Investment Recommendations

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timer Asked: Jun 2nd, 2018
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Question description

Suppose your rich uncle offers you a choice of generous gifts: $10,000 in cash today or $1,200 in cash at the end of each of the next ten years, totaling $12,000. Which gift should you take?

As a student in this course, you previously completed a course in the principles of business finance. That course introduced you to the concept of time-value-of-money (TVM), including the concepts of present value and future value. TVM expresses the perception that a dollar is worth more in your hand today than it is if you receive it the future. For example, you can use this concept to decide how much interest you must earn on an investment of a given amount of money in hand today in order for you to perceive that sum as having a value equal to another specified amount to be received, say, five years from today. You can also use this concept to determine how much less valuable to you a specified amount of money is if, instead of receiving it today, you receive it in, say, five years without the opportunity to invest it during that period.

This topic explores TVM concepts and how managers use them in making investment decisions. Examples of such decisions include whether to expand or replace a fleet of trucks, build a new manufacturing facility, launch a new product line (or discontinue an aging product line), acquire a competitor firm, or sell an existing division of a business.

By the way, if today’s market interest rates exceed approximately 3.5 percent, tell your uncle that you prefer the $10,000 in cash today to the ten-year $1,200 annuity, even if you have no reason to expect him to renege on his gift before the final $1,200 payment. That is, the immediate gift of $10,000 has a greater present value than the $1,200 annuity if you can invest either at a rate of return exceeding 3.46 percent. If, on the other hand, market interest rates are less than 3.46 percent, you should take the annuity.

By completing this assignment, you will learn how to analyze alternative investment opportunities using present value concepts and models and present your investment recommendations to a business’ executives with supporting calculations and explanations.

Please use the file entitled Topic5aTemplate for this assignment. It is located in the Content section of the course, under Course Resources, Assignment Templates. Once you have downloaded the file, complete all the necessary work, and rename the file with your Last and First name. For example, if your name is John Doe, then you would rename the file as Topic5aDoeJohn. Once you have done this, you must upload the completed assignment to the appropriate assignment location of this course.

Contents Topic 5  Introduction and Purpose  Time-Value-of-Money (TVM) Concepts — — — — — — —  Time-Value of Money and Opportunity Cost TVM Concepts: Future Value and Present Value Compounding of Returns: Nominal versus Effective Rates of Return Investments and Financings involving a Series of Regular Cash Flows Terminology Opportunity Cost: Undiscounted versus Discounted Cash Flows Investments and Financings Involving Irregular Cash Flows □ Effect of cash flow structure on present value of cash flows □ Effect of cash flow frequency on present value of cash flows □ Effect of changes in discount rates on present value of cash flows Estimating the Fair Value of Corporate Bonds and Notes — Fair Value of a Business' Capital Financing and Unrecognized or Under-valued Assets  Net Present Value — Relevant Cash Flows and Sunk Costs — Capital Rationing and Ranking Multiple Investment Opportunities 1 Topic 5 Introduction and Purpose As a student in this course, you previously completed a course in the principles of business finance. Among other topics, that course examined time-value-of-money (TVM), including the concepts of present value and future value. That course introduced you to the use of TVM concepts to:  Determine the fair value of investment securities, such as bonds and stocks, and  Evaluate investment opportunities, such as the replacement of manufacturing equipment This background paper examines TVM concepts, focusing on managers’ use of present value models to analyze and select investment opportunities. These concepts and models are useful for analyzing a variety of investment or financing decisions, such as whether to:       Initiate a product research-and-development project, Launch a new product, or discontinue an aging product, Acquire additional plant and equipment in order to expand productive capacity, Replace production equipment with more efficient or more highly automated (cost-saving) equipment, Acquire a competitor firm, or sell an existing division of a business, and Refinance a business’ existing debt Once you firmly understand the concept of opportunity cost that underlies present value, you will quickly comprehend the models of present value analysis examined in this and the Topic 6 background papers. However, in applying these models to investment opportunities, managers must not lose sight of the following points:  Uncertainty of future cash flows and investment risk. The principal subject of present value analysis is future cash flows. Of course, the future is uncertain. The uncertainty of future cash flows is the source of investment risk. Consequently, the quality of managers’ ultimate investment decisions depends significantly on the accuracy and completeness of their cash flow projections. These cash flows may include, for example, sales and costs of new products, cost savings from investment in more efficient manufacturing equipment, proceeds from the eventual disposition of investment property, and income taxes related to these other cash flows.  Relevant cash flows. Related to the preceding point, present value analyses must include only relevant cash flows. Sunk costs – the cash flows representing costs a business incurs before managers make the decision to accept or reject an investment proposal – are not relevant cash flows.  Capital rationing. Frequently, managers must choose from among multiple investment proposals. Present value analysis provides the proper model for evaluating and ranking alternative investment opportunities. However, many businesses face a practical constraint on their investing because they have a limited amount financial capital available during a given period. Consequently, managers must ration capital so that they maximize the value created by all accepted investment opportunities. The Topic 6 background paper examines the use of present value analysis in connection with the capital budgeting process. 2 Topic 5 Learning Objective 1 Time-Value-of-Money (TVM) Concepts Time-Value of Money and Opportunity Cost The time-value-of-money (TVM) concept states that the value of a stated amount of money (such as US$1,000 or €1,500, or ¥10,000) depends on the timing of its receipt or payment. This is because a business may invest money with the expectation of earning a return on it.1 The sooner a business receives a particular amount of money, the sooner it can invest it and begin to earn that return. During the period that a business awaits the receipt of money, it incurs an opportunity cost because it cannot invest it.2 3 Return on investment takes the form of future cash inflows that exceed the initial cash outflows representing the business’ initial investment. TVM Concepts: Future Value and Present Value Future value refers to the value of a specified amount of money on a specified future date that a business invests between the current date (called “time zero”) and the specified future date. For example, the future value of $1,000 in one year, if invested today at a 10 percent annual rate of return, is $1,100 (assuming no interim compounding of returns during the year). Financial managers compute this future value as: Future value, or FV = $1,000 x (1 + 0.10) _____ 1 A common misconception by students of finance is that the TVM concept derives from price inflation (deterioration of a currency’s purchasing power). Of course, expectations of inflation (by businesses that invest financial capital and providers of debt and equity capital) affect the nominal rates of return they require from those investments. However, businesses and providers of financial capital reasonably expect a return on their investments even in the absence of price inflation, for the reason described above. Investors determine their required nominal rate of return, which includes the anticipated effect of inflation as: Required nominal rate of return = (1 + required real rate of return) x (1 + expected rate of inflation) – 1 where, the required real rate of return is an investor’s required rate of return excluding the effects of inflation. To illustrate, if an investor requires a real rate of return of 5.0 percent and she expects the long-run future rate of inflation to be 3.0 percent, her required nominal rate of return is: (1 + 0.05) x (1 + 0.03) – 1 = 0.0815, or 8.15 percent. 2 It may be useful to consider opportunity cost in another (possibly more familiar) context. Suppose you quit your job, for which you receive a $70,000 annual salary, in order to start a business. As is often the case for new businesses, assume that yours is “strapped for cash” in its first few years of operations while you develop a market for its products or services sufficient to generate profitable levels of operating cash flow. To help ensure your fledgling business gets off the ground, you instruct your part-time accountant to pay you an annual salary of only $24,000 for your services as president, CEO, CFO, VP-sales, and what not – an amount well below the market value of these services. When you evaluate your return on investment in the business during these early years, you should include as a cost the market value of your services as an employee of another business in excess of the salary you actually receive from your new business. This excess ($46,000) represents the value of your services that you forego when you pass up the opportunity to earn a market salary (“return”) in exchange for your services (“investment”). Mind you, this excess is an opportunity cost that you include in your “spreadsheet analysis” of your investment, but is not an expenditure arising from an arms-length exchange that you actually record in the business’ accounting records, as described in the Topic 3-4 background paper. 3 According to economists, investment opportunities exist because some of the businesses and individuals who have money prefer not to spend it immediately on items that do not increase an economy’s stock of income-producing assets. (These assets include, for example, manufacturing equipment, roads, aircraft, office buildings, and telecommunications infrastructure.) Instead, these “savers” deposit their money into interest-earning bank accounts and purchase corporate bonds, stocks, and other securities that yield returns (or into professionally managed retirement accounts and mutual funds that acquire these securities on behalf of these savers). Provided the rate of return on these investments is sufficiently high, savers continue to save, rather than spend their money currently (on, say, entertainment and travel). Economists refer to this discussion as “inter-temporal consumption preferences.” 3 Present value is the “inverse” of future value. That is, present value refers to value today (i.e., at “time zero”) of a specified amount of money an investor expects to receive on a specified future date. For example, the present value of $1,000 a business expects to receive in one year at a 10 percent annual rate of return is $909.09 (assuming no interim compounding of returns): Present value, or PV = $1,000 / (1 + 0.10) Present value answers the question, “What amount of money must my business invest today, assuming an annual rate of return of 10 percent, in order for the value of that money to grow to a future value of $1,000 in one year?” In general, FV = PV x (1 + r)n PV = FV / (1 + r)n where, FV is the future value of a specified amount of money invested for n periods, beginning “today,” PV is the present value of a specified amount of money to be received n periods from “today,” r is the periodic rate of return that an investor requires or expects to earn on a given investment, and n is the number of periods for which the money is invested (such as, 5 years, 12 quarters, 48 months, or 180 days) The Topic 6 background paper examines the determination of businesses’ required rate of return. Compounding of Returns: Nominal versus Effective Rates of Return Managers, capital markets participants, and financial institutions generally describe investments by referring to their nominal (or stated) annual rates of return (such as “the 8 percent debenture bonds that mature in 20X9,” or “the 6.5 percent note maturing next June”). However, most investments generate their returns (in the form of cash distributed to investors) more frequently than annually. For example,  Most bonds issued by U.S. corporations and government entities pay semi-annual interest to their holders; and  Most business loans made by banks require borrowers to pay interest monthly or quarterly. Investors (businesses and their capital providers) may reinvest those interim returns in the same or similar investments. This reinvestment opportunity gives rise to compound returns – that is, returns on previous returns4. In the case of investments that generate returns more frequently than annually (or borrowings that require interest payments more frequently than annually), the opportunity to compound returns requires investors to recast the nominal or stated rates in the form of an effective rate of return. The effective rate of return permits managers to compare alternative investments (or financing arrangements) that have different return frequencies. Managers must also know the effective rate of return in order to compute properly FV and PV amounts. Effective annual rate of return, re = (1 + r / n)n – 1 where, r is the nominal (stated) rate of return, and n is the number of return periods during a year _____ 4 On the subject of TVM, Nobel prize-winning physicist, Albert Einstein, apparently once said, "The most powerful force in the universe 2 is compound interest." (More powerful than E = MC ?! We can forgive Benjamin Franklin for making a similar observation two centuries earlier, well before Einstein shared his insights.) 4 Consider these two illustrations: Corporate bond. The effective rate of return for a corporate bond having a nominal (stated or “coupon”) interest rate of 10.0 percent and paying interest semi-annually is: re = (1 + 0.10 / 2)2 – 1 = 10.25 percent The bondholders’ effective annual rate of return, 10.25 percent, exceeds the nominal (or stated) rate of 10.0 percent because the bondholder may reinvest the first semiannual interest payment before the end of a year during which the bond is outstanding (say, in additional corporate bonds). Likewise, the bondissuing corporation’s effective borrowing rate exceeds the contractually stated (annual) rate of 10 percent because the requirement to pay money to bondholders (in the form of interest) during a year that the bonds are outstanding imposes an opportunity cost on the issuer. This is because the money representing the first semi-annual interest payment during a year the bond is outstanding is not available to the bond issuer for other investment opportunities. Bank note. The effective rate a business pays on a bank loan whose nominal (or stated) interest rate is 10 percent and which requires monthly interest payments is: re = (1 + 0.10 / 12)12 – 1 = 10.471 percent The business’ effective borrowing rate exceeds the contractually stated annual rate of 10 percent because the requirement to pay money to the bank (in the form of interest) during the year the loan is outstanding imposes an opportunity cost on the borrower. That is, the money (interest payments) that the business pays the bank during the year is not available to the borrower for other investments. Likewise, the bank’s effective rate of return on the loan exceeds the contractually stated annual rate of 10 percent because it may reinvest the borrower’s monthly interest payments in (say) additional interest-paying loans to other businesses. In the illustrations above, note that the effective rate on the 10 percent loan requiring monthly interest payments (10.471 percent) exceeds the effective rate on the 10 percent bond requiring (only) semi-annual interest payments. This illustrates the “power” of compounding. The more frequent the opportunity (for a bondholder or lending bank) to reinvest periodic returns, the greater is effective rate of return. For a borrower (such as a business that issues bonds or bank notes), as the frequency of required interest payments increases, so does the effective borrowing rate of the bond or bank note. In light of the preceding discussion, the future value and present value equations, defined more precisely, are: FV of cash flow occurring in period n = Cash flow at “time zero” x (1 + r)n PV of cash flow occurring in period n = Cash flow in period n (1 + r)n where, r is the periodic rate of return, stated on a basis consistent with n, and n is the number periods – years, semi-annual periods, quarters, months, days, etc. – until the occurrence of the future cash flow 5 Learning Objective 2 Investments and Financings Involving a Series of Regular Cash Flows The future value and present value equations above are suitable for analyzing investments or financing arrangements involving a single cash inflow and a single cash outflow. Of course, most investments or financing arrangements undertaken by businesses involve more than a single cash inflow and cash outflow. Financial managers use the following equations to determine the future value and present value of annuities – investments or financing arrangements involving a series of equal, periodic cash flows: FVannuity = Periodic cash flow (1 + r)n – 1 r x 1– PVannuity 5 = Periodic cash flow x 1 (1 + r)n r where, r is the investor’s required periodic rate of return from an investment, stated on a basis consistent with the frequency of the periodic cash flow – annual, semi-annual, quarterly, monthly, etc. n is number of periodic – annual, semi-annual, quarterly, monthly, etc. – cash flows comprising the annuity _____ 5 While the PVannuity equation may seem confounding, the underlying reasoning is compelling and not too difficult to comprehend. First, consider an “annuity-in-perpetuity,” in which an investor and her heirs are to receive a regular, periodic cash flow, C . . . well, in perpetuity (i.e., forever). The PV of this annuity-in-perpetuity is: PV = C / r. Notice that this expression is algebraically identical to C = PV x r, where an investment in the amount of PV yielding a perpetual annual return of r would produce annual cash flows of C until “the end of time.” Now, to determine the PV of an annuity that is not perpetual, the PVannuity equation subtracts from the PV of an annuity-inperpetuity, C / r, the PV of a second annuity-in-perpetuity whose periodic cash flows, also C, begin later. Exploiting a bit of algebra: PVannuity = C 1 n (1 + r) 1– x r C = r – C r 1 x (1 + r) n To illustrate, assume that C = $100, r = 10 percent, and the annuity period, n, is 5 years $100 $100 1 = – x 6 0.10 0.10 (1 + 0.10) = $1,000 – $564.47 = PV of annuity-inperpetuity that begins at end-of-year 1 – PV of an identical annuity-in-perpetuity, except that it begins at end-of-year 6 (5 years after the first annuity-in-perpetuity) = $435.53 = PV of a 5-year annuity beginning at the end of year 1 6 To illustrate a manager’s use of the PVannuity equation, consider a proposal by ABC Company’s managers to license to another firm certain intellectual property – a manufacturing process on which ABC Company holds a legally registered patent. Under a proposed 10-year licensing agreement, the licensee may use ABC Company’s process in exchange for an annual, end-of-year payment of $100,000. Management of ABC Company determined that the company’s required rate of return on investments, r, is 8.0 percent. Accordingly, the present value of the contractually specified license payments is 6 7: 1– PVannuity 1 (1 + 0.08)10 0.08 = $100,000 x = $100,000 x 6.7100814 8 = $671,008 (rounded) However, most managers find computerized spreadsheets (or a handheld financial calculator) easier to use for this purpose.9 Using an MS Excel spreadsheet, a manager may determine easily the present value of an annuity using the following function (formula): =PV(rate,nper,-pmt,-fv,0) , where Rate Nper Pmt FV 0 = = = = = r, Company ABC’s required rate of return: 0.08 (or, 8.0%) Number of periodic cash inflows: the 10 license payments Amount of periodic cash flow: the $100,000 annual license payment 0, in the case of “straight” annuity, such as Company ABC’s proposed license agreement Indicates that payments are due at end of each period throughout the proposed license agreement In the ABC Company illustration: MS Excel present value function (formula) Formula result =PV(0.08,10,-100000,0,0) $671,008 Terminology Financial managers refer to the process of determining the present value, or PV, of future cash flows as discounting, refer to the required rate of return, r, used in PV analysis as the discount rate10, and refer to the computed results as discounted cash flows, or simply DCF. Comparison of the equations above for the future value and present value of cash flows reveals that discounting is the mathematical inverse of compounding. _____ 6 Throughout this background paper (and the Topic 6 background paper), assume that cash flows occur at the end of the periods indicated (so-called cash flows “in arrears”), rather than the beginning of the periods. Application of the TVM equations examined in this background paper requires some minor adjustment in the case where the investment analyzed involves beginning-of-period cash flows. 7 The examination of investments and financing arrangements in this background paper ignores the effects of income taxes. The Topic 6 background paper examines income tax effects on investment decisions in connection with capital budgeting analysis. 8 Financial managers refer to this term as the annuity factor. 9 Before computer spreadsheets and handheld financial calculators came into widespread use in the 1980s, financial managers used tables that summarized discount factors and annuity factors for the possible combinations of discount rates and number of periods, which they applied to investment cash flows. 10 Some managers use the terms hurdle rate, target rate, or cut-off rate to refer to a business’ required rate of return, r. 7 Opportunity Cost: Undiscounted versus Discounted Cash Flows In the ABC Company illustration, above, the proposed license agreement requires the licensee to pay the company a total of $1,000,000 in licensing fees over the term of the 10-year agreement. This amount is the undiscounted (total) cash flows under the agreement. Notice that the discounted cash flows (DCF), or present value of these cash flows, $671,008, is about one-third less than the undiscounted total cash flows. The difference, or $328,992, represents the opportunity cost to ABC Company of not having the money representing the licensing payments “now” so that it can invest it another project that would yield a return. As a result, ABC Company managers would be indifferent between:   An agreement that requires the licensee to pay 10 annual end-of-year payments of $100,000, and An agreement that requires the licensee to pay the company a single upfront payment of $671,008 (and permits the licensee to use the company’s patented process for the ensuing 10 years)11 Investments and Financings Involving Irregular Cash Flows Many investments by businesses do not involve a series of regular cash flows.12 In these situations, managers cannot use the PVannuity equation and the related MS Excel function (formula), =PV(rate,nper,-pmt,-fv,0) above to evaluate investments. When investment opportunities involve irregular cash flows, the most effective and convenient means for evaluating their present value is a computer spreadsheet that:   Discounts each of the cash flows using the “single cash flow” equation, PV = FV / (1 + r)n, defined earlier, and Sums up the results of these individual PV computations To illustrate this approach to evaluating the present value of investments involving irregular cash flows, reconsider ABC Company’s proposal to license its patented manufacturing process. Instead of a fixed annual end-of-year license payment of $100,000, managers are considering an annual royalty payment based on the licensee’s annual sales: Annual royalty payment = Licensee’s annual sales of products manufactured using the licensed manufacturing process x 5 percent Management prepared the following present value analysis based on projected annual sales for each of the next 10 years, as provided by the prospective licensee: _____ 11 Now, whether the licensee would be willing and able to make a large upfront payment to ABC Company is an open question! 12 The Topic 6 background paper examines the capital budgeting process, which considers investments typically involving multiple, irregular cash inflows and cash outflows over several periods. 8 Year (n ) Projected Royalty sales (1) rate Projected Discount Discounted MS Excel royalty factor (2) PV of royalty formula for payment discount factors payment 1 / (1 + r ) n 73,611 =1/(1+0.08)^1 0.85734 71,588 =1/(1+0.08)^2 87,500 0.79383 69,460 =1/(1+0.08)^3 0.05 92,000 0.73503 67,623 =1/(1+0.08)^4 1,930,000 0.05 96,500 0.68058 65,676 =1/(1+0.08)^5 6 2,030,000 0.05 101,500 0.63017 63,962 =1/(1+0.08)^6 7 2,130,000 0.05 106,500 0.58349 62,142 =1/(1+0.08)^7 8 2,240,000 0.05 112,000 0.54027 60,510 =1/(1+0.08)^8 9 2,350,000 0.05 117,500 0.50025 58,779 =1/(1+0.08)^9 10 2,470,000 0.05 123,500 0.46319 57,204 =1/(1+0.08)^10 1 1,590,000 x 0.05 2 1,670,000 0.05 83,500 3 1,750,000 0.05 4 1,840,000 5 Total = 79,500 x 0.92593 1,000,000 = 650,556 This column displays the formula input in the "Discount factor" column of this worksheet. Use the "^" (carat) character - find it above the "6" key on your PC keypad - to indicate that the term, (1 + r), is to be taken to the n power. Of course, your Excel formula may refer to the contents of the "n" column (the first column in this worksheet) for the corresponding row , instead of using a fixed integer (1, 2, 3, etc.) in each row, as shown here to ensure your understanding. (1) Projection of annual sales of products manufactured using licensed manufacturing process (2) The discount rate is Company ABC's required rate of return, r : 0.08 (or, 8.0 percent) Effect of cash flow structure on present value of cash flows. Note that the total of projected royalty payments (undiscounted cash flows) in the above analysis, $1,000,000, is the same as the total of the undiscounted cash flows in the proposed licensing agreement. However, the total discounted present value of the royalty payments in this analysis, $650,556, is $20,452 less than the total discounted present value of the original $100,000-per-year license agreement, $671,008. To understand this difference, study carefully the “structure” or profile of the projected royalty payments and their PVs in the table above; compare these amounts to the payments and PVs in the table, below, which analyzes the original proposed licensing arrangement using the same approach and compares the PVs of each cash flow under both proposals: Year (n ) Licensing fee (original proposal) Discount factor Discounted PV of license payment (1) 1 100,000 2 100,000 0.85734 85,734 71,588 14,146 3 100,000 0.79383 79,383 69,460 9,923 4 100,000 0.73503 73,503 67,623 5,880 5 100,000 0.68058 68,058 65,676 2,382 6 100,000 0.63017 63,017 63,962 (945) 7 100,000 0.58349 58,349 62,142 (3,793) 8 100,000 0.54027 54,027 60,510 (6,483) 9 100,000 0.50025 50,025 58,779 (8,754) 10 100,000 0.46319 46,319 57,204 (10,885) Total 1,000,000 671,008 650,556 20,452 1 / (1 + r )n x 0.92593 = 92,593 Discounted PV of royalty payment (2) – 73,611 Diff. in PV of alternative proposals = 18,981 (1) PV of licensing payments included in original proposal (2) PV of royalty payments included in alternate proposal 9 Notice that, because of “inverse compounding” effects, the discount factors (in the third column of the table immediately above), are smaller in each succeeding period. As a result, holding constant the expected or contractual amount of a future cash flow and the discount rate, the farther into the future that the cash flow occurs, the lower is its present value. That is, managers discount distant cash flows more “severely” than near-term cash flows. Again, the greater discounting of cash flows that are more distant reflects the greater opportunity cost to a business of waiting longer to receive them so it can invest the money at a return, r. Next, notice that the annual licensing payment in the original proposal, $100,000, exceeds the projected royalty payment in each of the first five years of the 10-year arrangement. The total difference in payments for years 1 – 5 is $61,000. As a result, the present value of licensing payments (original proposal) in each of those five years exceeds the present value of projected royalty payments (alternative proposal). The total present value of the licensing payments (original proposal) in years 1 – 5 exceeds the total present value of the royalty payments (alternate proposal) in those years by about . . . In years 6 – 10, however, the $100,000 annual licensing payment (original proposal) is less than the projected annual royalty payments in the alternate proposal. The total difference in payments for years 6 – 10 is ($61,000). As stated above, managers discount these more distant cash flows more severely. As a result, the total present value of the royalty payments (alternate proposal) in years 6 – 10 exceeds the total present value of licensing payments (original proposal) in those years by about . . . For years 1 – 10 in total, the PV of the payments under the original proposal exceeds the PV of the payments under the alternate proposal by about . . . $51,300 ($30,800) $20,500 As a result, managers of Company ABC will prefer the original proposal that requires a $100,000 annual licensing payment over the alternate sales royalty arrangement.13 Effect of cash flow frequency on present value of cash flows. To illustrate further the effect of cash flow structure on present value, reconsider once more Company ABC’s original proposed licensing agreement, requiring a $100,000-per-year license payment. Instead of requiring an annual $100,000 payment, managers have proposed a requirement that the licensee pay Company ABC $25,000 at the end of each quarter (totaling $100,000 annually) throughout the term of the 10-year agreement. Using the PVannuity equation examined above, managers determined the present value of this alternative cash flow structure as follows: 1– PVannuity 1 (1 + 0. 019426547)40 0.019426547 = $25,000 x = $25,000 x 27.6326263 = $690,816 (rounded) Effective rate of return for cash flow series more frequent than annually. Recall that Company ABC’s required annual effective rate of return is 8.0 percent (or, 0.08). In order to evaluate a proposed investment having a series of (regular or irregular) cash flows occurring more frequently than annually, managers must recast the company’s annual effective required rate of return, as follows: _____ 13 In the case that the PV of the alternate (sales royalty) proposal exceeded the PV of the original (licensing fee) arrangement, managers of Company ABC must also consider seriously the inherent uncertainty of any ten-year sales forecast and the obvious incentive for the licensee to purposefully bias upward the amount of projected sales in each year. If those projections ultimately prove to be excessively optimistic, the licensee will benefit – at Company ABC’s expense – from a lower-than-projected royalty payment obligation. 10 rn, required rate of return for non-annual period, n = (1 + required annual effective rate of return, re) 1/n – 1 In the case of Company ABC’s proposed series of quarterly cash flows, managers may compute the discount rate using the above equation, as follows: rQuarterly = (1 + 0.08)1/4 – 1, or 4√(1 + 0.08) – 1 = 0.019426547 They may also compute the periodic rate of return, rn, in an MS Excel spreadsheet using the following formula: =(1+.08)^(1/4)-1. (Recall that “^” – the carat symbol on your computer’s “6” key – indicates that the term, (1 + r), is to be taken to the 1/n power.) Using an MS Excel spreadsheet, managers may determine the present value of this revised annuity using the function (formula) described earlier: =PV(rate,nper,-pmt,-fv,0) , where Rate Nper Pmt FV 0 = = = = = rn, Company ABC’s required quarterly rate of return, 0.019426547 (or, 1.9426547%) Number of periodic cash inflows: the 40 quarterly license payments Amount of periodic cash flow: the $25,000 quarterly license payment 0, in the case of “straight” annuity, such as Company ABC’s license agreement Indicates that payment due at end of annual periods through the end of the license agreement In the Company ABC illustration: MS Excel present value function (formula) Formula result =PV(0.019426547,40,-25000,0,0) $690,816 The table below uses the spreadsheet approach to compute the PV of the quarterly cash flow series included in the revised proposal of the original licensing agreement: Licensing Quarter fee (revised (n ) Discount Discounted MS Excel factor PV of license formula for 1 / (1 + r n)n proposal) payment discount factors 24,524 =1/(1+0.01942655)^1 0.96225 24,056 =1/(1+0.01942655)^2 25,000 0.94391 23,598 =1/(1+0.01942655)^3 25,000 0.92593 23,148 5 25,000 0.90828 22,707 =1/(1+0.01942655)^4 =1/(1+0.01942655)^5 6 25,000 0.89097 22,274 =1/(1+0.01942655)^6 7 25,000 0.87399 21,850 8 25,000 0.85734 21,433 =1/(1+0.01942655)^7 =1/(1+0.01942655)^8 9 25,000 0.84100 21,025 10 25,000 0.82497 =1/(1+0.01942655)^9 20,624 =1/(1+0.01942655)^10 11 25,000 0.80925 20,231 =1/(1+0.01942655)^11 12 25,000 0.79383 19,846 =1/(1+0.01942655)^12 1 25,000 2 25,000 3 4 : : x 0.98094 : = : : 36 25,000 0.50025 12,506 =1/(1+0.01942655)^36 37 25,000 0.49072 12,268 =1/(1+0.01942655)^37 38 25,000 0.48136 12,034 =1/(1+0.01942655)^38 39 25,000 0.47219 11,805 =1/(1+0.01942655)^39 25,000 0.46319 40 Total 1,000,000 11,580 =1/(1+0.01942655)^40 690,816 11 The total undiscounted cash flows are $1,000,000 over a 10-year period in both the original and revised licensing agreement proposals. However, the present value of quarterly license payments under the revised proposal, $690,816, is $19,808 greater than the present value of annual license payments under the original proposal, $671,008. This increase in present value represents the reduction in the opportunity cost to Company ABC because it does not wait as long to receive money (so that it can invest the money at a rate of return, r). The graphic below illustrates this difference in opportunity cost by examining the timing and present value of the cash flows in the first year of Company ABC’s original proposed licensing agreement (requiring annual payments of $100,000) and the revised proposal (requiring quarterly payments of $25,000): First Year’s Cash Flows under Original and Revised Licensing Agreement Proposals Original proposed licensing agreement – Annual end-of-year license payments of $100,000 Present value at time zero Annual payment 1 $92,593 $100,000 Revised proposed licensing agreement – End-of-quarter license payments of $25,000 Quarterly payment 1 24,524 Quarterly payment 2 Quarterly payment 3 Quarterly payment 4 $25,000 24,056 $25,000 23,598 $25,000 23,148 $25,000 95,326 $ 2,733 Difference When negotiating the terms of the ultimate licensing agreement with the prospective licensee, Company ABC’ managers will be aware that, while the revised (quarterly payment) proposal is a “better deal” for Company ABC, the prospective licensee will prefer the original (annual payment) proposal. This is because the licensee’s opportunity costs under the original proposal are less than under the revised proposal. That is, the present value of the original proposal is $19,808 less than the present value of the revised proposal. Effect of changes in discount rates on present value of cash flows. Careful examination of the PV equation examined earlier in this background paper reveals that the present value of cash flows changes inversely with changes in the discount rate (the required rate of return on investment, r). Holding constant the amounts and timing of cash flows from an investment, if a manager increases the discount rate, the present value of cash flows will decrease, and vice versa. PV of cash flow occurring in period n = Cash flow in period n (1 + discount rate)n (Managers’ primary interest in TVM concepts is the application of present value, rather than future value, analysis. This is because they confront the need to plan for a business’ future operations and make current decisions in anticipation of expected future conditions or events.) 12 To illustrate the effect of changes in discount rates on the present value of cash flows, consider once more the original proposed licensing agreement by ABC Company’s managers. That proposal requires the licensee to pay the company $100,000 at the end of each year for 10 years. The PV analysis of the cash flows assumed that Company ABC’s required rate of return, r, is 8.0 percent (or, 0.08). If, instead of 8.0 percent, Company ABC’s required rate of return is 10.0 percent, using the PVannuity equation, the present value of the cash flows under the originally proposed agreement decreases (by nearly 8.5 percent) from $671,008 to $614,457: 1– PVannuity 1 (1 + 0.10)10 0.10 = $100,000 x = $100,000 x 6.144567106 = $614,457 (rounded) Or, using an MS Excel spreadsheet and its present value function (formula), as described earlier: MS Excel present value function (formula) Formula result =PV(0.10,10,-100000,0,0) $614,457 The chart below summarizes the effect on the present value of a 10-year, $100,000 annuity of changes in discount rates, ranging from 6.0 percent to 12.0 percent. Present Value of Cash Flows under Proposed Licensing Agreement (10-year, $100,000 Annuity) $750,000 $700,000 $650,000 $600,000 $550,000 $500,000 6% 7% 8% 9% 10% 11% 12% Company ABC's Required Rate of Return, r (Discount Rate) The chart above suggests two important observations:  It is critical that managers select the proper discount rate to compute the PV of cash flows. For example, in the chart, the PV of the 10-year $100,000 annuity ranges from about $736,000 (using a 6.0 percent discount rate) to $565,000 (using a 12.0 percent discount rate) – a difference of $171,000 and a 30 percent change from the PV6% value!  As examined further in the Topic 6 background paper, as a business’ required rate of return increases, fewer investment opportunities will appear sufficiently attractive to justify accepting them. 13 Estimating the Fair Value of Corporate Bonds and Notes Businesses finance their investments – in property, plant, and equipment (PP&E), product research, manufacturing technology and processes, and other firms – with the cash flows they generate from their daily operations and a variety of equity and debt financial instruments. Equity instruments include principally common stock and preferred stock. Examples of debt instruments that businesses use to finance their investments include:      Corporate bonds (both collateralized and unsecured debentures) Notes issued to financial institutions in connection with loans (both collateralized and unsecured) Mortgages (collateralized by PP&E) Commercial paper (short-term, unsecured borrowings) Leases of real property, equipment, and vehicles Businesses are also investors in the bonds and commercial paper issued by other firms. At the time a business issues bonds or notes, it receives cash from bond investors or the financial institutions accepting the notes (a cash inflow). Once issued, the governing agreement (bond indentures and note agreements) require their issuers to make two kinds of cash payments (cash outflows):   Periodic payment of interest on the bond or note while it remains outstanding, and Repayment of the principal (par or face14) amount borrowed under the instrument upon its maturity Most corporate bonds and many bank notes require the issuer to repay the entire principal (par or face) amount borrowed in full upon its maturity. However, other debt instruments – including mortgages and many equipment leases – require the borrower to repay the principal amount borrowed throughout the term of borrowing.15 Managers can readily estimate the fair value of bonds or notes by computing the present value of their cash flows, using the PV equations defined earlier in this background paper, as the sum of the:   Present value of the bond’s or note’s interest payments (an annuity), plus Present value of the principal (par or face) amount that the issuer will repay at maturity The discount rate used to compute these present values is based on:   For publicly traded16 bonds, the current market interest rate for the particular bond issue For non-publicly traded bonds and notes, the current market interest rate for publicly traded bonds substantially similar to the non-publicly traded instrument under consideration. “Substantially similar” means that the market interest rate used to determine the discount rate corresponds to publicly traded bonds having a debt rating and remaining maturity similar to the non-publicly traded bond or note under consideration. _____ 14 Corporations issue bonds in individual denominations of $1,000 par or face amount. For instance, if the par or face amount of an entire bond issue is $250,000,000, the corporation issued 250,000 bonds each having a $1,000 par value. 15 Homeowners who acquired their homes subject to a traditional (say, 30-year or 15-year) mortgage are familiar with this debt repayment structure, called a “fully amortizing” loan. 16 In the U.S., publicly traded securities are those listed and traded on a national securities exchange (such as the New York Stock Exchange (NYSE) or the National Association of Securities Dealers Automated Quotation (NASDAQ) system, and registered, as required by federal law, with the U.S. Securities Exchange Commission (SEC). Bond dealers at several investment firms maintain a less formal market in many non-publicly traded bonds. 14 For example, in order to estimate the current fair value of non-publicly traded notes previously issued by a corporation in connection with a bank loan, a manager would first look up the current debt rating of the corporate issuer (using a financial Web search engine, such as Yahoo! Finance). Assume the manager learned that the corporation’s current debt rating is “AA” and the notes have a maturity date that is slightly less than six years away. She would next look up (using the financial Web search engine) the current market interest rate for AA-rated, five-year bonds (current annual market yields are generally available only for maturities of 2, 5, 10, and 20 years).17 Present value of bond or note interest payments. As indicated earlier in this background paper, the typical fixed-rate U.S. corporate bond requires the issuer to pay interest to bondholders semi-annually. Notes issued to financial institutions in connection with business loans typically require the borrower to make quarterly or monthly interest payments. Accordingly, financial managers may compute the present value of the interest cash flows using the PVannuity equation: 1– PV of interest payments (annuity) = Periodic interest payment x 1 (1 + y)n y Present value of bond or note principal (or face) amount. On the maturity date of a bond or note, the issuer repays the bondholders the principal (or, face) amount of the bonds. The maturity date of a bond or note coincides with the date of the final interest payment. PV of principal (face) amount = Principal (face) amount (1 + y)n where, y = Current annual market rate (yield) on bond, or on “substantially similar” bonds or note Number of periodic interest payments in each annual period (for most corporate bonds, this is 2) n = Number of interest payment periods until the bond’s or note’s maturity date (e.g., for a 5-year bond, this is 10) and Periodic interest = payment Principal (face) amount of bond or note x Bond’s “coupon” rate or note’s stated (contractual) annual rate Number of interest payments in each year Total present value of bond or note interest payments and principal (or face) amount. The total present value of a bond’s or note’s interest and principal cash flows represents the fair value of a publicly traded bond or the estimated fair value of a non-publicly traded bond or note. _____ 17 Other finance courses examine the operations of financial markets, including the determination of market prices (fair market values) and market rates of return for publicly traded securities, including corporate and government bonds, corporate stocks, and derivative instruments (such as options and futures). The Financial Accounting Standards Board in the U.S. (discussed in the Topic 3-4 background paper) defined fair value as “the price that would be received to sell an asset or paid to transfer a liability in an orderly transaction between market participants at the measurement date.” Note that, a given business’ required rate of return on investments, r, and the market rate of return on a particular debt security are different concepts. As examined in the Topic 6 background paper, managers seek out investments whose rate of return is equal to or greater than their business’ required rate of return, r. However, as examined in the Topic 7 background paper, businesses often invest in securities whose returns are less than their required rate of return, r, in order to achieve their day-to-day working capital management (liquidity) objectives. 15 To illustrate, Company MNO previously issued 20-year bonds having an 8 percent “coupon” rate, principal (face) amount of $100,000,000, and maturity date of June 30, 20X5 – which is 5 years, or 10 interest payment periods from today, July 1, 20X0 The bonds are non-publicly traded. Management believes that current market interest rates (yields) are at a historical low-point and is currently considering refinancing the bonds with new, lower-rate bonds. Management must first estimate the fair value of the existing bonds. The current fair value of the bonds indicates the likely minimum amount that the company will have to pay the current bondholders to induce them to redeem the existing, relatively high-rate bonds. The company’s current debt rating is “single-A” (accordingly to credit-rating agencies Standard & Poor’s and Moody’s Investor Services) and the current annual market rate (yield) for 5-year, A-rated bonds is 6.0 percent (or, 0.06). 1 (1 + .06 / 2)10 .06 / 2 1– PV of interest payments (annuity) PV of principal (face) amount Total PV of bond’s cash flow (bond’s estimated fair value)18 = $100,000,000 x 0.08 / 2 x = $4,000,000 x = $34,120,811 = $100,000,000 (1 + .06 / 2)10 = $ 74,409,392 = PV of interest payments + (annuity) = $ 34,120,811 = $108,530,203 8.53020283 PV of principal (face) amount + $74,409,392 Company MNO managers may also use an MS Excel spreadsheet to determine the present value of the bond’s cash flows using the function (formula) described earlier: =PV(rate,nper,-pmt,-fv,0) where: Rate = Nper Pmt = = FV 0 = = Current annual market rate (yield) on A-rated 5-year debt divided by the number of periodic interest payments in each annual period (for most corporate bonds, this is 2): 6.0% / 2 = 3.0% Number of remaining semi-annual interest payment periods until maturity: 5 years x 2 = 10 Periodic interest payment i.e., the coupon rate times the outstanding principal balance of the bonds divided by 2: 0.08 x $100,000,000 / 2 = $4,000,000 Future value – the amount of the debt principal outstanding, due at maturity: $100,000,000 Payment due at end of semi-annual periods through maturity The present value of the bond’s cash flows, and estimated fair value of the bonds, is: MS Excel present value function (formula) Formula result =PV(6%/2,5*2,-100000000*0.08/2,-100000000,0) $108,530,203 _____ 18 Other finance courses examine the valuation of bonds on dates between interest payment dates. 16 Fair Value of a Business' Capital Financing and Unrecognized or Under-valued Assets The Topic 3-4 Background Paper examines the limitations on the usefulness of financial statements. Recall that two kinds of such limitations are: — Trade-offs between the relevance and representational faithfulness (completeness or freedom from error) or verifiability of financial statements caused by the combination of conservatism and articulation. Under U.S. GAAP, accounting for such items as research and development (“R&D”) costs, internally generated intangible assets, and inventory reflect this trade-off and may impair the relevance of certain asset values reported in businesses' balance sheets. — Definitions of financial statement elements and measurement uncertainty. Measurement uncertainty and exclusion of most executory contracts from the definitions of “assets” and “liabilities” may impair the completeness of businesses' balance sheets. Following the revenue recognition principle, businesses generally must complete arms-length transactions in order to record increases in net assets. In accordance with the historical cost principle, businesses report most assets at amounts that reflect their original exchange value, rather than their current fair values. Managers may use present value concepts, together with an examination of other information about a business to identify:  The extent to which its balance sheet may fail to recognize “probable future economic benefits” (the Financial Accounting Standards Board's definition of “assets”) or under-value recognized assets, and  The possible kinds or categories of assets that could be unrecognized or under-valued Other information that may be useful in making this analysis is included in annual reports on Form 10K filed by public companies with the U.S. Securities and Exchange Commission. (The Topic 3-4 Background Paper examines the regulatory reporting framework of public companies in the U.S., including the periodic reports these companies must file with the SEC.) To perform this analysis, recall the basic accounting equation, examined in the Topic 3-4 Background Paper: Left side of balance sheet ASSETS Right side of balance sheet = LIABILITIES + STOCKHOLDERS’ EQUITY or INVESTMENTS = SOURCES OF FINANCING FOR THOSE INVESTMENTS Accordingly, managers can estimate the implied fair value of a business’ assets – recognized and unrecognized – by determining or estimating the fair value of its sources of financing, comprised of debt and equity. For publicly traded shares of common or preferred stock and certain bonds, managers may locate quoted market prices, as published by the securities exchanges. For non-publicly traded stocks and bonds, managers may prepare valuations of the business or its individual issues of securities using present value concepts. The table below illustrates the general framework for this analysis: Estimated fair value of or quoted market price for ABC Company’s: Common stock (10.0 million shares at $67.67 per share) Preferred stock, if any Debt, including bonds and notes $US in millions $ 676.7 – 583.3 Accounts payable, accrued and other liabilities, as reported in company’s balance sheet 240.0 Total fair value of company’s financing sources (liabilities and shareholders’ equity) and, therefore, the implied fair value of company’s investments (total assets) 1,500.0 Less total assets reported in company’s balance sheet as of the valuation date 1,400.0 Excess difference $ 100.0 17 The difference between the implied fair value of a business’ assets and the reported balance of total assets in the business’ balance sheet as of the valuation date reflects the limitations of the financial reporting model underlying U.S. GAAP (or IFRS). An excess difference represents the estimated fair value of assets unrecognized or under-valued in the balance sheet. (Other courses examine the accounting and financial implications of a deficiency, including the possibility of unrecognized asset impairment and, in the case that the amount of a business’ liabilities exceed the fair value of its assets, insolvency.) Managers may estimate the fair value of a business’ non-publicly traded bonds and notes using the present value methods described above and information contained in the business’ financial statements, as illustrated below. The financial statements of ABC Company for the fiscal year ended December 31, 20X2 include the following balance sheet and footnote information related to the company’s debt and shareholders’ equity. ABC Company Consolidated Balance Sheet December 31, 20X2 $US in millions Assets: Cash and cash equivalents Liabilities and shareholders' equity: $ Investments securities, at cost (to be held to maturity) 18 Accounts payable and accrued expenses $ 108 Income taxes payable Accounts receivable, net 213 27 37 Notes payable - current portion (Note 6) 20 Inventory, at lower of LIFO cost or market value 182 Bonds payable - current portion (Note 6) 70 Total current assets 345 Total current liabilities Property, plant, and equipment, at cost Less accumulated depreciation Property, plant, and equipment, net 1,420 Notes payable - noncurrent portion (Note 6) 140 (390) Bonds payable - noncurrent portion (Note 6) 350 1,030 Total liabilities Investments in affiliated businesses Total assets 330 820 25 Total common shareholders' equity (Note 9) $ 1,400 Total liabilities and shareholders' equity 580 $ 1,400 18 Excerpts from FY 20X2 financial statement footnotes . . . Note 6 - Debt The company's debt at December 31, 20X2 is comprised of notes and bonds payable, as follows: ($US in millions) The amounts of debt outstanding as of December 31, 20X2 that is payable in each of following five years and for all remaining years thereafter in the aggregate are: FYE Dec. 31, Weighted average Principal balance interest rate Working capital loans 4.625% Term loans 7.0 percent serial bonds outstanding $ 90 40 20X4 90 5.375% 120 20X5 85 7.000% 420 20X6 75 Total 580 20X7 60 Less current portion (90) Thereafter 490 Total Noncurrent portion $ 20X3 Principal due $ 180 $ 580 In January 20X1, the company issued a $25 million note to a syndicate of banks in connection with a seven-year term loan that bears a fixed 5.0 percent interest rate. The loan is secured by the company's assets and subject to financial and other covenants, including a requirement that the company maintain a total debt ratio not exceeding 1.5:1 (or 1.50). Note 9 - Shareholders' equity The company's articles of incorporation authorize it to issue up to 15 million shares of the company's common stock, par value $20 per share. At December 31, 20X2, 11.5 million shares of the company's common stock were issued and 1.5 million of those shares were held by the company as treasury stock. The company's articles authorize it to issue up to 1.0 million shares of 7.5 percent cumulative preferred stock, $100 par value. The company had issued no shares of preferred stock as of December 31, 20X2. Market Information The company’s bonds are currently rated "single A" (Standard & Poor’s) and "A2" (Moody's Investor Services).A Managers separately located current market yields on "single A" corporate debt securities, by term to maturity, as follows: 1 year 4.750% 6 years 6.625% 2 years 5.125% 7 years 7.000% 3 years 5.500% 8 years 7.375% 4 years 5.875% 9 years 7.750% 5 years 6.250% 10 years 8.125% The company's common stock currently trades at $67.67 per share on the NASDAQ. Managers estimated the fair value of the company’s outstanding debt “portfolio” using the information obtained above, as set forth below: 19 Remaining semi- Estimated fair Current yield on comparably rated debt value (PV of debt (3) principal annual interest payment Outstanding periods (Years debt principal at Year of to maturity Dec. 31, 20X2 maturity TIMES 2) ($US millions) 20X3 2 20X4 $ Semi-annual Interest (1) Rate Payment (2) Term Annual yield Semi- outstanding and annual interest payments) yield (4) (5) 90.0 3.250% $ 2.93 1 year 4.750% 2.3750% $ 91.5 4 90.0 3.250% 2.93 2 years 5.125% 2.5625% 92.3 20X5 6 85.0 3.250% 2.76 3 years 5.500% 2.7500% 87.3 20X6 8 75.0 3.250% 2.44 4 years 5.875% 2.9375% 76.6 20X7 10 60.0 A 3.250% 1.95 5 years 6.250% 3.1250% 60.6 180.0 B Thereafter 3 Years (B / A) (6) 20X8 12 60.0 1 Yr 3.250% 1.95 6 years 6.625% 3.3125% 59.6 20X9 14 60.0 2 3.250% 1.95 7 years 7.000% 3.5000% 58.4 20Y0 16 60.0 3 3.250% 1.95 8 years 7.375% 3.6875% 56.9 20Y1 18 - 3.250% - 9 years 7.750% 3.8750% - 20Y2 20 - 3.250% $ - 10 years 8.125% 4.0625% - Total $ 580.0 $ 583.3 (1) Assume all debt outstanding requires semi-annual interest payments and matures December 31 of years disclosed. The weighted average interest rate on company's "portfolio" of debt is estimated using footnote information, as follows: Debt footnote information Weighted Principal Wghtd avg int average balance Percent of rate X Percent interest rate outstanding Working capital loans 4.625% $ Term loans 7.0 percent serial bonds total of total 40.0 6.9% 0.319% 5.375% 120.0 20.7% 1.112% 7.000% 420.0 72.4% 5.069% 580.0 100.0% $ 6.500% Semi-annually, 3.25% (2) Semi-annual interest payments computed as: debt principal outstanding TIMES estimated semi-annual interest rate, in (1) (3) Company's debt rating and current annual yields on comparably-rated debt obtained via financial Websearch. (4) Semi-annual yield (discount rate) used to compute present value of debt principal outstanding and interest payments through maturity is the annual yield DIVIDE 2. [The effective annual yield = 1 + annual yield / 2 ) 2 - 1] (5) Present value of debt principal outstanding and interest payments for each maturity year computed using the MS Excel formula: =PV(rate,nper,-pmt,-fv,0) where: Rate = Semi-annual yield on comparably-rated debt for the maturity period indicated in (4) Nper = Remaining semi-annual interest payment periods until maturity (years to maturity TIMES 2) Pmt = Semi-annual interest payment, computed in (2) above FV = Future value - i.e., the debt principal outstanding for the maturity year indicated 0 = Payment due at end of semi-annual periods through maturity (6) Financial statement footnotes of companies disclose annual maturities of debt only for the first 5 years following the balance sheet date and disclose the remaining maturities of debt only as a "thereafter" total. For the purposes of estimating the fair value of a company's total debt, analysts estimate the amount of annual maturities after Year 5 by dividing the "thereafter" total by the amount of the debt maturing in Year 5 to estimate the average number of years over which the "thereafter" total matures. Analysts then assume that an amount similar to that maturing in Year 5 will also mature in each subsequent year (here, 20X8 - 20Y0). 20 A The table below summarizes the long-term debt ratings assigned to corporate debt securities by three principal debt-rating agencies. The rating agencies call securities rated below BBB- (S&P and Fitch) or Baa3 (Moody’s) “non-investment grade” or “speculative” because of the issuer presents pronounced credit (default) risk. S&P Moody’s Fitch Credit-worthiness category AAA Aaa AAA Prime AA+ Aa1 AA+ High grade AA Aa2 AA AA- Aa3 AA- A+ A1 A+ A A2 A A- A3 A- BBB+ Baa1 BBB+ BBB Baa2 BBB BBB- Baa3 BBB- Upper medium grade Lower medium grade 21 Net Present Value So far, this background paper has examined arrangements or financial instruments for which the cash flows are all inflows or all outflows. In the Company ABC licensing agreement proposal, all the cash flows examined were inflows to the company; in the Company MNO illustration, all the bond-related cash flows examined were outflows to the company. Most investments examined by a business require cash outflows (the initial investment), followed by cash inflows (returns on investment and, eventually, return of the initial investment). For example, a business may:      Acquire additional plant and equipment in order to expand productive capacity, Replace production equipment with more efficient or more highly automated (cost-saving) equipment, Launch a product research-and-development project, Introduce a new product, or Acquire a competitor or supplier business Managers evaluate the acceptability of these and similar proposed investments based on their net present value (NPV). NPV analysis is central to capital budgeting, examined in the Topic 6 background paper. However, to clarify the NPV concept at this point, consider the following brief illustration: Management of Company XYZ has proposed that the company acquire an additional drill press. Demand for the company’s products has risen to a level that exceeds its present productive capacity. An additional drill press will make it possible for the company to increase its production and sales by 20 percent, resulting in projected additional operating cash flows (OCF) in each of the next five years, as indicated at right: The equipment will cost $640,000 to purchase and install. Management estimates that its economic life will be five years, after which it will have no residual value. Year Projected increase in OCF 20X1 $150,000 20X2 180,000 20X3 200,000 20X4 170,000 20X5 140,000 Total $840,000 The company’s vice president of operations is confident that this proposal will “pencil out” favorably, because the projected additional OCF, $840,000, exceeds the cost of the equipment by $200,000. She prepared an NPV analysis of the drill press proposal using a computer spreadsheet, which is set forth below. In doing so, she discounted the relevant cash flows at the company’s required rate of return on investments, 9.5 percent (or, 0.095). (To simplify her analysis, she assumed that the projected increases in OCF occur at the end of years indicated.) 22 Relevant cash flows (1) Year (n) Discount factor (2) 1 / (1 + r ) n 20X0 0 20X1 1 150,000 0.91324 136,986 20X2 2 180,000 0.83401 150,122 20X3 3 200,000 0.76165 152,331 20X4 4 170,000 0.69557 118,248 20X5 5 140,000 0.63523 88,932 Net cash flows (640,000) x Discounted cash flows 1.00000 200,000 = MS Excel formulas for discount factors (640,000) NPV =1/(1+0.095)^0 =1/(1+0.095)^1 =1/(1+0.095)^2 =1/(1+0.095)^3 =1/(1+0.095)^4 =1/(1+0.095)^5 6,619 (1) Relevant cash flows are those which are incremental to the proposed investment (2) The discount rate is Company XYZ's required rate of return, r : 0.095 (or, 9.5%) Note that this analysis includes the initial investment (the cost of the drill press) as a negative cash flow at “time zero.” Managers do not discount cash flows occurring at the outset of an investment. To ensure this result, they use a discount factor is 1.0 in their spreadsheet analyses. An expression of the NPV analysis of the drill press proposal in the form of an equation is: NPV of drill press = proposal – Initial investment cash Year 1 OCF incr. + + outflow (cost of drill (1 + r)1 press) = ($640,000) = $6,619 + $136,986 + Year 2 OCF incr. (1 + r)2 $150,122 + + Year 3 OCF incr. (1 + r)3 $152,331 + + Year 4 OCF incr. (1 + r)4 $118,248 + + Year 5 OCF incr. (1 + r)5 $88,932 The analysis shows that the NPV of the drill press proposal is positive $6,619. It is immediately apparent that the NPV of the proposed investment is very small in comparison to the net undiscounted cash flows, $200,000. However, the important conclusion that managers should draw from this analysis is that, because the NPV is zero or positive, the expected rate of return on the proposed investment exceeds the company’s required rate of return on new investments. Therefore, the company should approve the investment proposal, provided that:  Management is confident that the projected increases in OCFs are substantially accurate19, and  The company has a sufficient amount of financial capital available to finance the acquisition of the drill press20 The general decision rules in NPV analysis are:   If the NPV of a proposed investment is zero or positive, accept the proposal If the NPV of a proposed investment is negative, reject the proposal Positive-NPV investments increase the value of a business to its owners, while negative-NPV investments destroy its value. ______ 19 The Topic 6 background paper examines sensitivity analysis, used in connection with capital budgeting. In the case of the proposed drill press investment, if actual results later prove that the projected increases in OCF were overstated by more than 1 percent in each year, 20X1 – 20X5, the NPV of the investment is negative, indicating (in hindsight) that managers should have rejected the proposal! 20 Management may need to ration a limited amount of available financial capital among multiple investment opportunities, as discussed below. The Topic 6 background paper examines businesses’ required rate of return (cost of capital). Company XYZ’s cost of capital establishes its required rate of return on new investments. 23 Relevant Cash Flows and Sunk Costs In the previous illustrations that examined Company ABC’s proposed licensing agreement, the PV analyses properly ignored the company’s initial costs of developing the manufacturing process that was the subject of the proposed agreement. This is because the cash flows representing those development costs are sunk costs. That is, the company developed and patented its manufacturing process for its own use some time before the prospect of licensing it arose. Therefore, those initial costs are not relevant to the analyses in these illustrations.21 (Hopefully, managers included those initial cash outflows in an earlier NPV analysis of the proposed investment in the manufacturing process.) For purposes of analyzing proposed investments, only incremental cash flows are relevant cash flows. Incremental cash flows are those that are:   Directly related to the proposed investment and Occur only if the business accepts the proposal As stated at the outset of this background paper, cash flows representing any costs a business incurs before managers make their decision to accept or reject an investment proposal are not relevant cash flows. The Topic 7 background paper examines the application of NPV analysis to setting customer credit policy. Learning Objective 2 Capital Rationing and Ranking Multiple Investment Opportunities In theory, a business should be able to obtain financing for all investments for which the capital budgeting analysis indicates the NPV is positive. This is because positive-NPV investments promise rates of return that exceed the business’ cost of capital and, therefore, they increase the value of the business to its owners. However, businesses generally face practical constraints on the amount of financial capital that is available to them in the short-term (say, one year). For example, the process of issuing common or preferred stock or bonds, or negotiating loans from a syndicate of commercial banks is time-consuming and costly. As a result, many businesses must ration available financial capital, accepting some opportunities while rejecting others. The proper method for ranking possible investments and rationing capital to the highest-ranked opportunities uses the profitability index (PI) (or, excess present value index): Profitability index (PI) = PV of cash flows subsequent to initial investment Initial investment cash flow = NPV of investment + Initial investment cash flow Initial investment cash flow Close examination of the PI equation above reveals that the PI for a proposed investment will be greater than 1.0 if its projected NPV is positive. Accordingly, following the general NPV decision rules listed above, businesses should accept investment proposals for which the PI is greater than 1.0. However, when a business has only limited capital available, it may ration that capital to investment opportunities by ranking them according their PI.22 _____ 21 The illustrations involving the proposed licensing agreement implicitly assumed that the prospective licensee would not use Company ABC’s manufacturing process to make products that would compete with those of Company ABC. In the case where such an arrangement would result in erosion of sales by Company ABC, managers’ NPV analysis should include the contribution margin related to projected lost sales. (The Topic 6 background paper examines sales erosion in connection with capital budgeting analysis of proposed new products.) Of course, if Company ABC’s managers expected the licensing agreement to lead to increased competition for the company, they would be extremely skeptical about “making the deal.” 22 However, the PI is not effective for rationing capital over more than one period (say, beyond one year). 24 To illustrate, assume that Company RST has an approved total capital budget of $12,000,000 for the coming fiscal year and managers have identified and estimated the NPV of the following eight investment opportunities, A through H: (1) (2) (2) - (1) (2) / (1) Project Initial investment cash flow PV of cash flows subsequent to initial investment NPV Profitability index (PI) A $7,200,000 $ 9,350,000 $2,150,000 1.30 B 1,260,000 1,440,000 180,000 1.14 C 1,440,000 2,250,000 810,000 1.56 D 960,000 1,260,000 300,000 1.31 E 1,140,000 1,300,000 160,000 1.14 F 2,100,000 2,415,000 315,000 1.15 G 2,400,000 2,150,000 (250,000) 0.90 H 1,080,000 1,090,000 10,000 1.01 Total 17,580,000 Absent any capital constraints, the company should pursue each of these projects, except Project G, for which the estimated NPV is negative. The remaining opportunities all have a positive NPV and therefore serve to increase the value of the company. In light of the company’s capital constraint, managers ranked the proposed investments (projects) based on their PIs, as follows: (1) (2) (2) - (1) (2) / (1) Project Initial investment cash flow Cumulative total initial investment cash flow PV of cash flows subsequent to initial investment NPV C $1,440,000 $ 1,440,000 $ 2,250,000 $ 810,000 $ 810,000 1.56 D 960,000 2,400,000 1,260,000 300,000 1,110,000 1.31 A 7,200,000 9,600,000 9,350,000 2,150,000 3,260,000 1.30 F 2,100,000 11,700,000 2,415,000 315,000 3,575,000 1.15 E 1,140,000 12,840,000 1,300,000 160,000 3,735,000 1.14 B 1,260,000 14,100,000 1,440,000 180,000 3,915,000 1.14 H 1,080,000 15,180,000 1,090,000 10,000 3,925,000 1.01 G 2,400,000 17,580,000 2,150,000 (250,000) 3,675,000 0.90 Cumulative total Profitability NPV index (PI) Of course, management immediately rejected project G because its estimated NPV is negative (and consequently, the rate of return on this investment is less than the company’s cost of capital). Initially, it appears that managers should approve projects C, D, A, and F (and reject the remaining proposals) because  These are the highest-ranking opportunities based on their respective PIs, and  The cumulative total initial investment required by these four projects, $11,700,000, is within the approved budget of $12,000,000 The estimated cumulative total NPV from these four investments is $3,575,000. 25 However, on closer inspection, managers noticed that, if the company approved Projects B and E, and rejected Project F, the company would be able to:  Invest the entire $12,000,000 of capital available, and  Maximize the cumulative total NPV from all five accepted projects at $3,600,000 (note that the total NPV of Projects B and E is $340,000, $25,000 more than the NPV of Project F, $315,000): (1) (2) (2) - (1) Project Initial investment cash flow Cumulative total initial investment cash flow PV of cash flows subsequent to initial investment NPV C $1,440,000 $ 1,440,000 $ 2,250,000 D 960,000 2,400,000 1,260,000 A 7,200,000 9,600,000 E 1,140,000 B F (2) / (1) Cumulative total Profitability NPV index (PI) Decision $ 810,000 $ 810,000 1.56 Approve 300,000 1,110,000 1.31 Approve 9,350,000 2,150,000 3,260,000 1.30 Approve 10,740,000 1,300,000 160,000 3,420,000 1.14 Approve 1,260,000 12,000,000 1,440,000 180,000 3,600,000 1.14 Approve 2,100,000 14,100,000 2,415,000 315,000 3,915,000 1.15 Reject H 1,080,000 15,180,000 1,090,000 10,000 3,925,000 1.01 Reject G 2,400,000 17,580,000 2,150,000 (250,000) 3,675,000 0.90 Reject Of course, strategic, operating, or other non-financial factors may affect managers’ decision to select Project F over Projects B and E. For example, Projects B and E may present political or reputational issues that it is not practical for managers to factor into their NPV analyses. ***** Course developer’s note on content of and sources used in preparing course background papers: In selecting the content and determining the organization of material for this course, the developer considered a number of factors, including the university’s MBA program outcomes, material examined in the program’s accounting and finance foundation courses, and material examined in subsequent MBA accounting and finance courses, in particular MBA A602 (Interpreting Accounting Information) and MBA F602 (Financial Decision-making), which, in turn, are prerequisites for other MBA accounting and finance courses. The course developer reviewed several accounting and finance texts, listed below, to ensure that the examination of models, concepts, methods, and terminology in the background papers is generally consistent with a variety of such texts over time. The course developer noticed that, on the one hand, there is substantial similarity among texts in the material (models, concepts, methods, and terminology) examined. The developer also noticed that, on the other hand, in spite of this similarity, none of these texts appears to include references to other texts (just original research articles, authoritative accounting literature, and the occasional federal statute, internal revenue code section, or IRS regulation). In addition, much of the material examined in the texts and the background papers is the subject of articles on several unrestricted Websites, such as Wikipedia.com. As such, the material contained in the background papers represents both essential and common knowledge for business managers. Atkinson, A. A., Banker, R. D., Kaplan, R. S. & Young, S. M. (1995). Management accounting. Englewood Cliffs, New Jersey: Simon & Schuster Co./Prentice-Hall. Horngren, Charles T. (1977). Cost accounting: A managerial emphasis. (4th ed.). Englewood Cliffs, NJ: Prentice-Hall. Kieso, D. E., Weygandt, J. J., & Warfield, T. D. (2004). Intermediate accounting. (11th ed.). New York: Wiley & Sons. Ross, S. A., Westerfield, R. W. & Jaffe, J. E. (1993). Corporate finance. (3rd ed.). Burr Ridge, IL: Richard D. Irwin. Wild, J. J., Subramanyam, K. R. & Halsey, R. F. (2004). Financial statement analysis. (10th ed.). New York: McGraw-Hill/Irwin. Wolk, H. I., Dodd, J. L. & Tearney, M. G. (2004). Accounting theory: Conceptual issues in a political and economic environment. (6th ed.). Mason, OH: Thomson Learning/South-Western. 26
Instructions: Using the company and market information provided below, complete the following two tabs in this MS Excel Workbook: – Computation of the estimated current fair value of the note issued by the company in 20X3 – Computation of the estimated current fair value of the company's "portfolio" of debt (notes and bonds) outstanding, as reported in its fiscal year end (FYE) 20X4 balance sheet The background papers, Present Value Concepts and Bond Valuation, and Financial Statement Concepts and Financial Reporting provide useful guidance for completing this assignment. Based on the results of your computed estimate of the fair value of the company's debt "portfolio" (the second tab following this one) and the additional information provided below, indicate (i) the apparent total fair value ($US) of assets unrecognized or under-valued in the FYE 20X4 balance sheet and (ii) the possible kinds or categories of assets that could be unrecognized or under-valued and the apparent reasons for this. (In formulating your response, it may be helpful to review pages 17 - 18 of the background paper, Present Value Concepts and Bond Valuation , including the illustration on those pages and pages 38 and 41 - 47 of the background paper, Financial Statement Concepts and Financial Reporting .) Limit the length of your response to 150 words. Replace the text in this cell with your response. Advanced Technology and Services Company Consolidated Balance Sheet December 31, 20X4 $US in millions Assets: Liabilities and shareholders' equity: Cash and cash equivalents 15 Accounts payable and accrued expenses Investments securities, at cost (to be held to maturity) 75 Income taxes payable 20 Accounts receivable, net 18 Notes payable - current portion (Note 5) 10 Inventory, at lower of LIFO cost or market value 192 Bonds payable - current portion (Note 5) 50 Total current assets 300 Total current liabilities 250 Notes payable - noncurrent portion (Note 5) 100 (380) Bonds payable - noncurrent portion (Note 5) 250 $ Property, plant, and equipment, at cost 1,045 Less accumulated depreciation Property, plant, and equipment, net 665 Investments in "strategic partner" suppliers 35 Total assets $ 1,000 $ 170 Total liabilities 600 Total common shareholders' equity (Note 7) 400 Total liabilities and shareholders' equity $ 1,000 Excerpts from FY 20X4 financial statement footnotes . . . Note 5 - Debt The company's debt at December 31, 20X4 is comprised of notes and bonds payable, as follows: ($US in millions) Weighted average interest Principal balance rate outstanding Notes payable to banks 4.00% Notes payable to other lenders 6.0 percent serial bonds $ The amounts of debt outstanding as of December 31, 20X4 that is payable in each of following five years and for all remaining years thereafter in the aggregate are: FYE Dec. 31, 20X5 Principal due $ 60 54 20X6 65 5.00% 56 20X7 60 6.00% 300 20X8 60 Total 410 20X9 55 Less current portion (60) Thereafter 110 Noncurrent portion $ 350 Total $ 410 In January 20X3, the company issued a $30 million note to a syndicate of banks in connection with a seven-year term loan that bears a fixed 4.25 percent interest rate. The loan is secured by the company's assets and subject to financial and other covenants, including a requirement that the company maintain a total debt ratio not exceeding 1.5:1 (or 1.50). Note 7 - Shareholders' equity The company's articles of incorporation authorize it to issue up to 25 million shares of the company's common stock, par value $5 per share. At December 31, 20X4, 22.0 million shares of the company's common stock were issued and 2.154 million of those shares were held by the company as treasury stock. The company's articles authorize it to issue up to 2.5 million shares of 8 percent preferred stock, $100 par value, for which dividends shall be cumulative. At December 31, 20X4, the company had issued no shares of preferred stock. Market information The company's 6.0 percent serial bonds are currently rated "single A" (Standard & Poors) and "A2" (Moody's Investor Services) Current market yields on "single A" corporate securities, by term to maturity are: 1 year 4.625% 6 years 6.500% 2 years 5.000% 7 years 6.875% 3 years 5.375% 8 years 7.250% 4 years 5.750% 9 years 7.625% 5 years 6.125% 10 years 8.000% The company's common stock currently trades at $25 per share on the NASDAQ. The facilitator will grade this assignment, assigning up to 100 points for it as follows: Maximum Earned Complete, accurate, and clear presentation of calculations of the estimated fair value of: – The specified individual company bond or note issue 10 – The company’s aggregate debt “portfolio” 75 (1) Clear and accurate indication of the apparent total fair value ($US) of assets unrecognized or under-valued in the balance sheet and (2) clear, concise, and complete description of the possible kinds or categories of assets that could be unrecognized or under-valued and the apparent reasons for this 15 Total points 100 points - S17S8W2 A1 Instructions: Use the information in the first worksheet tab (Instructions and company information) to complete the analysis in this tab. Show all computations in good form and label properly all amounts presented . Compute the current fair value of the bank note syndicated in 20X3, showing separately to the nearest whole $US dollar (1) the present value of the principal (face) amount of the note and (2) the present value of related interest payments due under the note. You may assume that the note interest payments are either annual or semiannual. Your choice!!! Present Value (PV) of a Bond Example: Given: Face Value of Bond $30,000,000 Discount Rate (YTM) Interest % Number of Periods PThe PV of a Bond is calculated below, using the Example information listed above PV Calculations Assuming Annual Payments PV or Price of bond = PV Calculations Assuming Semi-Annual Payments PV or Price of bond = 17S8W2 B1 Remaining semi-annual interest Outstanding payment debt principal at Year of periods (Years Dec. 31, 20X4 maturity (1) to maturity ($US millions) 17F8W2 Semi-annual Interest Rate Payment Estimated fair value (PV of debt principal Current yield on comparably rated debt outstanding and Semiinterest Annual yield annual payments) ($US Term 17S8W2 Use the in workshee company complete tab. A Thereafter B Years (B / A) Enter num labels, as shaded leaving th workshee Total (1) Assume all debt outstanding requires semi-annual interest payments and matures December 31 of years disclosed. (2) Show your computation of the estimated weighted average interest rate on the debt "portfolio" using footnote information, below: Debt footnote information Weighted average Principal interest balance rate outstanding Percent of total % Wghtd avg int rate X Percent of total To ensure your work whenever help enab understan reasoning "partial cr Year of maturity (1) Use the information in the first worksheet tab (Instructions and company information) to complete the analysis in this Remaining semi-annual Outstanding interest debt principal payment at Dec. 31, periods (Years 20X4 ($US 17F8W2 to maturity millions) To ensure maximum credit for your work, use formulas whenever possible. This will help enable the faciliator's understanding of your reasoning, which may justify "partial credit" for inaccurate Semi-annual Interest Rate Payment Term Annual yield Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error A Error Error Error Error Error B Error Years (B / A) Thereafter Enter numbers, formulas, or labels, as appropriate, in shaded worksheet cells only, leaving the remainder of this worksheet tab unchanged. Current yield on comparably rated debt 17S8W2 Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Total Error (1) Assume all debt outstanding requires semi-annual interest payments and matures December 31 of years d (2) Show your computation of the estimated weighted average interest rate on the debt "portfolio" using footno Debt footnote information Weighted Principal average balance Percent of interest rate outstanding total Wghtd avg int rate X Percent of total Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error Estimated fair value n comparably rated (PV of debt debt principal Semi- outstanding annual and interest Error Error Error Error Error Error Error Error Error Error Error Error Error Error Error ber 31 of years disclosed. olio" using footnote information, below: 17S8W2 D1 D5

Tutor Answer

NKURUMAH
School: UT Austin

Attached.

Instructions:
Using the company and market information provided below, complete the following two tabs in this MS Excel Workbook:
– Computation of the estimated current fair value of the note issued by the company in 20X3
– Computation of the estimated current fair value of the company's "portfolio" of debt (notes and bonds) outstanding, as
reported in its fiscal year end (FYE) 20X4 balance sheet
The background papers, Present Value Concepts and Bond Valuation, and Financial Statement Concepts and Financial
Reporting provide useful guidance for completing this assignment.
Based on the results of your computed estimate of the fair value of the company's debt "portfolio" (the second tab following this one)
and the additional information provided below, indicate (i) the apparent total fair value ($US) of assets unrecognized or under-valued in
the FYE 20X4 balance sheet and (ii) the possible kinds or categories of assets that could be unrecognized or under-valued and the
apparent reasons for this. (In formulating your response, it may be helpful to review pages 17 - 18 of the background paper, Present
Value Concepts and Bond Valuation , including the illustration on those pages and pages 38 and 41 - 47 of the background paper,
Financial Statement Concepts and Financial Reporting .) Limit the length of your response to 150 words.

PART A
of interest payments (annuity)=
Principal (face) amount of bond or note x Bond’s “coupon” rate or note’s stated (contractual) annual
Number of interest payments in each year
PV of interest payments (annuity)=

637,500 x 11.29607314

$ 30,000,000 x 4.25%/2 x

1 -

PV

1
(1+0.06/2)^14
0.06/2

= $ 7,201,246.626
Advanced Technology and Services Company
Consolidated Balance Sheet
December 31, 20X4
$US in millions

Assets:

Liabilities and shareholders' equity:

Cash and cash equivalents

15

Accounts payable and accrued expenses

Investments securities, at cost (to be held to maturity)

75

Income taxes payable

20

Accounts receivable, net

18

Notes payable - current portion (Note 5)

10

Inventory, at lower of LIFO cost or market value

192

Bonds payable - current portion (Note 5)

50

Total current assets

300

Total current liabilities

250

Notes payable - noncurrent portion (Note 5)

100

(380) Bonds payable - noncurrent portion (Note 5)

250

$

Property, plant, and equipment, at cost

1,045

Less accumulated depreciation
Property, plant, and equipment, net

665

Investments in "strategic partner" suppliers

35

Total assets

$

1,000

$

170

Total liabilities

600

Total common shareholders' equity (Note 7)

400

Total liabilities and shareholders' equity

$

1,000

Excerpts from FY 20X4 financial statement footnotes . . .
Note 5 - Debt
The company's debt at December 31, 20X4 is comprised of notes and
bonds payable, as follows:
($US in millions)

Weighted
average interest Principal balance
rate
outstanding

Notes payable to banks

4.00%

Notes payable to other lenders
6.0 percent serial bonds

$

The amounts of debt outstanding as of December 31, 20X4
that is payable in each of following five years and for all
remaining years thereafter in the aggregate are:
FYE Dec. 31,
20X5

Principal due
$

60

54

20X6

65

5.00%

56

20X7

60

6.00%

300

20X8

60

Total

410

20X9

55

Less current portion

(60)

Thereafter

110

Noncurrent portion

$

350

Total

$

410

In January 20X3, the company issued a $30 million note to a syndicate of banks in connection with a seven-year term loan that bears a
fixed 4.25 percent interest rate. The loan is secured by the company's assets and subject to financial and other covenants, including a
requirement that the company maintain a total debt ratio not exceeding 1.5:1 (or 1.50).
Note 7 - Shareholders' equity
The company's articles of incorporation authorize it to issue up to 25 million shares of the company's com...

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