June 2009

Part I: Financial Statement Overview
A. Basic Structure of the Financial Statements
B. Some Terms to Know
C. Key Financial Indicators
D. Financial Strength and Performance of the Firm
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Part II: Cost Accounting
A. Cost Concepts
B. Enterprise Budgeting
C. Historical Financial Statement Analysis
D. Future Trends in Financial Statements
Part III: Growth of the Firm
A. Economic Climate for Growth
B. An Economic Growth Model
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Part IV: Valuing Investment Projects
A. Time Value of Money
B. Capital Budgeting Methods
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C. Overview of Capital Budgeting Information Needs 66
D. Specific Applications of Net Present Value Method 74
Part V: Valuation of Externalities
A. Historical Assessments
B. Projecting Future Values
Part V: Adjustments for Risk
A. Exposure to Business Risk
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85
B. Risk/Return Preferences
C. Exposure to Financial Risk
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94
D. Optimal Capital Structure 96
E. Ranking Potential Projects and the Capital Budget 99
Appendix
101
2

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There are a minimum of three financial statements comprising the financial accounting system of all businesses: the balance sheet, the income statement, and the cash flow statement. An understanding of the basic designs of these statements and the interrelationships between them is essential to this course.
Other financial statements, such as the statement of change in owner equity, while not addressed in this course, basically feed off of these statements.
The balance sheet is a statement of a firm’s assets and claims on these assets.
The basic structure of the statement is illustrated in Figure 1 below. The
Figure 1 – Structure of the Balance Sheet. left-hand side of the balance sheet lists the firm’s assets in order of their asset liquidity, or ability to be converted to cash quickly without disrupting

the ongoing operations of the firm. Naturally, therefore, cash would be the first asset found in the balance sheet along with other current assets, or assets like time deposits, accounts receivable, and inventories of unsold production that can presumably be converted to cash quickly without disrupting the firm’s operations. Long term assets require more time to convert to cash and can disrupt the ongoing nature of the firm’s operations.
Examples include machinery, equipment, and trucks and other motor vehicles as well as the least liquid assets of all assets owned by the firm, such as buildings and land.
There are at least two types of balance sheets: a book value balance sheet and a current market value balance sheet. A book value balance sheet reflects the basis the firm has it its long term assets, or their original purchase price less accumulated depreciation. A current market value balance sheet, on the other hand, reflects the market value of intermediate and long term assets as of the date of the balance sheet.
The firm’s income statement provides a record of revenue from the firm’s operations and the expenses associated with generating this revenue. The
Figure 2 – Structure of the Income Statement.
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general structure of this financial statement is illustrated in Figure 2. The bottom line of this financial statement is a measure of net income (either net cash income or total net income), which represents a measure of the firm’s profitability during the current year. We will examine a number of other measures of profitability later in this booklet.
The income statement can take on at least two forms: a cash income statement like the one illustrated in Figure 2 above where revenue and expenses are registered when payment is either received or expenses paid, and an accrual statement where revenue and expenses are measured when they are incurred. This is the difference, for example, between cash receipts from product sales versus the value of production when accounting for the gross revenue of the firm in the current year.
The cash flow statement provides a record of the sources and uses of cash for the firm during the year. A key element of this statement is the cash position of the firm, or the difference between cash available minus cash
Figure 3 – Structure of the Cash Flow Statement.
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6 required to meet uses of cash by the firm. A negative cash position requires the firm borrow to cover the negative balance at a minimum. Cash available includes the firm’s beginning cash balance carried over from the previous year’s balance sheet plus cash received from the sale of current production.
The cash flow statement can also take at least three forms: an annual cash flow statement, a quarterly cash flow statement, and a monthly cash flow statement. The latter format is extremely useful in establishing a line of credit with the firm’s creditors for the current year.
Additional detail on all three financial statements will be provided in Power
Point slide shows presented during lectures in this course.

7
Before proceeding with key topics in the financial analysis of an agricultural firm, we need to refresh your memory on key terminology and introduce you to others.
Liquidity is generally defined as the ability to generate cash quickly to meet claims on the business without disrupting the ongoing operations of the business. There are three forms of liquidity: (1) asset liquidity, (2) credit liquidity and (3) cash flow liquidity.
Asset liquidity – the ability to convert assets to cash quickly to meet claims on the business without disrupting the ongoing operations of the business . If the firm can convert its current assets to cash, retire its current liabilities and have cash left over, the firm is said to be liquid. Assets that can be converted to cash quickly are referred to as current assets, and include financial instruments (cash itself, stocks and bonds and accounts and notes receivable) as well as non-financial assets like unsold production inventories and inventories of purchased inputs. Assets on a firm’s balance sheet are typically ordered in terms of their liquidity, which explains why cash appears first in the asset column of the balance sheet and land appears last. While land may be sold quickly, its sale will affect the ongoing nature of the firm’s business operations.
Credit liquidity – the ability to borrow cash quickly to meet claims on the business without disrupting the ongoing operations of the business. This concept is related to the firm’s unused credit reserves, or the maximum amount of credit lenders will typically extend to a firm based upon its debt/equity structure. The unused portion of a production line of credit
(LOC), for example, is a measure of short term credit liquidity. The amount of unused term debt borrowing capacity given a lender’s external credit rationing based on a leverage ratio, for example, is a long term measure of credit liquidity.

8
Cash flow liquidity – Cash flow liquidity is a periodic measure of liquidity, usually monthly. The firm’s monthly cash flow statement, for example, reflects the cash flows available less cash flows required during the month. If the ensuing difference between these totals, or net cash balance, is positive, the firm has liquidity during that month to meet unexpected claims on the business.
Solvency refers to the ability of the firm to convert all its assets to cash, retire all of its liabilities and have cash left over. Note the emphasis on all assets and all liabilities as opposed to current assets and current liabilities when we discussed the concept of asset liquidity described above.
Profitability refers to the ability of a firm to generate a level of revenue that exceeds its total costs of production. The bottom line of the firm’s income statement reflects the net income of the firm, one of many measures of profitability. Care must be taken when assessing profitability over time to account for changes in the purchasing power of money. Nominal net income refers to net income not been adjusted for inflation while real net income reflects adjustments for changes in the purchasing power of the firm’s profits from one year to the next.
Economic efficiency refers to the ability of the firm to use its resources to achieve a desired result with little or no wasted effort or expense. This differs from technical efficiency or productivity (i.e., yield per unit of input use) that does not take prices or unit costs of production into account.
Debt repayment capacity refers to the ability of the firm to meet its scheduled term debt and capital lease payments and have cash left over.
This concept is closely linked to the concept of unused credit reserves in the

9 literature, or the difference between the maximum capacity to borrow as viewed by lenders and the amount of borrowed capital the firm has already undertaken.
Present value refers to the value today of a sum of money or stream on payments to be received in the future, discounted back to the present using an appropriate required rate of return. Future value, on the other hand, refers to the value at a specific future date of a sum of money or stream of payments (perhaps to an annuity).
Risk
The possible variation associated with the expected return or value measured by the standard deviation or coefficient of variation. There are many forms of risk, including price risk, interest rate risk, yield risk, political risk, relationship risk, etc.). This collectively is often referred to as business risk , or the relative dispersion or variability in the firm’s expected earnings. This differs then from financial risk, or the potential loss in equity associated with the use of leverage (debt and equity capital). Finally, risk can also be classified as systematic risk (or non-diversifiable risk) and unsystematic risk
(the portion of the variation in investment returns that can be eliminated by diversification).
Physical capital refers to those assets on the firm’s balance sheet that are not in the form of financial instruments. Examples include inventories of unsold production, machinery and equipment, inventories of production inputs, trucks, buildings and land. Financial capital, on the other hand, typically refers to financial instruments (cash, stocks and bonds) as well as the equity capital the owners firm have invested in the firm.
Explicit costs are those expenses such as wages paid to hired labor where a cash payment to others is required. Implicit costs on the other hand are

10 those expenses such as depreciation or opportunity costs that do not involve the payment of money.
Variable expenses are those expenses that vary with the level of production.
Fuel and fertilizer expenses are two examples. Fixed expenses, on the other hand, are those expenses that do not vary with the level of production. A property tax payment, which must be paid even if output of the firm is zero, is a form of fixed expenses.
This refers to the capital structure that minimizes the firm’s composite cost of capital for a given amount of debt and equity capital. This will be influenced by the relative cost of financing capital acquisition opportunities with debt and equity capital.
The decision making process associated with investment in fixed assets
(machinery and equipment, land and buildings. There are various forms of capital budgeting methods available, including the payback period method, the profitability index method, the internal rate of return method and the net present value method. Each will be covered in depth later in this booklet.
Financial analysis refers to the assessment of a firm’s financial condition or well being. Its objectives are to determine the firm’s financial strengths and identify its weaknesses. The primary tool in financial analysis is financial ratios or indicators of liquidity, solvency, profitability, economic efficiency, and debt repayment capacity.

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More terms and jargon will be added as we proceed thru this booklet.
Various methods used in financial analysis will also be introduced, including structural econometric business forecasting. We will define these terms as they are introduced.

12
There are several approaches to measuring the liquidity of a firm depending on whether you are talking about asset liquidity, credit liquidity or cash flow liquidity.
Two common measures of asset liquidity are the current ratio and the level of working capital. The current ratio is given by:
(1) Current ratio = current assets

current liabilities where current assets are those assets that can be converted to cash within the year and current liabilities are those liabilities that are due within the year. If this ratio is greater than 1.0, the firm is said to be liquid, or able to retire all its current liabilities with its current assets and have cash left over. Studies have shown, however, that the firm can be liquid and still fail. Other ratios
(acid test ratio and cash ratio) represent variations of equation (1), where specific categories of current assets are excluded from the numerator.
The level of working capital is given by:
(2) Working capital = current assets – current liabilities
If the level of working capital is positive, then the firm has sufficient current assets to cover all its current liabilities and still have cash left over. This term is sometimes referred to as net working capital.
We will discuss measures of credit liquidity and cash flow liquidity later in this booklet.
There are numerous approaches to measuring the solvency of the firm. They all involve balance sheet data and are transformations of one another. These measures include the debt ratio, the net worth ratio, the asset ratio and the leverage ratio. Each is defined as follows:

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(3) Debt ratio = total debt or liabilities

total assets
(4) Net worth ratio = total net worth or equity

total assets
(5) Asset ratio = total assets

total debt or liabilities
(6) Leverage ratio = total debt or liabilities

total net worth or equity
Suppose the firm’s total assets are $100 and its total debt or total liability is
$25. In this case the firm’s debt ratio would be 0.25, its net worth ratio would be 0.75, its asset ratio would be 4.0, and its leverage ratio would be
0.33. All ratios indicate this firm would be solvent; it could convert all of its assets ($100) to cash, retire all of its liabilities ($25), and still have cash left over ($75).
In addition to the level of net income, which we said earlier is a measure of profitability, other commonly used measures exist. These include the rate of return on assets (ROA) and the rate of return on equity capital (ROE).
Another measure is the net or operating profit margin. These measures can be defined as follows:
(7) Rate of return on assets = (net income + interest expense)

total assets
(8) Rate of return on equity = net income

total equity or net worth
(9) Net profit margin = (EBIT – tax)

total revenue where EBIT represents earnings before interest and tax payments, or net income minus interest and tax payments.
Suppose a firm had the following characteristics: $100 in total assets, $25 in total debt, total revenue of $200, interest expenses of $5, taxes of $10 and other expenses totaling $130. The firm’s net income would be $55 (i.e.,
$200 - $130 - $5 - $10) and its EBIT would be $70 (i.e., $55 + $5 +$10).
This would result in a ROA of 60% (i.e., {[$55 + $5]

$100}

100); an ROE

14 of 73% (i.e., [$55

$75]

100), and a net profit margin of 30% (i.e., {[$70 -
$10]

$200}

100).
Like the other financial indicators, there are a variety of measures of economic efficiency used by financial analysts. These include a number of expense ratios (interest expense ratio, variable expense ratio, depreciation expense ratio) as well as several turnover ratios (total asset turnover and fixed asset turnover). These ratios are defined as follows:
(10) Interest expense ratio = interest expenses

total revenue
(11) Variable expense ratio = total variable expenses

total revenue
(12) Depreciation expense ratio = depreciation expenses

total revenue
(13) Total asset turnover ratio = total revenue

total assets
(14) Fixed asset turnover ratio = total revenue

fixed assets
Assume the firm’s depreciation expense is $20 and its total fixed assets are
$85. Continuing with the example discussed above, the firm’s interest expense ratio would be 2.5% (i.e., [$5

$200]

100), its variable expense ratio would be 55% (i.e., {[$130 - $20]

$200}

100), its depreciation expense ratio would be 10% (i.e., [$20

$200]

100), its total asset turnover ratio would be 2.0 (i.e., $200

$100) and its fixed asset turnover ratio would be 2.35 (i.e., $200
 $100). This means the firm’s interest expenses, variable expenses and depreciation expenses are 2.5%, 55% and 10% of every dollar of total revenue, respectively. The firm furthermore turns over its total assets twice each year and fixed assets 2.35 times each year.
Finally, measures of debt repayment capacity include term debt and capital lease coverage ratio, times interest earned ratio, and debt burden ratio to name a few. They are calculated as follows:

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(15) Term debt and capital
lease coverage ratio
= (EBIT – taxes)

term debt and capital lease payments
(16) Times interest earned = (EBIT–taxes)

scheduled interest payments
(17) Debt burden ratio = total debt outstanding

net income
The financial indicators in equations (15) and (16) should be greater than one. This would indicate the firm has, at minimum, the capability to service their commitments as scheduled. Obviously the greater these ratios are, the greater the comfort zone for the lender.
Equation (17) indicated the number of periods needed to retire total debt outstanding if net income was used entirely for this purpose. If the net income statistic used comes from an annual income statement, then this ratio would reflect the number of years necessary to retire the firm’s entire debt.
While this may reflect the eventual application of net income, it does indicate to a lender the firm’s ability to retire debt from operations.

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Financial analysis was defined earlier as “the assessment of a firm’s financial condition or well being”. Its objectives were said to be “determine the firm’s financial strengths and identify its weaknesses”. A number of financial indicators were defined and interpreted.
Nothing however was said about the basis for comparison other than a specific level so satisfy the definition of liquidity, etc.
Often the most accurate or reveling assessment of a firm’s financial strength and performance involves assessing the trends in a number of ratios for the firm over time and the deviations from the financial achievements of other similar or “like kind” firms. This is called historical financial analysis and
comparative financial analysis, respectively.
Historical financial analysis involves comparing the firm’s current performance with its performance in previous years, and identifying the underlying reasons for deviations from expectations. This involves computing the above measures for liquidity, solvency, profitability, economic efficiency and debt repayment capacity (one measure from each group should do) for the latest available year and comparing the values of each measure with say the Olympic average over the last five years (drop the high and low when computing the average).
Understanding why any undesirable deviations in liquidity, solvency, profitability and other categories of financial indicators occurred during the most recent period may help formulate strategies that prevent further occurrences. There may very well be a good explanation tied to one-time events beyond the control of the producer. Conducting a comparative financial analysis with similar firms will help confirm this conclusion

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As the name suggests, comparative financial analysis involves comparing the financial strength and performance of the firm with that of similar firms.
The current weak performance of the firm may not be a one-time event beyond the control of the producer, but rather something similar firms did not experience, at least not to the same degree.
1
A study by W. H. Beavers showed that the financial ratios of firms that subsequently fail are different from those firms that survived.
2 Beavers tracked the current ratio, debt ratio, rate of return on assets, and the reciprocal of the debt burden ratio described earlier in this booklet
(equations (1), (3), (7) and (17) respectively). This study will be emphasized in a slide show presented during one of the lectures in this course.
Catching undesirable differences from other firms in its peer group early enough to minimize or eliminate their long-term effects is paramount to the long run success of the firm. The gap between the successful firms and the firms that failed in the Beavers study was not that great in the initial year.
The growth in the use of borrowed funds to cash flow operations in subsequent years, however, eventually led to sharp differences between the successful and failing firms as additional interest expenses grew and ROA declined.
Pro forma analysis refers to the process of forming expectations about, or forecasting future trends for, annual returns and risk confronting the firm as it makes important investment and financing decisions. Much more will be said about this topic as we move through this booklet.
1 References to similar or “like kind” firms refers to comparisons with firms of similar size producing the same products in the same geographical area for the same market structure.
2 W. H. Beavers, “Financial Ratios and Predictors of Failure”, in Empirical Research in
Accounting: Selected Studies, Supplement to Journal of Accounting Research, Volume 66:77-
111.

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The bottom line is that completion of financial statements to meet external reporting requirements only to then store them in a filing cabinet ignores a rich source of information on assessing the financial health of the business.
Furthermore, calculation of the various measures described in equations (1) thru (17) in the previous section of this booklet does not necessarily help matters much. The issue is whether or not the firm’s performance improved over last year’s results or the Olympic average over the last 5 years. And, if not, why? This requires the use of historical financial analysis. In addition, comparative financial analysis can tell us whether a down trend in these various performance indicators is something unique to the firm, or if it is being experienced by other “like kind” firms as well.

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The firm faces a number of decisions with regards to input choices and product choices over time. Let’s begin with short run, with the existing firm having a given amount of land and capital, and a given level of management resources. Let’s further assume for the moment that the firm produces a single product. While we assume conditions of perfect competition, imperfect competitors follow most but not all decision rules discussed here.
Up to this point we have been assessing the allocation of current resources to maximize profits. An important question pertaining to investment expenditures and planned growth of the firm is how large the firm should be and the combination of resources to use in expansion. These are two separate issues.
Figure 4 – Economies of Size.

Q
1
45
How large should the firm be? Many industries have been the subject of studies focusing on the economies of size. Firms often benefit from growth due to increases in efficiency as well as perhaps being able to buy in bulk and hence pay a lower price for inputs. Let’s discuss the previous graph to better understand the issues involved.
At a current market price of P, firm size #1 would not be covering its cost of production (i.e., SAC > P at Q
1
). Of the options in this graph, the firm needs to operate at a minimum of Q
2
units of output. At size #2, the firm would be earning an average profit of P – SAC
2
at Q
2
.
Should the firm expand to size #4, earning an average profit of P – SAC
4
?
The answer to this question is a qualified “No” in an industry where there are no barriers to entry or exit. Why? Suppose as other firms entered, supply increased shifting the market supply curve to the right and depressing the price of the product to P
LR
. Firm size #4 would face the prospect of downsizing its operations since it is no longer covering its costs of production at Q
4
with P
LR
. This brings up the problem of asset fixity faced by many businesses, or the inability to sell specialized fixed assets in periods of economic decline.
Suppose the firm was raising cotton and had recently purchased a $300,000 cotton picker. Should cotton prices fall sharply (like from P to P
LR
above) and the firm wanted to flex to another commodity, it might find it hard to dispose of the cotton picker in a weakened secondary farm machinery market. A cotton picker has no use to growers of other commodities or to non-farm sectors because of its specialized nature. Furthermore, other cotton farmers may well be attempting to sell high cost capital items at the same time.
Firm size #3 is the only size depicted in this graph that is positioned to remain a viable business should the price fall to P
LR
. It is operating at the minimum point on the long run average cost (LAC) curve, where P
LR
= LAC
= MC
3
. The LAC curve, which is an envelope of a series of short run average cost (SAC) curves, is known as the long run planning curve . Up to the minimum point on the LAC curve, the firm can benefit from increasing economies of size. After that point, the firm would experience decreasing economies of size. Previous studies for many firms show a third range of the LAC curve exhibiting constant returns to size, where the LAC curve is relatively flat before decreasing returns occur.

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A large segment of a firm’s balance sheet is concentrated in fixed assets in the short run. In agriculture, the firm’s tillable land base, its milking capacity, its feedlot capacity, etc. requires capital expansion if more production is to be forthcoming. Other forms of fixed capital such as harvesting equipment may involve the decision of whether to increase capital or labor, and if so, how much?
Figure 5 – Economics of Resource Expansion.
Suppose the firm depicted above wanted to double its output from 10 units to 20 units. You will recall that an isoquant indicates how different combinations of inputs can produce an identical amount of output, and that the point of tangency between the iso-cost line and the isoquant indicates the profit maximizing level of input use. The firm is currently producing 10 units of output using one unit of capital and 5 units of labor (point A) in the above graph. Given the goal of doubling its output, the firm faces the decision of how much to expand its use of capital and labor.

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Before digging into the analytics underlying specific investment analysis models, we think it is beneficial to gain an understanding the how internal and external factors influence the growth of firm equity. An important lesson learned here is the notion that the use of debt capital is a “double edged sword” .
Let the following symbols represent specific variables: r Rate of return on assets i Rate of interest on debt capital
D Beginning debt outstanding
E Beginning net worth or equity
A Beginning total assets t
Y
Income tax rate w Rate of withdrawals from income
Y Net income
Net income before taxes would be given by:
(18) Y = [r(D + E) – i(D)] while the level of retained earnings or change in equity would be given by:
(19) Y = [r(D + E) – i(D)](1 – t
Y
)(1 – w)
Rearranging terms, we see that
(20) Y = [(r – i)D + rE] (1 – t
Y
)(1 – w)
Dividing both sides of this equation by the beginning level of equity, the rate of return on equity capital would be given by:
(21) ROE = [(r – i)L + r](1 – t
Y
)(1 – w) where L is the debt-to-equity ratio, or L = D/E.

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Equation (21) gives us a simple yet comprehensive economic model that allows us to examine the effects of internally and externally imposed constraints on growth.
Internally imposed constrains on growth refers to decisions made by the producer that affect the annual growth in equity. Assume the following values for the variables in the growth model: r 10% or .10 i 7% or.07
D $0
A $100,000 t
Y
25% or .25 w 0% or 0.0
Given these values, the rate of return on equity capital or ROE would be:
(22) ROE = [(.10 – .07)0 + .10](1 – .25)(1 – 0)
= [.10](.75)(1.0)
= .075 or 7.5%
If the firm withdrew 50 percent of after-tax income for other uses, the firm’s
ROE would be equal instead to:
ROE = [(.10 – .07)0 + .10](1 – .25)(1 – .50)
= [.10](.75)(.50)
= .0375 or 3.75%
The firm above internally rationed its use of debt capital to avoid exposure to financial risk. If the firm instead had borrowed $100,000, giving it a debtto-asset ratio of 0.50 or a debt-to-equity ratio of 1.00, its ROE would be:
ROE = [(.10 – .07)1.0 + .10](1 – .25)(1 – .50)
= [.03 + .10](.75)(.50)
= .04875 or 4.875%

49 which is higher than the ROE given previously. Thus, the internal rationing of the use of debt capital and the decision to withdraw equity from the firm for other uses such as family living expenses affects the rate of return and economic growth achieved by the firm.
Externally imposed constrains on growth refers to external policies or events occurring in the economy that an individual consumer has little or no control over, but that affect the annual growth in equity. Let’s assume that the firm is characterized by the following values: r 10% or .10 i 7% or.07
D $50,000
A $100,000 t
Y
25% or .25 w 50% or 0.50
The firm’s ROE under these conditions would be:
(23) ROE = [(.10 – .07)1.0 + .10](1 – .25)(1 – .50)
= [.03 + .10](.75)(.60)
= .0585 or 5.85%
If the firm must pay a one percentage point risk premium for its term loans, which results in a 8% cost of debt capital, the ROE would fall to:
ROE = [(.10 – .08)1.0 + .10](1 – .25)(1 – .50)
= [.02 + .10](.75)(.60)
= .054 or 5.4% which is 0.45 percentage points lower than earned by others who do not have to pay this risk premium of term loans.
If lenders not only charge a one percentage point risk premium but also limited the firm to a 75 percent debt-to-equity ratio (an example of external credit rationing), the firm’s rate of return on equity or ROE would be:

50
(24) ROE = [(.10 – .08)0.75 + .10](1 – .25)(1 – .40)
= [.015 + .10](.75)(.60)
= .05175 or 5.175% which is .675 percentage points lower than the ROE given by equation (24) that excluded the risk premium and credit rationing.
Another external constraint on economic growth is imposition of income taxes. If the effective income tax rate is 35 percent rather than 25 percent, staying with the parameters in equation (24), we see the value of ROE would be:
(25) ROE = [(.10 – .08)0.75 + .10](1 – .35)(1 – .40)
= [.015 + .10](.65)(.60)
= .04485 or 4.485% which is now .915 percentage points lower than the value given earlier in equation (23).
The use of debt capital can be seen as a two-edge sword. As long as the rate of return on assets (r) is greater than the cost of debt capital (i), or r > i., the use of debt capital contributes to the growth of the firm’s equity. The firm however is exposed to financial risk when borrowing if events lead to the situation where the rate of return on assets (r) is less than the interest rate on debt capital (i), or r < i.
Let’s assume that the rate of return on assets fell from 10% to 2% in a given year while the interest on outstanding debt was 8 percent. Holding all other conditions, we see that the firm’s ROE would fall to:
(26) ROE = [(.02 – .08)0.75 + .02](1 – 0)(1 – 0)
= [(-.06).75 + .02](1.00)(1.00)
= -.025 or –2.5%
The value of the income tax rate would be zero due to the negative net farm income. The rate of withdrawal would also be zero for the same reason
(which explains the two “1.00” appearing in this equation.

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Thus, while the firm’s ROA was 2 percent, the rate of growth in equity would be negative. The more leveraged the firm is, the greater a low ROA will have upon the firm.
For example, assume the firm in this case had a leverage ratio of 2.0 rather than .75. Prove to yourself that the value of RGE would be – 10%.
More will be said about business and financial risk as we begin discussing evaluating and ranking investment opportunities later in this booklet.
Internal factors affecting growth:
1. Implicit cost of capital,
2. Lack of understanding under performance relative to benchmarks,
3. Withdrawals lowering retained earnings, and
4. Aversion to risk affecting investment decisions (internal capital rationing).
External factors affecting growth:
1. Income tax rates,
2. External capital rationing,
3. Explicit cost of capital, and
4. Other externalities such as weather affecting net income.

52
The concept of the time value of money is based upon the economic fact that
$1 today is worth more than the promise of $1 at some future date because of its current earnings potential. Other reasons for preferring payment today may include your personal preference to spend this dollar now on a consumer good rather than postponing consumption until later. Or perhaps the promise of a payment at a future date carries with it less than complete certainty that the payment will be received.
We will focus on the economics of the time value of money. The time value of money can be viewed either within the context of present value of future sums, or future value of present sums. One is the opposite of the other.
We will confine our discussion to the present value of future sums or stream of income given our interest in capital budgeting.
Letting FV
N
represent the value of a payment to be received N periods from now. We want to know what the present value of that future payment is today. To find this value, we must discount FV
N
back N periods by the rate of return (R) we could have received as our next best opportunity, or:
(27) PV = FV
N
/(1+R) N or
(28) PV = FV
N
(PIF
R,N
) where PIF
R,N
is the present value interest factor for interest rate R and N periods in the tables distributed in class and PV is the present value of a sum FV
N
received N periods from now.
3
3 The PIF
R,N
interest factors in the Appendix are based upon the formula 1/(1+R) N . The EPIF interest factors used starting in equation (30) are based upon the formula (1- PIF
R,N
)) ÷ R.

53
For example, what is the present value of $500 to be received 10 years from today if the discount rate is 6 percent?
(29) PV = $500/(1+.06) 10
= $500[1/(1.791)]
= $500(.558)
= $279
Thus, the present value of the $500 to be received in 10 years is $279.
Suppose instead of receiving $500 in a single payment 10 years from now, you were offered the opportunity to receive annual payments of $50 over the next 10 years. Since these payments are of equal value over the 10-year period and the discount rate is the same over time, we can use the following approach to calculating the present value of this stream of payments:
(30) PV = NCF
E
(EPIF
R,N
)
= $50(7.360)
= $368 where EPIF
R,N represents the equal payment-present value interest factor found in the equal payment interest factor table. The value of EPIF
.06,10
is
7.360, which gives us a present value of $368. Thus, the present value of a stream of $50 annual payments over a 10 year period ($368) is greater than the present value of a single payment of $500 received 10 years from now
($279). Why? Because of the time value of money received earlier in the
10- year period.
We could have arrived at the same value taking the longer approach of calculating the present value of each annual payment and then adding the payments together, or:
(31) PV = NCF
1
(PIF
.06,1
) + NCF
2
(PIF
.06,2
) + …. + NCF
10
(PIF
.06,10
)
= $50(.943) + $50(.890) + …. + $50(.558)
= $368

54 which is the same as:
(32) PV = NCF
1
[1/(1+R)] + NCF
2
[1/(1+R) 2 ] + …. + NCF
10
[1/(1+R) 10 ]
= $50(1/(1+.06)] + $50[1/(1+.06) 2 ] + …. + $50[1/(1+.06) 10 ]
= $368
Remember the assumption in equation (30) is that both the size of the annual payments and the annual discount rate chosen are identical in each year.
Suppose that, instead of receiving an equal annual stream of $50 payments, you received the $500 in two installments: $250 after 5 years and $250 after
10 years. Equation (30) no longer is applicable in this case. We can instead use a modified form of the approaches outlined in equations (31) and (32) as follows:
(33) PV = NCF
5
(PIF
.06,5
) + NCF
10
(PIF
.06,10
)
= $250(.747) + $250(.558)
= $186.75 + $139.50
= $326.25 or
(34) PV = NCF
5
[1/(1+R) 5 ] + NCF
10
[1/(1+R) 10 ]
= $250[1/(1+.06) 5 ] + $250[1/(1+.06) 10 ]
= $326.25
This present value is less than the present value of the steady stream of $50 annual payments ($368 given by equation (31) or (32)) since less is received earlier in the period, but more than the single payment received 10 years from now ($279 given by equation (29)).
Thus far we have assumed a single valued discount rate over the 10-year life of this analysis. If an investor is potentially exposed to unique degrees of risk exposure over the economic life of the investment project, we need to account for this when calculated the present value.

All the equations involving calculation of the present value of a future stream thus far has assumed identical discount rates (i.e., R
1
= R
2
= … =
R
N
). The use of the present value interest factor tables distributed in class rests on this assumption. That means that equations (31) and (32) are not applicable if this assumption does not hold. Let’s relax this assumption be restating equation (32) as follows:
(35) PV = NCF
1
[1/(1+R
1
)] + NCF
2
[1/{(1+R
1
)(1+R
2
)}] + ….
+ NCF
N
[1/{(1+R
1
)(1+R
2
)…(1+R
N
)}]
If the discount rate increases by one-half a percentage point each year for reasons we will explore later, the right-hand side of equation (35) will take the form:
= $50(1/(1+.06)] + $50[1/{(1+.06)(1+.065)}] + ….
+ $50[1/{(1+.06)(1.065)…(1+.105)}]
We have covered a number of variations in the calculation of the present value of a future sum or stream of cash flows over time. There are several popular applications of these concepts we can explore before proceeding with the topic of capital budgeting.
Several examples come to mind. One is a perpetuity or an annuity that continues forever. Another is the expected cash rent received from an infinitely lived asset like land. Assume you can charge a cash rent of $50 per acre for land annually and the annual discount rate is 6 percent. The present or “capitalized” value of this tract of land can be approximated as follows:
(36) PV = NCF
E
÷ R
E
= $50/.06
= $833.33 per acre.
55

56
In another example, the present value of a $100 perpetuity discounted back to the present at 5 percent is:
(37) PV = $100/.05
= $2,000
We will use this concept later when evaluating two mutually exclusive investment projects with unequal lives.
The procedure for solving for an annuity payment when the discount rate, number of payments and present value are known can also be used to determine the level of payments associated with paying off a loan in equal installments over time. For example, suppose a company wanted to purchase a piece of machinery.
To do this, it borrows $6,000 to be repaid in 4 equal payments at the end of each of the next four years. The interest rate to be paid to the lender is 15 percent on the outstanding portion of the loan. What we don’t know is the value of this payment. Given the information, we know that
(38) $6,000 = PI(EPIF
.15,4
)
$6,000 = PI(2.855) so
(39) PI = $6,000/2.855
= $2,101.58
Thus, the annual principal and interest payment for this $6,000 4-year loan carrying an interest rate of 15 percent is $2,101.58.
We can state this problem in terms of the PI payment as follows:
(40) PI = LOAN/(EPIF
R,N
)
We can calculate the separate principal and interest payments for this loan that is needed to measure interest expenses for taxable income purposes.
Let’s assume a $1,000 loan with annual payments over a 5-year period at an

57 interest rate of 8 percent. Using equation (40), the principal and interest payments would be:
(41) PI = $1,000/(EPIF
.08,5
)
= $1,000/(3.993)
= $250.46 or $250.46 annually starting at the end of the first year. The interest portion of this payment in the first year would be equal to:
(42) I = $1,000(.08)
= $80.00
The principal portion of this payment in the first year would therefore be:
(43) P = $250.46 - $80.00
= $170.46 which means the interest payment in year two would be based upon $829.54 rather than $1,000. The entire loan repayment schedule would be:
Table 1 – Amortization table for $1,000 loan at 8% for 5 years.
Year P I PI Balance
1 $170.46 $80.00 $250.46 $829.54
2 184.10 66.36 250.46 645.45
3 198.82 51.64 250.46 446.63
4 214.72 35.73 250.46 231.90
5 231.90 18.55 250.46 0.00
Equation (40) can be twisted in any of four ways. First, you can solve for the level of the principal and interest payment or PI as we did above given the interest rate R, number of payments N and loan amount (LOAN). Second, you can solve for the level of the loan that is associated with a given payment PI, interest rate R and number of payments N, or:
(44) LOAN = PI(EPIF
R,N
)

58
The last two options require solving for the equal payment present value interest factor, or:
(45) (EPIF
R,N
) = LOAN/PI and then finding the corresponding values of R (if N is known) or N (if R is known) in the equal payment interest factor (EPIF
R,N
) tables distributed in class.
While the focus here has been on the present value of a future sum
(equations 27 and 28) and future streams of annual sums (equations 30 through 32), some applications may require reversing the timing perspective of a decision. This can be done by solving for the future value (FV) rather than present value (PV) in equations 27 and 28 and dividing by rather than multiplying by the annual interest rate factors in the subsequent equations.
For the purposes of this course, our focus will remain on bringing future values back to the present, or present value analysis.

59
Capital budgeting involves the analysis of the additional net cash flows associated with investment projects over their entire economic life. The objective of capital budgeting, simply put, is to determine if the net benefits from making the investment is positive or negative. The following discussion describes for capital budgeting methods presented in the following order: payback period method, internal rate of return method, and net present value method.
The purpose of the payback period method is simply to find the number of years it would take for an investment to pay for itself. Suppose you are considering two mutually exclusive projects. Both cost $10,000 and have an economic life of 5 years. Further assume that the net cash flows generated by these two investment opportunities (project A and project B) are represented by the net cash flows below:
Table 2 – Net cash flows for two projects.
Year Project A Project B
1
2
3
$3,000
3,000
3,000
$2,000
3,000
5,000
4
5
Total
3,000
3,000
15,000
2,000
1,000
13,000
Finally, assume that the terminal value (the market value of any assets acquired in by the project) at the end of the 5 th year in both instances is equal to zero. We will tackle that issue later in this course.
Based on this information, the payback period or length of time required to recover your initial investment of $10,000 is 4 years for project A and 3 years for project B. That is, 4 years would elapse before you would accumulate enough net cash flows from project A to “pay back” the initial
$10,000 as opposed to just 3 years for project B.

60
If we were to rank these projects according to the length of their payback period, we would prefer project B over project A.
The payback period method is computationally easy to use. It also provides a measure of the project’s liquidity. However, it fails to consider the timing of the net cash flows generated by a project both before the payback period has been reached as well as afterward. It largely ignores the time value of money. Finally, there is no objective decision rule associated with the method. That is, we are not maximizing profits, minimizing costs or attempting to satisfy some other objective.
To remedy the deficiencies noted above for the payback period method, we can use a capital budgeting technique that accounts for the present value of the entire stream of net cash flows over the life of the project. One such technique is the net present value method. In the case where the discount rate is expected to remain constant over the entire economic life of the investment project (i.e., R
1
= R
2
= … = R
N
), the net present value of an investment project (NPV) is given by
(46) NPV = NCF
1
(PIF
R,1
) + NCF
2
(PIF
R,2
) + …. + NCF
N
(PIF
R,N
) - C where C is the initial capital outlay for the assets acquired under the project.
Since this outlay is made at the start of the project, no discounting is needed.
We can restate equation (46) as follows:
(47) NPV = NCF
1
[1/(1+R)] + NCF
2
[1/(1+R) 2 ] + .. + NCF
N
[1/(1+R) N ] - C where NCF
1
once again represents the annual net cash flow generated by the project in year 1, NCF
2
represents the net cash flow generated by the project in year 2, etc., R is the discount rate and N is the number of years in the life of the project. Finally, C represents the original cash purchase price less any cash discounts (but not the trade-in value of used machinery deducted from the purchase price at the time of the purchase). You should recognize equations (46) and (47) as being very similar to equations (31) and (32) from a discounting of a net cash flows standpoint.

61
The net present value of an investment project can be viewed as the “profit” or dollar measure of the amount saved by making this investment now.
Given the assumptions of profit maximization and complete certainty, you should accept those projects whose net present values are positive (i.e., NPV
> 0). You will be indifferent between whether or not to invest when the net present value equals zero (i.e., NPV = 0), and you should reject all projects whose net present value is negative (i.e., NPV < 0). We will address the issue of budget constraints later in this booklet when ranking projects.
Let us assume that you expect a constant discount rate of 5 percent over the
5-year economic lives of two mutually exclusive investment projects: project
A and project B. The net present values for both projects are reported in
Table 4 below:
Table 3 - Determination of the NPV for Projects A and B.
Project A Project B
(1) (2) (3) (4) (5) (6)
Net Cash Present Value Present Value Net Cash Present Value Present value
Flow Interest Factors of NFC i
Flow Interest Factors of NFC i
Year (NCF i
) PIF
0.05,I
(1) x (2) NFC i
PIF
0.05,I
(4) x (5)
(i)
1 $ 3,000 0.952
2 3,000 0.907
3 3,000 0.864
$ 2,856
2,721
$ 2,000
3,000
2,592 5,000
0.952 $ 1,904
0.907 2,721
0.864 4,320
4 3,000 0.823
5 3,000 0.784
2,469
2,352
2,000
1,000
0.823 1,646
0.784 784
$ 15,000 $ 12,990 $ 13,000
Less initial cost - 10,000 Less initial cost
$ 11,375
- 10,000
Net present value $ 2,990 Net present value $ 1,375
This table shows, for example, that project A has a higher net present value than project B, because it generates higher net cash flows in the first year of the project where the interest factor is at its highest and also has a higher cumulative net cash flow over the entire 5-year period. While both projects should be considered since each was found to have a positive net present value, project A should be preferred over or ranked higher than project B.
This represents a reversal of the rankings given by the payback method. A profit-maximizing farm operator should consider investing in both of these projects as long as their combined cost is less than or equal to the amount of funds available to finance new projects.

62
In the case where NCF
1
= NCF
2
= … NCF
N
, we can simplify the computational procedure along the lines initially suggested by equation (46) by instead using
(48) NPV = NCF
E
(EPIF
R,N
) – C where NCF
E
represents the equal annual net cash flows generated by the new investment project. For example, we could have used equation (48) instead of equation (46) to compute the net present value for project A.
Locating the interest factor (EPIF
R,N
) in the equal payment interest factor table and substituting this value into equation (48), we see that the net present value for project A is equal to:
(49) NPV = $3,000(4.329) - $10,000
= $2,990 which is identical to the net present value reported for project A in Table 3.
The net present value formula presented in equations (46) and (47) should be seen as a special case of the present value formulas presented in equations
(31) and (32). We shall limit the examples studied for the moment to those which permit us to use equations (46) and (47); that is, we shall assume a constant discount rate over the economic life of the project.
The present value discussion thus far was based upon assuming a particular discount rate. One can ask the question of how much higher or lower this rate would have to be before the net present value of these projects would fall to zero . This information is provided by another capital budgeting technique incorporating the time value of money concept: the internal rate of return method.
The internal rate of return for an investment project is defined as that discount rate in equations that equate the present value of the annual net cash flows with the project’s net capital outlay. For discount rates lower than the internal rate of return (i.e., IRR>R), the net present value of the project will be positive. Conversely, the net present value of an investment project will

63 be negative if the discount rate is higher than the internal rate of return (i.e.,
IRR<R). Thus, we would accept all projects where IRR>R, and we would rank these projects according to the size of their IRR.
In computing the internal rate of return, therefore, we must find that value of
R which results in a net present value equal to zero, or
(50) NPV = NCF
1
(PIF
R,1
) + NCF
2
(PIF
R,2
) + …. + NCF
N
(PIF
R,N
) – C

0 which is nothing more than equation (46) set equal to zero. If the net cash revenue flows are identical in each year of the investment project, we can instead use
(51) NPV = NCF
E
(EPIF
R,N
) – C

0 which is nothing more than the equation (48) set equal to zero. Thus, all that remains is to find that value of R in these equations which results in a NPV equal to zero.
Suppose that you wanted to know the internal rate of return for project A and project B described above. For project A, the internal rate of return can be found by substituting the values for Y
E
and C into equation (51), or
(52) $3,000(EPIF
R,5
) - $10,000 = 0
Solving equation (52) for the interest factor (EPIF
R,5
), we see that
(53) (EPIF
R,5
) = $10,000/$3,000
= 3.333
The internal rate of return is then found by locating that value of R associated with the equal payment present value interest factor (EPIF
R,N
) of
3.333 for N = 5 in the equal payment interest factor (EPIF
R,N
) tables. Doing this, we find a value of R that is approximately equal to 15 percent. This would suggest that your opportunity of return (R) would have to exceed 15 percent before you should consider not investing in project A. For project B, where equation (50) rather than equation (51) must be used, the value of R yielding a net present value of zero must be found by trial and error.

64
The search procedure is begun by selecting the value of R you think most closely approximates the true value of R into equation (50). If the resulting solution for the net present value is greater than zero, you have underestimated the true value of R and must try a higher value in equation
(50). If the solution value, however, was less than zero, you have overestimated the true value of R and must try a lower value in subsequent attempts.
This iterative procedure is continued until the solution for the net present value is approximately equal to zero. In the case of project B, the internal rate of return is approximately equal to 10 percent. Thus, based upon a comparison of these internal rates of return, we would again prefer project A to project B because since IRR
A
> IRR
B.
Although any project can have only one net present value (NPV), a single project under certain circumstances can have more than one internal rate of return (IRR). The reason for this can be traced to the calculation of the IRR.
If the initial capital outlay is the only negative value in equation (50) and all of the annual net cash flows are positive, there is no problem. Problems occur when there are sign reversals in the annual cash flow stream. There can be as many solutions for IRR as there are sign reversals. To illustrate, consider the following example:
Year 1 net cash flow
Annual cash flows
+10,000
Year 2 net cash flow
Year 3 net cash flow
- 10,000
+12,000
This pattern of cash flows over a two year period has two sign reversals; from +$10,000 to -$10,000 and then from -$10,000 to +$12,000. So there can be as many as two positive IRRs that will result in a NPV of zero.
Which solution is correct? Neither solution is valid! Neither provides any insight to the true project returns. Thus when there is more than one sign reversal in the flows of funds over the project’s economic life, the possibility of multiple IRRs exists, and the normal interpretation of the IRR loses its meaning.

65
The payback period method, because of its failure to account for the level of cash flows beyond the payback period, does not in itself represent a desirable capital budgeting method. It is the only method that suggested project B should be ranked higher than project A! The net present value and the internal rate of return methods, which do account for these factors, will provide the same order of ranking for mutually exclusive investment projects in most but not all cases. The possibility of multiple solutions with the internal rate of return method poses a problem. Another issue is that the net present value method discounts the net cash flows at the investor’s desired discount rate while the internal rate of return method assumes that the net cash flows can be reinvested at their internal rate of return (which may not be true).
In practice, many analysts will report as many as all four of the statistics discussed in this section. The net present value method, however, remains the appropriate basis for ranking the economic benefits generated by two or more mutually exclusive investment projects. The IRR is reported generally because many are familiar with this statistic and can directly compare it with the cost of debt capital or borrowed funds. The payback period also gives analysts an insight to the liquidity associated with alternative projects.

66
The net cash flows generated by an investment project represent the net change in the annual net cash flows generated by expanding the firm’s resources by making an investment. These annual net cash flows require a forward assessment of all the forces that affect future net cash flows over the economic life of the investment. The following table will help make its measurement clear:
Table 4 – Measuring Annual Net Cash Flows for Year 1.
Item:
1. Cash receipts
2. Cash operating expenses
3. Depreciation
4. Tax deductible expenses (2+3)
5. Taxable income (1 – 4)
6. Income tax payments (5 times 25%)
7. Net income after taxes (1 – 4 – 6)
8. Net cash flow (7 + 3)
Before new investment
$25,000
-15,000
-3,000
18,000
7,000
1,750
5,250
8,250
After new investment
Net change
$30,000 $5,000
-18,000 -3,000
-4,000 -1,000
22,000 4,000
8,000
2,000
1,000
250
6,000
10,000
750
1,750
Table 4 shows that the additional cash receipts generated by the investment project is $5,000 in year 1. The firm’s cash operating expenses (i.e., fuel expenses, hired labor expenses, fertilizer and chemical expenses) are expected to increase $3,000 annually while depreciation expenses are expected to increase by $1,000. This means the firm’s tax deductible expenses will be $4,000 higher than the current level if the investment project is undertaken. Subtracting these tax deductible expenses from cash receipts results in an increase in taxable income of $1,000.
If the tax rate is equation to 25 percent, income tax payments would be $250 higher annually, giving a net income after taxes of $750. Finally, we have to add back in the depreciation expenses used to compute tax deductible expenses (a non-cash flow) to measure the annual net cash flows associated with the project. Table 4 above indicates that this annual net cash flow in year 1 would be equal to $1,750.

67
This calculation must be made for each year covered by the capital budgeting decision. If we assume the annual net cash flows are identical over the entire economic life of the project, however, we can use equation
(51) when computing the net present value of the project.
The economic life of an investment project represents the length of time the firm intends to hold the assets acquired. It does not represent the service life
(sometimes called the useful life) of the assets, or the amount the amount of time taken before they wear out. For example, suppose that the firm plans to purchase a piece of equipment that normally wears out over a ten-year period but only plans to hold this piece of equipment for three years. Thus, the economic life of the investment is three years while the service life of the equipment is ten years . This distinction is important when accounting for the effects that the terminal value of a project has upon its feasibility.
On another front, two investment projects can also have different or
“unequal” service lives. Thus far, as in Table 3, we have assumed that two or projects have identical service lives. When this assumption is not valid, we cannot directly compare the net present values generated by two or more investment projects.
Suppose we were considering investing in one of two projects that provide identical services to the firm. One project has a service life of five years while the other has a service life of three years. While both projects provide identical services in a specific year, one project would require more frequent replacement. An each project must be replaced as it wears out over time in order to maintain the firm’s productive capital stock.
One approach to comparing these two projects is to compute the equivalent
level annuity that yields the same net present value if invested at a rate R over a period of N years. Let us assume that, as an alternative to project A which had a five-year economic life in Table 3, the firm is considering project C, which also costs $10,000 but generates equal annual net cash flows (NCF
E
) of $4,500 over a three-year service life. Continuing to assume that the firm requires a 5 percent discount rate and that the terminal value is equal to zero, the net present value over its original service life is:

68
(54) NPV = NCF
E
(EPIF
R,N
) – C
= $4,500(EPIF
0.05,3
) - $10,000
= $4,500(2.723) - $10,000
= $2,254 based upon applying equation (48) presented earlier. Note this is approximately $736 less that the net present value reported for project A in
Table 3 ($2,990 - $2,254).
The equivalent level annuity for an investment project is equal to the present value of NPV if invested at rate R for N periods. You will recall that we said in equation (48) that the present value of an equal annual net cash flow is equal to the value of the net cash flow (NCF
E
) multiplied by the “equal payment” present value interest factor (EPIF
R,N
).
Letting A eA
represent the equivalent level annuity for project A, we can rearrange terms in equation (49) to show that:
(55) A eA
= NPV
A
÷ EPIF
0.05,5
= $2,990 ÷ 4.329
= $691
Similarly, the equivalent level annuity for project C is equal to:
(56) A eC
= NPV
C
÷ EPIF
0.05,3
= $2,254 ÷ 2.723
= $828
Thus, while project A had a higher net present value during its original service life, project C is preferred after you take into account of how quickly project C ends. As long as both projects have the same discount rate and can be repeated over time, this approach will lead to the appropriate ranking. If a different discount rate is required for whatever reason, we must take the additional step of converting the equivalent level annuity into perpetuity.
For project A, this means we must compute:
(57) NPV 
A
= A eA
÷ R
A where NPV 
A
represents the net present value of an “infinity-lived” project.

69
Another approach to evaluating two investment projects with different service lives is to find the shortest common replacement chain . Assume we are considering two projects with different service lives, project AA and project BB. The cash flows for these projects are as follows:
Table 5 – Net present values for two projects with unequal lives.
Project AA Project BB
(1) (2) (3) (4)
Net Cash Net Net Cash Net
Year Flow Investment Flow Investment
0 $2,000
1 $ 600 $ 375
2 600
3 600
375
375
4 600
5 600
6 -
7
8
9
10
-
-
-
-
NVP
AA
= $600(3.791) - $2,000
= $274.60
375
375
375
375
375
375
375
$2,000
NVP
BB
= $375(6.145) - $2,000
= $304.37
The net present value of project BB therefore exceeds that of project AA.
Note, however, that the service life for project BB is twice as long as project
AA’s.
If we take the replacement chain approach to account for the differences between their service lives, the shortest common service life would be ten years, the exact length of project BB’s service life.
Taking this into account, we can put both projects on an equal footing using the replacement chain approach as follows:

70
Table 6 – Net present value for two projects with unequal
lives after applying the Replacement Chain approach.
Project AA Project BB
(1) (2) (3) (4)
Net Cash Net Net Cash Net
Year Flow Investment Flow Investment
0 $2,000 $2,000
1 $ 600
2 600
3 600
4 600
5 600
6 600
7 600
8 600
$ 375
375
375
375
$2,100 375
375
375
375
9 600
10 600
375
375
NVP
AA
= $600(6.145) - $2,000 - $2,100(0.621) NVP
BB
= $375(6.145) - $2,000
= $382.80 = $304.37
By replacing the equipment acquire in project AA at the start of the 6 th year
(i.e., at the end of the 5 th year) for $2,100 and repeating its use for another five-year period, we see that NVP
AA
> NVP
BB
. This reverses the investment conclusion we would have reached if we did not account for the unequal lives.
The ranking given by the analysis in Table 6 is identical to the ranking suggested by the equivalent annual annuity approach. The value of A eAA would be $63.43 ($274.60/EPIF
.05,5
) while the value of A eBB
would be
$39.42 ($304.37/EPIF
.05,10
).
Original and Terminal Value
Information is also needed on the original net capital outlay when the assets are acquired as well as their terminal or market value at the end of the economic life of the investment project. The net capital outlay was represented by C in equations (46), (47) and (48). This value should be the net cash purchase price after installation and any cash discounts.

71
The terminal value of assets purchased in an investment project must also be accounted for before the net present value of the project can be determined.
This value may be nothing more than the salvage value in the case of depreciable assets if the economic life of the investment project coincides with the service life of these assets. If the economic life is less than the service life, the terminal value will play a key role in determining the economic feasibility of the project. This value is what you expect to be able to sell these assets at the end of the project’s life. If land is involved, the terminal value may be considerably higher than its original value at the beginning of the project’s economic life.
Let T represent the terminal value of an asset at the end of the economic life of an investment project. Because the firm receives this value at a specific point in the future, we must discount this value back to the present. We can modify equation (46) to include this discounted terminal value as follows:
(58) NPV = NCF
1
(PIF
R,1
) + NCF
2
(PIF
R,2
) + …. + NCF
N
(PIF
R,N
) – C +
T(PIF
R,N
)
Similarly, equation (47) can be modified to include the discounted terminal value as follows:
(59) NPV = NCF
1
[1/(1+R)] + NCF
2
[1/(1+R) 2 ] + …. + NCF
N
[1/(1+R) N ] –
C + T[1/(1+R) N ]
Finally, in the case where NCF
1
= NCF
2
= … NCF
N
, we can simplify the computational procedure along the lines suggested by equation (48) by instead using
(60) NPV = NCF
E
(EPIF
R,N
) – C + T(PIF
R,N
)
Let’s return to the example contained in Table 3. The net present value of project A was $2,990 while the net present value of project B was $1,375.
Let’s now assume that, while the terminal value of the assets acquired under project A is zero, the terminal value of the assets acquired under project B is
$2,500.

72
The net present value of project B now becomes
(61) NPV = $11,375 - $10,000 + $2,500(PIF
0.05, 5
)
= $11,375 - $10,000 +$2,500(0.784)
= $3,335 where $11,375 represents the present value of the annual net cash flows over the five-year period illustrated in Table 3. The existence of the discounted terminal value now makes project B’s net present value of $3,335 higher than project A’s net present value of $2,990.
Another application of the terminal value is when you know in advance that the economic life of the investment project will be less than the service life of the assets acquired in the project. Suppose you plan to retire in two years and want to know whether or not it is profitable to invest in a project that normally would have a service life of five years. Focusing on project A in
Table 3, let’s assume you expect to sell the assets acquired under project A for $7,000 at the end of the second year of the project. Using equation (60) above, we see that:
(62) NPV = $3,000(EPIF
0.05,2
) - $10,000 + $7,000(PIF
0.05, 2
)
= $3,000(1.859) - $10,000 +$2,500(0.907)
= $1,926
Thus, you would accept this particular project if your discount rate was 5 percent.
An interesting twist on equation (62) is to find the terminal value that results in a net present value of zero. We can rearrange equation (60) to read:
(63) T = [C – NCF
E
(EPIF
R,N
)] ÷ (PIF
R,N
)
= [$10,000 – $3,000(EPIF
0.05,2
)] ÷ (PIF
0.05,2
)
= [$10,000 – $3,000(1,859)](1.103)
= $4,878
Thus, the terminal value of the assets acquired under this project would have to be below $4,878 before the firm should consider rejecting investment in this particular project.

73
The selection of an appropriate discount rate when calculating the net present value of an investment project involves finding that rate which reflects the after-tax rate of return the firm requires to cover the opportunity cost of not undertaking its next best alternative of a similar maturity and
risk exposure.
We will initially assume that this discount rate is identical over the entire economic life of the project and that it reflects the investor’s true opportunity cost associated with similar projects. We will relax this assumption later in this booklet when we focus more intensively on accounting for business and financial risk.

74
The purchase of depreciable assets required that we account for their cumulative depreciation when determining the net present value of the asset.
Let’s continue to assume for the moment that the annual net cash flows generated by the project are identical as are the annual discount rates. This allows us to use the following equation:
(64) NPV = NCF
E
(EPIF
R,N
) – C + T(PIF
R,N
)
The uniqueness of this decision is in the valuation of the terminal value or T.
In the case of depreciable assets, the market value of assets at the end of the economic life of the investment project is quite small, particularly when the economic and service lives are identical. At this point, the terminal value will be represented by the salvage value from depreciating the asset over time for tax purposes. There is typically no capital gain to be taxed when depreciable assets are disposed of at the end of the project. One exception to this rule is permanent buildings associated with real estate.
The purchase of real estate assets (land and accompanying buildings) is unique in that you have to account for capital gains income when determining the net present value of the asset. Recall from our earlier discussion that there are several deficiencies associated with simple capitalization formula which involved treating the value of land as a perpetuity or “infinitely lived” asset. The net present value of an investment in real estate with the characteristics of equation (63) is given by:
(65) NPV = NCF
E
(EPIF
R,N
) – C + T(PIF
R,N
) – [t
CG
(T – C)](PIF
R,N
) where t
CG
is the capital gains tax rate, and where the terminal value T is given by:
(66) T = C ÷ PIF
G,N

75
The variable G represents the rate of appreciation in real estate values expected over the investment project. It is often the cash in agriculture where the after-tax value of the terminal value often exceeds the present value of the annual net cash flows associated with the operations of the firm.
When participating in an auction or simply offering to purchase real estate in a one-on-one negotiation, it is important to know what the maximum value you can afford to pay for a tract of real estate. This value can be found by merely rearranging the terms in equation (65) to solve for the original purchase price which results in a net present value of zero!
To illustrate, suppose you are considering the purchase of some additional land that is expected to increase your firm’s annual net cash flows by $75 per acre. Let’s assume that no additional equipment is required to operate this additional land. Further assume you plan to retire in 20 years and are interested in knowing the maximum price you can justify paying now from an economic standpoint. A final set of assumptions is needed: (a) comparable tracts of land in your area are currently selling for $1,000 (i.e.,
V
0
= $1,000), (b) land is expected to appreciate at a seven percent annual rate over the next 20 years, (c) your capital gains will be taxed at a 25 percent tax rate, and (d) that your discount rate is 5 percent.
Given these assumptions, the present value of the future economic benefits from ownership of this land per acre would be: 4
(67) PV = NCF
E
(EPIF
R,N
) + {V
0
÷ PIF
G,N
}(PIF
R,N
)
– [t
CG
({V
0
÷ PIF
G,N
} – V
0
)](PIF
R,N
)
= $75(EPIF
0.05,20
) +{$1,000 ÷ PIF
0.07,20
}(PIF
0.05,20
)
– [0.25({$1,000 ÷ PIF
0.07,20
} – $1,000)](PIF
0.05,20
)
= $75(12.462) + {$1,000 ÷ 0.258}(0.377)
– [0.25($1,000 ÷ 0.258} – $1,000)](0.377)
= $935 + $1,461 – [0.25($2,876)](0.377)
= $935 + $1,461 – $271
= $2,125
4 We have simplified the algebra here by assuming the expected terminal value is based upon the value of comparables in the area and not the asking price set by the seller. That is, V
0
does not necessarily equal C.

76
You can justify making this investment as long as the net present value of this project is greater than zero (NPV = PV – C = $0). This suggests that the maximum you can bid for this tract of land on a per acre basis, or C, is also
$2,125, or that:
(68) $0 = PV – C
= $2,125 – C
Transposing C to the left-hand side, we see that C, the maximum bid price, is equal to $2,125.
If you had ignored the capital gains component when determining how much to bid, you would have incorrectly concluded that you could not justify bidding the current market value of land (V
0
) since the present value of the annual net cash flows ($935) is less than $1,000. Obviously you do not have to bid $2,125 if land is currently going for comparable values in the area.
The point is that you could pay more and still come out ahead.
It should be emphasized that, if the current value of land in the area (V
0
), the rate of land appreciation (G), the expected net cash flows (NCF
E
) or your aversion to risk captured in the discount rate (R) change, you have to compute a new maximum bid price . You will notice the valuation approach presented in equation (67) is a far more complex valuation tool than the simple capitalization formula given in equation (36) back on page 31. The added complexity, however, is necessary since the firm will not hold this land in perpetuity .
In summary, it is important to test the sensitivity of this bid price assuming different rates of appreciation of real estate, different market factors influencing expected future net cash flows, and different aversions to risk.

77
An important consideration in the financial decision making processes of firms is the valuation of variables over which the firm has little or no control. A perfect example in agriculture is crop yields. Forming knowledgeable expectations about future trends in this and other externalities is imperative to making sound investment and financing decisions.
The old GIGO rule (garbage in – garbage out) is a good rule to keep in mind.
Successful firms will find use for all the information available at its disposal, including historical on past product and input prices and productivity (e.g., bushels per acre, gain per pound of feed). Gross revenue or simply revenue for a particular enterprise is given by:
Revenue

Product price/unit

output/unit

number of units used
Historical product and input prices can help explain deviations from historical trends in the financial indicators discussed earlier in equations (1) through (17) given uniform or constant productivity (i.e., output per unit of input). However, future trends and deviations from trend are influenced by changes in productivity, external global market events in both domestic and competitor nations influenced by government policies, financial crises in client nations, and other factors that present new risks and returns.
Yields in crop and livestock production are more local in nature.
Understanding long run trends in crop yields and deviations about these trends, for example, can be instrumental to making projections of future revenue flows. Assume the annual yields in wheat production over the last ten years on a farm were as depicted in the scatter diagram below:

78
42
40
38
36
34
32
30
Historical Wheat Yields
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 where this scatter reflects the following observations:
1996 = 35.6
2000 = 31.8
2004 = 41.2
1997 = 34.1
2001 = 37.7
2005 = 36.8
1998 = 40.2
2002 = 39.1
1999 = 36.5
2003 = 36.4
The average or mean of this time series is 36.94, which was found by using the AVE function in the Excel spreadsheet. The standard deviation for this same time series is equal to 2.80, which was found by using the STD function in the Excel spreadsheet.
These elements of this historical probability distribution can be depicted as shown below:

79
This information suggests that we can be approximately 70 percent confident that the yield on the firm’s tract of land planted to wheat will range between 34.14 bushels and 39.74 bushels.
The “least squares” line passing through the scatter diagram above can be found by using regression analysis in Excel. Using the SLOPE and
INTERCEPT functions in the Excel spreadsheet, we see that the linear time trend over the 1996 – 2005 time period is given by:
(69) Yield = - 632.318 + 0.334545(Year)
The percent deviations about this historical time trend can be super-imposed on the forecasted long run yield trend starting in 2006 to assess how sensitive an investment decision is to past weather variability. More will be said about this topic in the next section.
Armed with this information, we can assess the long run yield trend for the firm’s local yields by substituting successive years into equation (69). This equation suggests that the yield for wheat in 2006, for example, would be:
(70) Yield = - 632.318 + 0.334545(2006)
= 38.78 or 38.78 bushels per acre. This process can be extended over the life of the investment project to forecast future trends in yields reflecting annual productivity gains due to improved varieties or cultural practices, giving us a projection like that illustrated in the figure below:
42.00
41.50
41.00
40.50
40.00
39.50
39.00
38.50
Long Term Yield Trend
2006 2007 2008 2009 2010 2011 2012 2013 2014

80
We can then superimpose observed yield deviations in the past on this longterm trend to examine the sensitivity of the investment project’s feasibility to known weather patterns in alternative scenario simulations. For example, one simulation of the NPV could be based upon the long term yield trend while a second simulation might be based upon deviations about this trend reflecting a reoccurrence of past weather patterns.
Another approach is to compute a cumulative density function or CDF that illustrates the probability that the yield will be less than or equal to a specific yield over the time interval used to estimate the CDF.
This suggests, given historical data for corn, that there was a 50 percent probability that the price of corn in the 2008/09 marketing year would be less than $4.00 per bushel.

81
One of the more important dimensions to financial decision-making is the formation of expected future values of income and cost streams over time.
Accountants and economists alike have a term they use for this; it is called pro forma analysis . There are a varied of approaches one can take when conducting pro forma analysis. Some are simple, such as using last year’s price or buying projections from private consultants, while others are more sophisticated, as we will demonstrate. We will start with the simple approaches.
Perhaps the easiest approach to acquiring forward information on commodity and input prices is from government and university sources.
Many universities, in conjunction with government agencies, provide 12-24 month outlook materials for producers of major crop and livestock commodities. The information is free, but is often somewhat dated. The
Amber Waves publication available at www.usda.ers.gov
is a prime example of monthly market assessments available to U.S. producers.
More detailed and frequently updated price information is available at a cost from private sources. This can range from market newsletters to contractual consulting arrangements with consulting companies specializing in specific sectors of an economy or global market.
Another option is to make your own projections of what future trends in commodity and unit input prices will be over the economic life of an investment project. For example, one can use the naïve model
approach, which assumes that
(71) P i
= P i-1 where P i
is the projected price in the ith year and P i-1
is the price in the previous year. While this approach is used because of its simplicity, recent commodity price trends for wheat easily refute the validity of this approach.

82
Another historical-based approach is to employ the Olympic average approach. This involves using past prices for 5 or more years, dropping the
“high” and the “low” price, and computing the arithmetic average for the remaining observations. This approach will most likely out-perform the naïve model approach, but still ignores probabilistic future events that can lead to sharp departures from historical-based expectations. Other more sophistical time series models require a much longer sample period.
As an alternative to the market outlook information and historical-based approaches, one can estimate market demand-supply relationships for the commodities produced by the firm or employ elasticity estimates from previous studies for these commodities. Let the demand for the ith crop be given by:
P
E
Demand
Q
E
Q
Q
Q
Supply
D
S
D
= f(P, Y_T, W, ...)
= f(P, MIC, …)
= Q
S
Solve for P
E
and Q
E where the demand curve will shift with changes in the price of substitutes, consumer income, exchange rate relationships with client nations and other domestic and export demand developments. The supply curve will shift with changes in productivity, marginal input costs and other domestic and import supply developments.

83
Time series data on these variables, combined with the use of regression analysis to estimate the demand and supply relationships in double log form, provides price and income elasticity estimates that are useful in pro forma analysis in absence of simulating estimated demand and supply equations.
For example, the reciprocal of the econometrically-estimated own price elasticity of supply for a commodity of say 0.25 gives us the price flexibility for the commodity, or
(72) %

P = 4.0(%

Q)
This suggests that a one percent increase in the supply of a commodity coming onto the market will cause a 4 percent drop in the price of the commodity. This begins to help the firm assess the magnitude of future price fluctuations.
More expansive econometric analyses that capture the structure of multimarket relationships can provide an appropriate basis for making long run projections of commodity and unit costs of projections. Simulation of these relationships is referred to as structural pro forma analysis. This involves the assessment of alternative scenarios that result in a distribution of market prices for commodities and inputs to the firm’s operations as it considers investment projects. These scenarios include potential developments in farm programs, weather and disease, macroeconomic policies, foreign trade policies and global market developments. Much like we did for historical observations for the firm’s yield history, we can compute the standard deviations and coefficients of variation for annual distributions of net cash flows reflecting the effects of each scenario.
We shall assume for the moment that we dealing with three scenarios, a
“best case” scenario, a “worst case” scenario and a “most likely” scenario.
This results in a triangular normal probability distribution where the two equally distributed tails of this distribution reflect the subjective probabilities associated with the “best case” and “worst case” scenarios.
The probabilities assigned to these two tails will likely increase over time, reflecting the increasing uncertainty as we move away from the current period and out over the remainder of the investment project’s economic life.

More sophisticated probability distributions can be developed using programs like Simetar. For example, one can test for the assumption of normality assumed in the triangular probability. Often, multivariate empirical distributions are the most representative of real world relationships. This is beyond the scope of this course.
84

85
Let’s assume a normal triangular probability distribution for the annual net cash flow in the ith year can be expressed mathematically as follows:
(73) E(NCF i
) = P i,1
(NCF i,1
) + P i,2
(NCF i,2
) + P i,3
(NCF i,3
) where:
E(NCF i
) Expected additional net cash flow attributable to the project in
P i,1 the ith year
Probability that “optimistic” economic conditions will occur in
P i,2 the ith year
Probability that “most likely” economic conditions will occur
P i,3
NCF i,1 in the ith year
Probability that “pessimistic” economic conditions will occur in the ith year
Net cash flow if “optimistic” economic conditions occur in the ith year
Net cash flow if “most likely” economic conditions occur in
NCF i,2
NCF i,3 the ith year
Net cash flow if “pessimistic” economic conditions occur in the ith year
Given the assumption above, the expected value E(NCF
1
) or mean of this triangular probability distribution is equal to its “most likely” value, or
NCF i,2
given in equation (73) above.
There are two traditional measures of business risk, the standard deviation above the mean or expected value and the coefficient of variation. Using

86 our notation above, the standard deviation associated with the net cash flows generated by the project in the ith year is given by:
(74) SD(NCF i
) =

[P i,1
(NCF i,1
- E(NCF i
)) 2 + P i,3
(NCF i,3
- E(NCF i
)) 2 ] or
(75) SD(NCF i
) =

2[P i,1
(NCF i,1
- E(NCF i
)) 2 ]
You will notice several shortcuts taken in equations (74) and (75). First, the deviation between the potential net cash flow associated with the “most likely” scenario and the mean of the probability distribution is absent from equation (74). This term drops out under the normal triangular probability distribution assumed here since these two terms are identical! Second, since both tails of this distribution are identical in absolute terms, we can multiply either one of them by 2.0 and drop the other as shown in equation (75).
While the standard deviation is useful for other reasons, it is not a very good measure of risk is it offers to basis of comparison to the mean of the distribution. We can rectify that by calculating the coefficient of variation as follows:
(76) CV(NCF i
) = SD(NCF i
)

E(NCF i
) where CV(NCF i
) represents the coefficient of variation for net cash flow in the ith year, or business risk per dollar of expected net cash flow . We will use this statistic as our measure of the firm’s annual exposure to business risk associated with a particular investment project later in this booklet.

87
Now that we have a measure of the unique annual exposure to business risk, we need to relate that to the firm’s required rate of return, or the discount rate used in assessing the net present value associated with the investment project. To do this, we must first assess the firm’s aversion to business risk.
This can be done in the context of a “hurdle” rate, or the minimum rate of return the firm requires for accepting additional risk.
Firm’s respond to exposure to risk. Few are risk neutral when evaluating investment projects unless they inadvertently ignore the risk associated with the expected returns from a project.
Required
Rate of return
RRR
H,i
RRR
L
, i
R
F,i
CV i
Highly risk averse
Lowly risk averse
Risk neutral
Coefficient of variation
This suggests that the risk neutral investor will not require any additional return over the risk-free rate of return. The lowly risk-averse investor will require RRR
L
, i
as a hurdle or required rate of return while the highly riskaverse investor will require RRR
H,i
. The difference between R
F,i
and either
RRR
L
, i
or RRR
H,i
represents the business risk premium or additional return for taking additional risks.
Assume you are a consultant discussing an investment project with a client and he has told you that he requires a minimum rate of return of 12% if he is to invest in a project with a risk of 6 cents on the dollar (i.e., a coefficient of variation of 0.06). This response helps you develop what is know as a risk/return preference function. To see this, let’s use the following general form of the risk/return preference function:

88
(77) RRR i
= R
F,i
+ b i
(CV i
) where:
RRR i b i
Required rate of return in the ith year
Slope of the firm’s risk/return preference curve (
(78) b i
= (RRR i
- R
F,i
) ÷ CV i

RRR i
/(

CV
For example, if the risk free rate of return (R
F,i
) is 5%, then we can solve equation (77) for the slope of the risk/return preference curve b i
as follows: i
) which in our example above would be equal to:
(79) b i
= (.12 - .05) ÷ .10
= 0.70
Thus the risk/return preference function in this case can be expressed as follows:
(80) RRR i
= .05 + 0.70(CV i
)
This risk /return preference curve can be displayed graphically as follows:
Required
Rate of return
RRR i
=.12
R
F,i
=.05
0.10
}
Slope equal to 0.70
Business Risk
Premium = .07
Coefficient of variation
It is important to note that each year can have a unique required rate of return. Why? There are several reasons: (a) the risk free rate of return (R
F,i
)

89 can change from one year to the next, (b) the coefficient of variation (CV i
) can change from one year to the next, and (c) the slope of the risk/return preference curve can change.
The difference between the required rate of return and the risk free rate of return for an opportunity of equal maturity is known as the business risk premium . This represents the additional rate of return you require over a risk free investment for taking on the business risk involved in the project in the ith year.
These annual values of RRR i
represent the discount rates associated with the corresponding annual net cash flows. We can now adjust our net present value model for depreciable assets to account for the presence of business risk as follows:
(81) NPV = E(NCF
1
)

(1+RRR
1
) + E(NCF
2
)

[(1+RRR
1
)(1+RRR
2
)] + …
+ E(NCF n
)

[(1+RRR
1
)(1+RRR
2
)…(1+RRR n
)] +
T[(1+RRR
1
)(1+RRR
2
)…(1+RRR n
)] – C where:
E(NCF
1
) Expected additional net cash flow attributable to the project in year 1
1/(1+RRR
1
) Present value discount factor in year 1 reflecting required rate of return based upon unique risk exposure in year 1
T
C
Expected terminal value of assets acquired
Initial net outlay for assets acquired
To illustrate, let’s assume the following states of nature facing a firm in year
1 which is considering an investment that will enhance its annual net cash flows:
Table 8 – Elements of Triangular Probability
Distribution.
State of nature:
1. Optimistic
2. Most Likely
3. Pessimistic
Net cash flow
$8,382
7,620
6,858
Probability
5.00%
90.00%
5.00%

90
We know from our previous discussion that the expected net cash flow in the ith year or E(NCF
1
) will be $7,620. Let’s prove that to be true using equation (73) as follows:
(82) E(NCF
1
) = 0.05($8,382) + 0.90($7,620) + 0.05($6,858)
= $419.10 + $6,858.00 + $342.90
= $7,620
Using equation (74), we can calculate the standard deviation associated with the annual net cash flows in year 1 of this project as follows:
(83) SD(NCF i
) =

[0.05($8,382 - $7,620) 2 + 0.05($6,858 - $7,620) 2 ]
=

$29,032.20 + $29,032.20
= $240.97
We could have also used equation (75) to calculate this standard deviation given the normal nature of our triangular probability distribution and achieved the same solution:
(84) SD(NCF i
) =

[2.0(0.05($8,382 - $7,620) 2 )
=

2.0[$29,032.20]
= $240.97
The next step is to calculate the coefficient for the net cash flows expected in year 1 under this investment project. Using the format outlined in equation
(76) we see that the coefficient of variation would be:
(85) CV(NCF i
) = $240.97

$7,620
= 0.0316 or approximately 3.2 cents per dollar of expected net cash flow in year 1.
Given the specification of the risk/return preference function given in equation (80), we see that the required rate of return in year 1 would be:
(86) RRR
1
= .05 + 0.70(0.0316)
= .05 + .022
= .072

91 or 7.2%. This process is completed for each year in the economic life of the project.
For example, assume the expected value of the net cash flows E(NCF i
) over the remaining 3 years of the 4-year economic life of this investment and their corresponding standard deviations are as follows:
Table 9 – Expected Value and Standard Deviation.
Year
1
2
3
4
Expected
Value
$ 7,620
10,920
14,220
14,220
Standard deviation
$241
488
779
899
The corresponding annual coefficients of variation, business risk premiums and required rates of return using equation (86) would be:
Table 10 – Required return and business risk premium.
Year
1
2
3
4
Coefficient Risk-free Business risk Required of variation rate of return premium rate of return
0.0316
0.0447
0.0548
0.0632
5.95% 2.21% 8.16%
7.16% 3.13% 10.29%
7.12% 3.83% 10.95%
7.26% 4.43% 11.69%
In addition to these annual net cash flows, the firm expects to receive a terminal value of $7,810 when it sells the assets acquired under this project at the end of the 4 th year.
The annual required rates of return in Table 10 above are then included in equation (90) when calculating the net present value for this project costing
$45,000 as follows:
(87) NPV = $7,620

(1+.0816) + $10,920

[(1+.0816)(1+.1029)] + … +
$14,220

[(1+.0816)(1+.1029)…(1+.1169)] +
7,810[(1+.0816)(1+.1029)…(1+.1169)] – $45,000

92
We can express this calculation in table form to give you a better idea about the individual components of equation (87) as follows:
Table 11 – Use of Risk Adjusted Discount Rates.
(1) (2) (3)
Net Cash Present Value Present Value
Year Flow Interest Factors of NFC i
(i) (NCF i
) (1) x (2)
1 $ 7,620
2 10,920
3 14,220
4 14,220
0.9246 $ 7,045
0.8383 9,154
0.7556 10,745
0.6765 9,620
4 7,810
$ 54,790
0.6765
Less initial cost
5,283
$41,847
- 45,000
Net present value $ - 3,153
.9246 = 1/(1+.0816)
Thus, we would reject this project after adjusting for risk since the net present value is negative.
If we discounted the net cash flows above at the risk-free rate of return (R
F,i
), we would have calculated a net present value of:
Table 12 – Use of Risk Free Discount Rates.
(1) (2) (3)
Net Cash Present Value Present Value
Year Flow Interest Factors of NFC i
(i) (NCF i
) (1) x (2)
1 $ 7,620
2 10,920
3 14,220
0.9438 $ 7,192
0.8808 9,618
0.8222 11,692
4 14,220
4 7,810
0.7666 10,901
0.7666 5,987
$ 54,790
Less initial cost
$45,390
- 45,000
Net present value $ 390

93
Using the risk-free discount rate would have led us to conclude that this was an economically feasible investment opportunity!
Finally, how important was it for us to account for the possibility of increasing risk over time rather than use the interest factor calculated for year 1 in Table 11? This table involves using the 8.16% required rate of return reported for year 1 in Table 10 when calculating the interest factors for the subsequent years. The results of this adjustment are reported in
Table 13 below:
Table 13 – Use of Constant Risk Discount Rates.
(1) (2) (3)
Net Cash Present Value Present Value
Year Flow Interest Factors of NFC i
(i) (NCF i
) (1) x (2)
1 $ 7,620
2 10,920
3 14,220
4 14,220
0.9246 $ 7,045
0.8548 9,334
0.7903 11,238
0.7307 10,391
4 7,810
$ 54,790
0.7307
Less initial cost
5,707
$43,715
- 45,000
Net present value $ - 1,285
Thus we still would have concluded that the business risk involved with this project would have made it an infeasible economic opportunity , although the net present value is less negative than that reported in Table 11.

94
The economic growth model presented in equation (24) helped us see the advantages and disadvantages associated with the use of financial leverage to grow the firm. If the rate of return on assets exceeds the rate of interest on debt capital, leverage will contribute to the growth of the firm’s equity.
However, if the rate of return on assets is less than the rate of interest on debt capital, leverage will detract from the growth of the firm’s equity.
Leverage thus is associated with financial risk . The greater the use of leverage, or greater the debt-to-equity ratio, the greater the potential exposure to loss in equity capital well be.
We can modify the risk/return preference function presented initially in equation (77) to reflect financial risk as follows:
(88) RRR i
= R
F,i
+ b i
(CV i
) + c i
(L i
) where b i
(CV i
) represents the business risk premium and c i
(L i
) represents the financial risk premium . We can visualize the addition of the financial risk premium below:
Reflects
+ c i
(L i
)
Required
Rate of return
RRR i
RRR i
R
F,i
CV i
Financial risk premium
Business risk premium
Coefficient of variation
It can be shown using equation (77) that the required rate of return for a project in the ith year of a project having a risk per dollar of expected net cash flows of 8 cents and risk free rate of return of 5 percent would be:

95
(89) RRR i
= .05 + 0.70(.08)
= .106
Adding the financial risk premium to equation (89), we see that:
(90) RRR i
= .106 + c i
(L i
)
Let’s now assume that the firm said it would require a rate of return equal to
15 percent given its exposure to business and financial risk if its leverage ratio was 1.0. Given this information we can compute the coefficient in the financial risk premium by transposing terms, or:
(91) c i
(L i
) = .15 - .106
Solving for the coefficient associated with the liquidity variable, we see that
(92) c i
= (.15 - .106) ÷ L i
= .044 ÷ 1.0
= .044 which represents the change in the required rate of return for a given change in the firm’s leverage position, or 
RRR i
/

L i
.
With the addition of the financial risk premium, we now assemble the entire risk/return preference function. This function, which includes both the business risk premium and the financial risk premium as well as the risk-free rate of return on assets of similar maturity, takes the form:
(93) RRR i
= .05 + .70(CV i
) + .044(L i
)
This equation suggests that the higher the coefficient of variation associated with expected annual net cash flows over the life of a project or the higher the firm’s debt relative to equity, the greater the “hurdle” or required rate of return a new project will have to “clear” in order to be economically acceptable to the firm’s decision makers.

96
Thus far we have focused on the required rate of return, mentioning the cost of debt capital only in comparison to the rate of return on assets (ROA) when discussing the rate of growth in equity capital and when discussing a project’s internal rate of return, or IRR. Even then we only addressed the explicit cost of debt capital, or the externally determined rate specified on the mortgage or note.
There implicit costs of debt capital that cause firms to internally ration their use of debt capital that were more or less implied when we discussed the concept of financial risk and the financial risk premium. As the firm reduces its credit liquidity as it uses up its credit reserves, its implicit cost of debt capital rises, causing the total cost of debt capital
Percent
Total cost 12%
9%
Use of credit capacity
75%
Implicit cost
Explicit cost to rise as depicted in the graph above. This concept is an important component to analyzing the firm’s weighted average cost of capital and optimal capital structure.
The weighted average cost of capital (WACC) employed by the firm is given by the following equation:

97
WACC = W
EQ
(r
E
) + W
DT
(r
D
) where W
EQ
is the relative importance of equity in the firm’s balance sheet, r
E is the cost of equity capital, W
DT
is the relative importance of debt in the firm’s balance sheet, and r
D
is the total cost of debt capital. The optimal capital structure of the firm’s balance sheet is given by the least cost combination of debt and equity capital. We can illustrate the point where this occurs is the graph below:
$/unit
1.0
Cost of equity capital
Weighted average cost of capital
Cost of debt capital
D/E ratio
Two features are worth noting in the graph above. The first is the fact that the cost of debt capital is less than the cost of equity capital. How can this be? Think of the cost of debt capital as the minimum opportunity rate of return available to the firm. After all, one of the opportunities available to using the firm’s equity capital is to make loans to others at the going cost of debt capital!
The other feature has to do with the shape of the weighted cost of capital curve and the optimal location on that curve. This curve falls sharply at low debt/equity ratios since the cost of equity capital is higher and carries a higher weight. The optimal location on the weighted average cost of capital curve is at its lowest point . At this point, the firm is minimizing its cost of capital. Any other combination of debt and equity capital would reduce the returns from the firm’s portfolio.

98
A numerical example corresponding to the graph depicted above is presented below:
Table 14 – Calculation of the Weighted Cost of Capital.
Leverage ratio
0.0
0.5
1.0
1.5
2.0
Source of
capital
Debt
Equity
Debt
Equity
Debt
Equity
Debt
Equity
Debt
Equity
Unit cost WACC
0.04
0.06 0.060
0.04
0.06 0.053
0.04
0.06 0.050
0.05
0.08 0.062
0.06
0.10 0.074
We see above that the least cost combination of debt and equity capital occurs where the firm achieves a 50-50 balance of debt and equity capital on its balance sheet. At this point we see that the weighted average cost of capital is 5 percent.

99
The final topic covered in this handout is the role that the capital budget plays in the selection of economically feasible investments to fund in the current period. Let’s assume the firm is facing the following investment opportunities this year and has a $90,000 capital budget to work with:
Table 15 – Cost and Benefits from Alternative Projects.
(1) (2) (3)
Cost of
Present
Value of
Net Cash
Project Project Flows
A $10,000 $14,500
B 24,000
C
D
7,500
43,000
E 5,250
33,120
8,850
46,500
3,360
Net
Present
Value
(2) – (1)
$4,500
9,120
1,350
3,400
-1,890
Totaling up the costs of the five projects the firm is considering, we see that this total ($89,750) does not exceed the amount of debt and internal equity capital available this year to the firm ($90,000, which is comprised of
$50,000 in debt capital and $40,000 in equity capital). What projects would you advise this firm to invest in?
First, we can throw out project E because it has a negative net present value.
This leaves us with $84,500 in projects that have a positive net present value. Should the firm invest in all four projects?
If the firm wants to minimize its cost of financing (i.e., use 50 percent retained earnings and 50 percent debt capital given by the minimum point on its weighted average cost curve in the previous example), the answer is no .
For example, if the firm sticks by this least-cost decision rule, it would prefer to spend only $77,000 on new investment projects in the current period, using $38,500 in equity capital and $38,500 in debt capital. The firm in this instance would invest in projects A, B, and D. The firm would hold the unused portion of its available equity capital (i.e., $1,500 or $40,000 -
$38,500) in reserve in the short run in the form of a liquid income-earning

100 asset. And it would not borrow additional debt capital it might otherwise employ ($11,500 or $50,000 - $38,500).
If the firm had invested in all four projects costing $84,500, and used up its available debt capital first, the D/E or leverage ratio for these projects would be approximately 1.45 ($50,000/($84,500 - $50,000), which is much higher than its cost minimizing target capital structure of 1.0.
In fact, all other combinations of available debt and equity capital to finance all four projects would also lead to a capital structure other than 1.0.
Other factors such as achieving a greater market share in the short run might well convince a firm to invest in all four projects fitting within its available budget, thus ignoring the optimal capital structure rule. However, a firm bumping up against its maximum leverage ratio rationed externally to it by its lender (and hence more exposed to financial risk) will be more apt to consider this concept when taking on new projects.

101

102
The firm faces a number of decisions with regards to input choices and product choices over time. Let’s begin with short run, with the existing firm having a given amount of land and capital, and a given level of management resources. Let’s further assume for the moment that the firm produces a single product. While we will assume conditions of perfect competition, imperfect competitors also follow most but not all decision rules discussed here.
The level of profit is maximized for both perfect and imperfect competitors in product decisions by producing were marginal cost equals marginal revenue, or at output O
MAX
in the graph below.
At a price of $45, this firm will maximize its profits (gray area) by earning an average profit of $16 ($45 average revenue minus $29 average total cost).
If the market price were to fall to P
BE
, the firm would break even (zero

103 economic profits) if it produced quantity O
BE
. Finally, the firm would just cover its variable costs of production by operating at quantity O
SD
if the price fell to P
SD
. The firm’s supply curve in the current period therefore begins at O
SD
and proceeds upward to the right where higher prices bring about increases in supply.
What is the level of variable inputs is associated with profit maximization
(or cost minimization)? Let’s start with a single variable input, hired labor.
The level of hired labor desired by the firm will depend on its marginal productivity (
 output/
 input), the expected price of the product, and the marginal input cost of labor (wage rate). We see in the graph below that the profit maximizing level of input use (L
MAX
) occurs at the point where the marginal value product, or additional revenue received from selling generated by the additional unit of labor, is just equal to the wage rate, or

104 cost of the additional unit of labor. The area below the marginal value product curve and above the marginal input cost or wage rate represents the cumulative net benefit received by the firm.
Thus a decrease in the wage rate increases the profit maximizing level of input use. A decrease in the wage rate increases the profit maximizing level of input use. One final point: there is a direct correspondence between O
MAX and L
MAX
in the last two graphs.
Let’s now move to two variable inputs, and the factors that affect the substitution between inputs for a firm producing a single product. Line AB
In the graph above represents an iso-cost line, where “iso” is a Greek word meaning “equal”. The firm is spending the same amount of money or budget at all points along that line. Line A*B* represents a higher budget expenditure. The curve associated with 100 units of output is called an isoquant. The firm would be producing 100 units of output or equal level of output at all points along that curve.

105
At the point where the iso-cost line is just tangent to the isoquant, the firm is minimizing its cost of production. In the graph above, this occurs at point G.
That is, C
1
units of capital and L
1
units of labor represent the least cost combination of these two inputs in producing 100 units of output. Stated in mathematical terms, the following relationship holds at point G:
MPP
LABOR
wage rate
=
MPP
CAPITAL
rental rate which can be rearranged to read
MPP
LABOR
MPP
CAPITAL wage rate
=
rental rate
This says that the marginal physical product per dollar spend on labor equal the marginal physical product per dollar spent on capital. In general terms, a firm should allocate its expenditures on inputs so that the marginal benefits per dollar are equal. In summary, input use depends on input prices, desired output and technology.
What happens if the price of one of the inputs changes? To the extent that inputs are technical substitutes in production, a change in the price of one of the inputs will cause the profit maximizing firm to use less of that input and more of its substitute. In the graph below, line AB is the original iso-cost line in the previous graph. At point G, the firm is again using C
1
units of capital and C
2
units of labor.
Now assume the wage rates decline such that the firm can afford a maximum labor of B* given its budget instead of B. Thus the iso-cost line becomes
AB* rather than line AB. This gives us a new point of tangency with the

106 isoquant associated with 100 units of output. The profit maximizing firm in this case would now use more labor (L
2
rather L
1
) and less capital (C
2
rather than C
1
). The goal again for a profit maximizing firm is to satisfy the mathematical condition where expenditures on inputs is allocated such that the marginal benefits per dollar are equal.
Another perspective on the allocation of expenditures is to stay within a given budget. We can ask ourselves what the profit maximizing output in the current year is for a given budget. Let’s assume that a firm faces an operating budget in the current period given by line MN in the graph below.
This constraint is affected by the amount of internal and external sources

107 of funds the firm has at its disposal as well as the prices of the inputs. The isoquants in the graph above reflect the technical operating capacity of the firm. That is, perhaps the firm can produce up to 125 units of output given its current physical and managerial resources. The graph above indicates, however, that the firm would maximize its profits subject to its budget constraint MN by producing 75 units of output using C
3
units of capital and
L
3
units of labor.
F. Price Under Perfect Competition
The firm is a price taker under conditions of perfect competition in the market in which it sells its product and the markets in which it purchases variable production inputs. The product price represents marginal revenue or MR discussed on page 102 which the input price represents marginal input cost or MIC discussed on page 103.

108
For example, the perfectly competitive firm “looks” to the market for a product price signal. This is based upon expectations for demand and supply, which in equilibrium means that demand equals supply. The graph on the right above is explained more fully in section A on page 102.
G. Price Under Imperfect Competition
Unlike the perfectly competitive firm. The imperfect competitor will have the ability to influence the price of the product in which it sells its production. The monopolist, a form of imperfect competition, also will produce where marginal cost equals marginal revenue at point A in the graph below. Because they have the power to set price, they can with a knowledge of the demand curve charge a higher price (P
E
) given by
“reading” up from point A to point C in the graph below and setting a price that consumers have revealed they would be willing to pay.

109
This allows the firm to earn a higher level of economic profits while producing a smaller quantity than would occur under perfect competition.
H. The DuPont Model
An extension of the managerial accounting concepts discussed in this booklet is the decomposition of the rate of return on assets (ROA) into the contribution by the net profit margin and the total asset turnover ratio. The first component emphasizes the prices and costs of operations while the second component focuses on the management of the firm’s assets.
The graph on the following page shows the linkages incorporated in the firm’s ROA. These linkages can be traced back to key elements of the

110 firm’s balance sheet and income statement. Focusing on the net profit margin, efforts to promote the value of sales and/or lower cost improve net profit margin.
The profit margin can be improved by: reducing expenses by:
 using less costly materials,
 find ways to improve productivity and
 review fixed costs (advertising, R&D, management and development programs).
The profit margin can also be improved by raising prices:
 requires pricing power,
 requires brand loyalty and
 is easier for firms with unique high quality goods or services.
Asset turnover can be improved by increasing sales while holding investment in assets relatively constant by:
 disposing of obsolete and redundant assets,
 speeding up collections of receivables and
 evaluating credit terms and policies.

111

112

113

114