return on Book Value

In some cases, the investment decisions resulting from the IRR and profitability index methods agree with those of NPV. Decisions made using the payback period and return on book value methods usually are suboptimal from the standpoint of maximizing shareholder valu
e


Financial Ratios

0 comments
 Financial Ratios 
Financial ratios are useful indicators of a firm's performance and financial situation. Most ratios can be calculated from information provided by the financial statements. Financial ratios can be used to analyze trends and to compare the firm's financials to those of other firms. In some cases, ratio analysis can predict future bankruptcy.
Financial ratios can be classified according to the information they provide. The following types of ratios frequently are used:
  • Liquidity ratios
  • Asset turnover ratios
  • Financial leverage ratios
  • Profitability ratios
  • Dividend policy ratios

Liquidity Ratios

Liquidity ratios provide information about a firm's ability to meet its short-term financial obligations. They are of particular interest to those extending short-term credit to the firm. Two frequently-used liquidity ratios are the current ratio (or working capital ratio) and the quick ratio.
The current ratio is the ratio of current assets to current liabilities:
Current Ratio
=
Current Assets
Current Liabilities

Short-term creditors prefer a high current ratio since it reduces their risk. Shareholders may prefer a lower current ratio so that more of the firm's assets are working to grow the business. Typical values for the current ratio vary by firm and industry. For example, firms in cyclical industries may maintain a higher current ratio in order to remain solvent during downturns.
One drawback of the current ratio is that inventory may include many items that are difficult to liquidate quickly and that have uncertain liquidation values. The quick ratio is an alternative measure of liquidity that does not include inventory in the current assets. The quick ratio is defined as follows:
Quick Ratio
=
Current Assets - Inventory
Current Liabilities

The current assets used in the quick ratio are cash, accounts receivable, and notes receivable. These assets essentially are current assets less inventory. The quick ratio often is referred to as the acid test.
Finally, the cash ratio is the most conservative liquidity ratio. It excludes all current assets except the most liquid: cash and cash equivalents. The cash ratio is defined as follows:
Cash Ratio
=
Cash + Marketable Securities
Current Liabilities

The cash ratio is an indication of the firm's ability to pay off its current liabilities if for some reason immediate payment were demanded.
Asset Turnover Ratios

Asset turnover ratios indicate of how efficiently the firm utilizes its assets. They sometimes are referred to as efficiency ratios, asset utilization ratios, or asset management ratios. Two commonly used asset turnover ratios are receivables turnover andinventory turnover.
Receivables turnover is an indication of how quickly the firm collects its accounts receivables and is defined as follows:
Receivables Turnover
=
Annual Credit Sales
Accounts Receivable

The receivables turnover often is reported in terms of the number of days that credit sales remain in accounts receivable before they are collected. This number is known as the collection period. It is the accounts receivable balance divided by the average daily credit sales, calculated as follows:
Average Collection Period
=
Accounts Receivable
Annual Credit Sales / 365

The collection period also can be written as:
Average Collection Period
=
365
Receivables Turnover

Another major asset turnover ratio is inventory turnover. It is the cost of goods sold in a time period divided by the average inventory level during that period:
Inventory Turnover
=
Cost of Goods Sold
Average Inventory

The inventory turnover often is reported as the inventory period, which is the number of days worth of inventory on hand, calculated by dividing the inventory by the average daily cost of goods sold:
Inventory Period
=
Average Inventory
Annual Cost of Goods Sold / 365

The inventory period also can be written as:
Inventory Period
=
365
Inventory Turnover

Other asset turnover ratios include fixed asset turnover and total asset turnover.
Financial Leverage Ratios

Financial leverage ratios provide an indication of the long-term solvency of the firm. Unlike liquidity ratios that are concerned with short-term assets and liabilities, financial leverage ratios measure the extent to which the firm is using long term debt.
The debt ratio is defined as total debt divided by total assets:
Debt Ratio
=
Total Debt
Total Assets

The debt-to-equity ratio is total debt divided by total equity:
Debt-to-Equity Ratio
=
Total Debt
Total Equity

Debt ratios depend on the classification of long-term leases and on the classification of some items as long-term debt or equity.
The times interest earned ratio indicates how well the firm's earnings can cover the interest payments on its debt. This ratio also is known as the interest coverage and is calculated as follows:
Interest Coverage
=
EBIT
Interest Charges

where EBIT = Earnings Before Interest and Taxes
Profitability Ratios

Profitability ratios offer several different measures of the success of the firm at generating profits.
The gross profit margin is a measure of the gross profit earned on sales. The gross profit margin considers the firm's cost of goods sold, but does not include other costs. It is defined as follows:
Gross Profit Margin
=
Sales - Cost of Goods Sold
Sales

Return on assets is a measure of how effectively the firm's assets are being used to generate profits. It is defined as:
Return on Assets
=
Net Income
Total Assets

Return on equity is the bottom line measure for the shareholders, measuring the profits earned for each dollar invested in the firm's stock. Return on equity is defined as follows:
Return on Equity
=
Net Income
Shareholder Equity

Dividend Policy Ratios

Dividend policy ratios provide insight into the dividend policy of the firm and the prospects for future growth. Two commonly used ratios are the dividend yield and payout ratio.
The dividend yield is defined as follows:
Dividend Yield
=
Dividends Per Share
Share Price

high dividend yield does not necessarily translate into a high future rate of return. It is important to consider the prospects for continuing and increasing the dividend in the future. The dividend payout ratio is helpful in this regard, and is defined as follows:
Payout Ratio
=
Dividends Per Share
Earnings Per Share

Use and Limitations of Financial Ratios

Attention should be given to the following issues when using financial ratios:

  • A reference point is needed. To to be meaningful, most ratios must be compared to historical values of the same firm, the firm's forecasts, or ratios of similar firms.
  • Most ratios by themselves are not highly meaningful. They should be viewed as indicators, with several of them combined to paint a picture of the firm's situation.
  • Year-end values may not be representative. Certain account balances that are used to calculate ratios may increase or decrease at the end of the accounting period because of seasonal factors. Such changes may distort the value of the ratio. Average values should be used when they are available.
  • Ratios are subject to the limitations of accounting methods. Different accounting choices may result in significantly different ratio values

Future Value

0 comments

Future Value

The future value of a sum of money invested at interest rate i for one year is given by:

FV = PV ( 1 + i )

where

FV = future value
PV = present value
i = annual interest rate

If the resulting principal and interest are re-invested a second year at the same interest rate, the future value is given by:

FV = PV ( 1 + i ) ( 1 + i )

In general, the future value of a sum of money invested for t years with the interest credited and re-invested at the end of each year is:

FV = PV ( 1 + i ) t

Solving for Required Interest Rate or Time

Given a present sum of money and a desired future value, one can determine either the interest rate required to attain the future value given the time span, or the time required to reach the future value at a given interest rate. Because solving for theinterest rate or time is slightly more difficult than solving for future value, there are a few methods for arriving at a solution:

1.

Iteration - by calculating the future value for different values of interest rate or time, one gradually can converge on the solution.
2.

Financial calculator or spreadsheet - use built-in functions to instantly calculate the solution.
3.

Interest rate table - by using a table such as the one at the end of this page, one quickly can find a value of interest rate or time that is close to the solution.
4.

Algebraic solution - mathematically calculating the exact solution.

Algebraic Solution

Beginning with the future value equation and given a fixed time period, one can solve for the required interest rate as follows.

FV = PV ( 1 + i ) t

Dividing each side by PV and raising each side to the power of 1/t:

( FV / PV ) 1/t = 1 + i

The required interest rate then is given by:

i = ( FV / PV ) 1/t - 1

To solve for the required time to reach a future value at a specified interest rate, again start with the equation for future value:

FV = PV ( 1 + i ) t

Taking the logarithm (natural log or common log) of each side:

log FV = log [ PV ( 1 + i ) t ]

Relying on the properties of logarithms, the expression can be rearranged as follows:

log FV = log PV + t log ( 1 + i )

Solving for t:

t = 


log ( FV / PV )

log ( 1 + i )


Interest Factor Table

The term ( 1 + i ) t is the future value interest factor and may be calculated for an array of time periods and interest rates to construct a table as shown below:
Table of Future Value Interest Factors

t \ i


1%


2%


3%


4%


5%


6%


7%


8%


9%


10%

1


1.010


1.020


1.030


1.040


1.050


1.060


1.070


1.080


1.090


1.100

2


1.020


1.040


1.061


1.082


1.103


1.124


1.145


1.166


1.188


1.210

3


1.030


1.061


1.093


1.125


1.158


1.191


1.225


1.260


1.295


1.331

4


1.041


1.082


1.126


1.170


1.216


1.262


1.311


1.360


1.412


1.464

5


1.051


1.104


1.159


1.217


1.276


1.338


1.403


1.469


1.539


1.611

6


1.062


1.126


1.194


1.265


1.340


1.419


1.501


1.587


1.677


1.772

7


1.072


1.149


1.230


1.316


1.407


1.504


1.606


1.714


1.828


1.949

8


1.083


1.172


1.267


1.369


1.477


1.594


1.718


1.851


1.993


2.144

9


1.094


1.195


1.305


1.423


1.551


1.689


1.838


1.999


2.172


2.358

10


1.105


1.219


1.344


1.480


1.629


1.791


1.967


2.159


2.367


2.594

11


1.116


1.243


1.384


1.539


1.710


1.898


2.105


2.332


2.580


2.853

12


1.127


1.268


1.426


1.601


1.796


2.012


2.252


2.518


2.813


3.138

13


1.138


1.294


1.469


1.665


1.886


2.133


2.410


2.720


3.066


3.452

14


1.149


1.319


1.513


1.732


1.980


2.261


2.579


2.937


3.342


3.797

15


1.161


1.346


1.558


1.801


2.079


2.397


2.759


3.172


3.642


4.177

Perpetuities

0 comments

Perpetuities

A perpetuity is a series of equal payments over an infinite time period into the future. Consider the case of a cash payment C made at the end of each year at interest rate i, as shown in the following time line:

Perpetuity Time Line

0





1





2





3









PV


C


C


C





Because this cash flow continues forever, the present value is given by an infinite series:

PV = C / ( 1 + i ) + C / ( 1 + i )2 + C / ( 1 + i )3 + . . .

From this infinite series, a usable present value formula can be derived by first dividing each side by ( 1 + i ).

PV / ( 1 + i ) = C / ( 1 + i )2 + C / ( 1 + i )3 + C / ( 1 + i )4 + . . .

In order to eliminate most of the terms in the series, subtract the second equation from the first equation:

PV - PV / ( 1 + i ) = C / ( 1 + i )

Solving for PV, the present value of a perpetuity is given by:

PV = 


C

i
Growing Perpetuities

Sometimes the payments in a perpetuity are not constant but rather, increase at a certain growth rate g as depicted in the following time line:

Growing Perpetuity Time Line

0





1





2





3









PV


C


C(1+g)


C(1+g)2





The present value of a growing perpetuity can be written as the following infinite series:

PV = 


C

( 1 + i )

C ( 1 + g )

( 1 + i )2

C ( 1 + g )2

( 1 + i )3


+ . . .


To simplify this expression, first multiply each side by (1 + g) / (1 + i):

PV ( 1 + g)

( 1 + i )

C ( 1 + g )

( 1 + i )2

C ( 1 + g )2

( 1 + i )3


+ . . .


Then subtract the second equation from the first:

PV - 


PV ( 1 + g)

( 1 + i )

C

( 1 + i )

Finally, solving for PV yields the expression for the present value of a growing perpetuity:

PV = 


C

i - g

For this expression to be valid, the growth rate must be less than the interest rate, that is, g < i .