Scarica Understanding the Link between Interest Rates, Inflation, and Cash Flow - Prof. Poletti e più Appunti in PDF di Finanza solo su Docsity!
PRIMO READING: NET PRESENT VALUE
Consider the example of a firm contemplating investing $1 million in a project expected to pay out $200,000 per year for nine years. Should the firm accept the project? One might say yes at first glance, as $1.8 million payout is higher than the investment, but the investment is to be done immediately whereas the payout is uncertain and in the future. Thus we need to know the relationship between a dollar today and a (possibly uncertain) dollar in the future before deciding on the project. This relationship is the time-value-of-money concept. It is important in capital budgeting, lease versus buy decisions, accounts receivable analysis and so on. THE ONE PERIOD CASE Dom Simkowitz wants to sell a piece of raw land in Alaska. He has two offers, one for $10,000 paid now, one for $11,424 paid in one year. He is sure that both are honest and that he will receive the sum anyway. Which offer should he choose? If he chooses the first offer and puts the 10.000 in the bank at a 12% interest rate, he will have at the end of the year So he should take the second cause $11,424 > $11,200. This analysis uses the concept of future value or compound value , which is the value of a sum after investing over one or more periods. The compound value of $10,000 is $11,200. An alternative method is the present value. How much money must Don put in the bank today so that he will have $11, next year?
So in other words, the present value of $11,424 is $10,200, meaning that he should still take the second offer. Both future value and present value analysis MUST lead to the same decision. (LOUISA DICE PAG 3 UGUALE A QUESTO) Now both of the previous examples dealt with certainties, as both Louisa and Don were certain of their future returns. Unfortunately business people frequently do not know future cash flows. If the investment is risky, the expected revenue of it in the future should be discounted with a higher %. Unfortunately examples with risk poses problems not faced by diskless examples. With diskless cash flows, the approveriate interest rate can be determined by simply checking with a few banks, while with risky investments we do not know which is the correct discount rate to be applied. THE MULTIPERIOD CASE Suppose an individual loans out $1. At the end of the year she can either take the $1 + r (interest rate) out of the market, or she can leave the increased sum (1 + r) in the market to be loaned again. Supposing an interest rate of 9%
How much would an investor need to lend today so that she could receive $ two years from today? This process of calculating the present value of a future cash flow is called discounting and it is the opposite of compounding. So with a sure interest rate of 9% we are indifferent between having $0.84 today or $1 in two years. is called the present value factor and it is used to calculate the present value of a future cash flow.
(ESEMPI DA PAG 6 A PAG 8) NET PRESENT VALUE FORMULA PERPETUITY It is a constant stream of cash flows without end. You may think these are not applicable to reality but there is a British gov. bond called consols which entitles the investor to receive yearly interest from the British gov forever. How can the price of a consol be determined? Consider a console paying a coupon of C dollars each year and doing so forever. Applying the PV formula gives us Even though these geometric series have an infinite number of terms, the whole series has a finite sum because each term is only a fraction of the preceding term. So basically the Formula for Present Value of Perpetuity is:
Consol 2 is a consol with its first payment at date T+1. From the perpetuity formula, this consul will be worth C/r at date T. However we do not want the value at date T. we want the value now; in other words, the present value at date 0. We must discount C/r black by T periods. Therefore, the present value of consul 2 is (LEGGERE BENE ESEMPIO PAG 12 SU LOTTERIA)
The term we use to compute the value of the stream of level payments, C for T years is called annuity factor. In the above example it is 9.8181. For simplification we may refer to the annuity factor as That is the present value of $1 a year for T years at an interest rate of r. This kind of expression can be hard, we present four problems below. PROBLEM N 1: A DELAYED ANNUITY Danielle will receive a four year annuity of $500 per year, beginning at date 6. If the interest rate is 10%, what is the present value of her annuity? Students tend to think that $1,584.95 is the present value at date 6, because the annuity begins at date 6. However our formula values the annuity as one period prior to the first payment. This can be seen in the typical case where firs payment is at date 1 and the formula values annuity as of date 0 here.
PROBLEM N 3: INFREQUENT ANNUITY
Following problem treats with an annuity with payments occurring less frequently than once a year. Betty receives an annuity of $450, payable once every two years. It stretches out over 20 years. The first payment occurs at date 2, that is, two years from today. The annual rate of interest is 6%. The trick is to determine the interest rate over a two year period. The interest rate over two years is 1.06 x 1.06 - 1 = 12.36% That is, $100 invested over two years will yield $112. What we want is the present value of $450 annuity over 10 periods, with an interest rate of 12.36% per period. This is PROBLEM N 4: EQUATING PRESENT VALUE OF TWO ANNUITIES Harold and Helen are saving for college education of they daughter Susan. They estimate the cost of college will be $30,000 per year when their daughter reaches college in 18 years. Annual interest rate over the next few decades will be 14%. How much money must they deposit in the bank each year so that they daughter will be completely supported through four years of college? To simplify we assume Susan is born today. Her parents will make the first of her four annual tuition payments on her 18th birthday. They will make equal bank deposits on each of her first 17 birthdays, but no deposit at date 0.
We can be sure they will be able to withdraw fully $30,000 per year if the present value of the deposits is equal to the present value of the $30,000 withdrawals. This calc requires 3 steps. The first two determine the present value of the withdrawals. The final step determines yearly deposits that will have a present value equal to that of the withdrawals. Thus, deposits of $1,478.59 made at the end of each first 17 years and invested at 14% will provide enough money to make tuition payments of $30,000 over the following four years.
CHAPTER 2: ACCOUNTING STATEMENTS AND CASH FLOW
BALANCE SHEET
is an accountant’s snapshot of the firm’s accounting value on a particular date. It has two sides: on the left are the assets on the right the liabilities and stockholder’s equity. The balance sheet states what the firm owns and how it is financed. The accounting definition underlying the balance sheet describes it as: Assets = Liabilities + Stockholder’s equity This MUST always hold, as stockholder’s equity is the definition of what remains after assets and liabilities are taken into account. Here we find a fictitious Balance Statement. Assets are on the left, and are listed in order by the length of time it takes an ongoing firm to convert them into cash. Same goes for liabilities, which are listed on the order they need to be paid.
Liability and Equity reflect the types and proportions of financing, which depends on management’s choice of capital structure. Accounting Liquidity Refers to the ease and quickness with which assets can be converted into cash. Current Assets are the most liquid, including cash and those assets that will be turned into cash within a year from the date of the balance sheet Accounts Receivable is the amount not yet collected from customers for goods or services sold to them (after adjustments for potential bad debts) Inventory is composed of raw materials to be used in production, work in process and finished goods. Fixed Assets are the least liquid kind of asset. Tangible fixed assets include property, plant and equipment and they usually do not convert to cash from normal activity, and are thus not used to pay expenses. Some fixed assets are intangible , such as the value of a trademark, a patent, of customer recognition. The more liquid a firm’s assets, the less likely the firm is to experience problems meeting short-term obligations. Unfortunately liquid assets have lower rates of return than fixed ones. For example cash generates no investment income. Debt vs Equity Liabilities are obligations of the firm that require a payout of cash within a stipulated time period. Many liabilities involve a contractual obligation to repay a debt + interests. Frequently associated with nominally fixed cash burdens, called debt service , putting a firm in default of the contract if not paid. Stockholder’s Equity is a claim against the firm’s assets that is residual and not fixed. When the firm borrows, it gives the bondholders first claim on the firm’s cash flow.
A second section reports as a separate item the amount of taxes levied on income. Finally we find the bottom line / net income. It is often expressed per share of common stock, that is, earnings per share. Generally Accepted Accounting Principles Revenue is recognised on an income statement when the earnings process is virtually completed and an exchange of goods or services has occurred. Therefore the unrealised appreciation in owning property will not be recognised as income. This provides a device for smoothing income by selling appreciated property at convenient times (when earnings from other businesses are down). The matching principle of GAAP dictates that revenues be matched with expenses. Thus income is reported when earned or accrued, even though no cash flow has occurred (for example when goods are sold for credit, sales and profits are reported).
Non-cash Items Economic value of assets is intimately connected to their future incremental cash flows. However cash flow does not appear in the income statement. There are several non cash items that are expenses against revenues, but do not affect cash flow. The most important of these is depreciation. However, taxes not paid today will have to be paid in the future and still represent a liability for the firm. It shows on the balance sheet as deferred tax liability. From the cash flow perspective though, deferred tax is not a cash outflow. Time and Costs Short run is a period of time in which certain equipment, resources and commitments of the firm are fixed, but it is long enough for the firm to vary its output by using more labour and raw materials. It is not a precise period, it varies from industry to industry. Fixed costs are for example bond interests, overhead and property taxes.
FINANCIAL CASH FLOW
Perhaps the most important item of a financial statement. This statement helps to explain the change in accounting cash and equivalents, which for US composite is $33 million in 19X2. Refer to Table 2.1 that cash and equivalents increases from $107 million in 19X1 to $140 million in 19X2. However, we will look at cash flow from a different perspective, the perspective of finance. First cash flow is not the same as net working capital. For example, increasing inventory requires using cash. Because both inventories and cash are current assets, this does not affect net working capital. Cash flow instead would decrease when inventory increases. Cash flows from the firm’s assets (operating activities) CF(A); must be equal to the cash flows to the firm’s creditors CF(B) and equity investors CF(S) Another important component of cash flow involves changes in fixed assets. For example, when USX sold its coal mining operations to Exxon in 1981, it generated cash flow. The net change in fixed assets equals sales of fixed assets minus the acquisition of fixed assets. The result is the cash flow used for capital spending:
The total outgoing cash flow of the firm can be separated into cash flow paid to creditors and cash flow paid to stockholders. The cash flow paid to creditors represent a regrouping of the data in Table 2.3 and an explicit recording of interest expense. Creditors are
