Unformatted text preview: Review material for the Finance section of ETS exam Index Corporate Finance 0B Time Value of money 15B Capital Budgeting 16B Working capital management 17B Financial statement analysis 18B Cost of capital and capital structure 19B Investments 1B Risk and return 20B Valuation of securities 21B Financial markets and environments 2B International Finance 2B Finance review for ETS 11/10/08 1 Corporate Finance Time Value of Money 3B Future Value and Compounding Investing for a single period If you invest $X today at an interest rate of r, you will have $X + $X(r) = $X(1 + r) in one period. Example: $100 at 10% interest gives $100(1.1) = $110 Investing for more than one period Reinvesting the interest, we earn interest on interest, i.e., compounding FV = $X(1 + r)(1 + r) = $X(1 + r)2 Example: $100 at 10% for 2 periods gives $100(1.1)(1.1) = $100(1.1)2 = $121 In general, for t periods, FV = $X(1 + r)t where (1 + r)t is the future value interest factor, FVIF(r,t) Example: $100 at 10% for 10 periods gives $100(1.1)10 = $259.37 13B Present Value and Discounting The Single‐Period Case Given r, what amount today (Present Value or PV) will produce a given future amount? Remember that FV = $X(1 + r). Rearrange and solve for $X, which is the present value. Therefore, PV = FV / (1 + r). Example: $110 in 1 period with an interest rate of 10% has a PV = 110 / (1.1) = $100 Discounting – the process of finding the present value. Present Values for Multiple Periods PV of future amount in t periods at r is: PV = FV [1 / (1 + r)t] where [1 / (1 + r)t] is the discount factor or the present value interest factor, PVIF(r,t) Example: If you have $259.37 in 10 periods and the interest rate was 10%, how much did you deposit initially? PV = 259.37 [1/(1.1)10] = 259.37(.3855) = $100 Discounted Cash Flow (DCF) – the process of valuation by finding the present value More on Present and Future Values Present versus Future Value 14B Finance review for ETS 11/10/08 2 Present Value factors are reciprocals of Future Value factors: PVIF(r,t) = 1 / (1 + r)t and FVIF(r,t) = (1 + r)t Example: FVIF(10%,4) = 1.14 = 1.464 PVIF(10%,4) = 1 / 1.14 = .683 Basic present value equation: PV = FV [1 / (1 + r)t] Determining the Discount Rate Start with the basic time value of money equation and rearrange to solve for r: FV = PV(1 + r)t r = (FV / PV)1/t – 1 Or you can use a financial calculator to solve for r (I/Y on the calculator). It is important to remember the sign convention on most calculators and enter either the PV or the FV as negative. This is where most students run into difficulties when solving for r. One way to help them remember the sign convention is to have them enter all cash inflows as positive and cash outflows as negative, regardless of the type of problem being solved. Example: What interest rate makes a PV of $100 become a FV of $150 in 6 periods? r = (150 / 100)1/6 – 1 = 7% or PV = ‐100; FV = 150; N = 6; CPT I/Y = 7% Finding the Number of Periods FV = PV(1 + r)t – rearrange and solve for t. Remember your logs! t = ln(FV / PV) / ln(1 + r) Or use the financial calculator, just remember the sign convention. Example: How many periods before $100 today grows to $150 at 7%? t = ln(150 / 100) / ln(1.07) = 6 periods Rule of 72 – the time to double your money, (FV / PV) = 2.00 is approximately (72 / r%) periods. The rate needed to double your money is approximately (72/t)%. Example: To double your money at 10% takes approximately (72/10) = 7.2 periods. Example: To double your money in 6 years takes approximately (72/6) = 12%. Future and Present Values of Multiple Cash Flows Future Value with Multiple Cash Flows 23B Finance review for ETS 11/10/08 3 There are two ways to calculate the future value of multiple cash flows: compound the accumulated balance forward one period at a time, or calculate the future value of each cash flow and add them up. Present Value with Multiple Cash Flows There are two ways to calculate the present value of multiple cash flows: discount the last amount back one period and add them up as you go, or discount each amount to time zero and then add them up. A Note on Cash Flow Timing In general, we assume that cash flows occur at the end of each time period. This assumption is implicit in the ordinary annuity formulas presented. Valuing Level Cash Flows: Annuities and Perpetuities Present Value for Annuity Cash Flows Ordinary Annuity – multiple, identical cash flows occurring at the end of each period for a fixed number of periods. The present value of an annuity of $C per period for t periods at r percent interest: PV = C[1 – 1/(1 + r)t] / r Example: If you are willing to make 36 monthly payments of $100 at 1.5% per month, what size loan can you obtain? PV = 100[1 – 1/(1.015)36] / .015 = 100(27.6607) = 2,766.07 or use the calculator: PMT = ‐100; N = 36; I/Y = 1.5; CPT PV = 2,766.07 (Remember that P/Y = 1 when using period rates.) 24B Finding the payment, C, given PV, r and t PV = C[1 – 1/(1 + r)t] / r C = PV {r / [1 – 1/(1 + r)t]} Example: If you borrow $400, promising to repay in 4 monthly installments at 1% per month, how much are your payments? C = 400 {.01 / [1 – 1/(1.01)4]} = 400(.2563) = 102.51 or use the calculator: PV = 400; N = 4; I/Y = 1; CPT PMT = ‐102.51 Finance review for ETS 11/10/08 4 Finding the number of payments given PV, C, and r PV = C [1 – 1/(1 + r)t] / r t = ln[1 / (1 – rPV/C)] / ln(1 + r) Example: How many $100 payments will pay off a $5,000 loan at 1% per period? t = ln[(1 / 1 ‐ .01(5000)/100)] / ln(1.01) = 69.66 periods or use the calculator: PV = 5000; PMT = ‐100; I/Y = 1; CPT N = 69.66 periods (remember the sign convention; you will receive an error if you don’t enter either the PMT or the PV as negative) Finding the rate given PV, C, and t There is no analytical solution. Trial and error requires you to choose a discount rate, find the PV and compare to the actual PV. If the computed PV is too high, then choose a higher discount rate and repeat the process. If the computed PV is too low, then choose a lower discount rate and repeat the process. Or you can use a financial calculator. Example: A finance company offers to loan you $1,000 today if you will make 48 monthly payments of $32.60. What rate is implicit in the loan? N = 48; PV = 1000; PMT = ‐32.60; CPT I/Y = 2% (Remember the sign convention.) This is a monthly rate, consistent with N as number of months, and PMT as payment per month. Future Value for Annuities FV = C[(1 + r)t – 1] / r Example: If you make 20 payments of $1,000 at the end of each period at 10% per period, how much will you have in your account after the last payment? FV = 1,000[(1.1)20 – 1] / .1 = 1,000(57.275) = $57,275 or use the calculator: PMT = ‐1,000; N = 20; I/Y = 10; CPT FV = 57,275 (Remember to clear the registers before working each problem.) A Note on Annuities Due Annuity due – the first payment occurs at the beginning of the period instead of the end. Perpetuities Perpetuity – series of level cash flows forever PV = C / r Finance review for ETS 11/10/08 5 Preferred stock is a good example of a perpetuity. Comparing Rates: The Effect of Compounding Periods Effective Annual Rates and Compounding Stated or quoted interest rate – rate before considering any compounding effects, such as 10% compounded quarterly Effective annual interest rate – rate on an annual basis, that reflects compounding effects, e.g., 10% compounded quarterly has an effective rate of 10.38% Calculating and Comparing Effective Annual Rates (EAR) EAR = [1 + (quoted rate)/m]m – 1 where m is the number of periods per year Example: 18% compounded monthly is [1 + (.18/12)]12 – 1 = 19.56% EARs and APRs Annual percentage rate (APR) = period rate times the number of compounding periods per year The quoted rate is the same as an APR. 25B Loan Types and Loan Amortization Pure Discount Loans Borrower pays a single lump sum (principal and interest) at maturity. Treasury bills are a common example of pure discount loans. 26B Interest‐Only Loans Borrower pays only the interest each period and then pays the entire principal at maturity. Corporate bonds are a common example of interest‐only loans. Amortized Loans Borrower repays part or all of principal over the life of the loan. Two methods are (1) fixed amount of principal to be repaid each period, which results in uneven payments, and (2) fixed payments, which results in uneven principal reduction. Traditional auto and mortgage loans are examples of the second type of amortized loans. Finance review for ETS 11/10/08 6 Capital Budgeting 4B Net Present Value The Basic Idea Net present value – the difference between the market value of an investment and its cost. While estimating cost is usually straightforward, finding the market value of assets can be tricky. The principle is to find the market price of comparables or substitutes. Estimating Net Present Value Discounted cash flow (DCF) valuation – finding the market value of assets or their benefits by taking the present value of future cash flows by estimating what the future cash flows would trade for in today’s dollars. 27B The Payback Rule Defining the Rule Payback period – length of time until the accumulated cash flows equal or exceed the original investment. Payback period rule – investment is acceptable if its calculated payback is less than some prespecified number of years. Analyzing the Rule ‐No discounting involved ‐Doesn’t consider risk differences ‐How do we determine the cutoff point ‐Bias for short‐term investments Redeeming Qualities of the Rule ‐Simple to use ‐Bias for short‐term promotes liquidity Summary of the Rule Advantages: Easy to understand Adjusts for uncertainty of later cash flows Biased towards liquidity Disadvantages: Ignores the time value of money 28B Finance review for ETS 11/10/08 7 Requires an arbitrary cutoff point Ignores cash flows beyond the cutoff date Biased against long‐term projects The Internal Rate of Return Internal rate of return (IRR) – the rate that makes the present value of the future cash flows equal to the initial cost or investment. In other words, the discount rate that gives a project a $0 NPV. 29B IRR decision rule – the investment is acceptable if its IRR exceeds the required return. NPV and IRR comparison: If a project’s cash flows are conventional (costs are paid early and benefits are received over the life), and if the project is independent, then NPV and IRR will give the same accept or reject signal. Problems with the IRR Non‐conventional cash flows – the sign of the cash flows changes more than once or the cash inflow comes first and outflows come later. If the cash flows are of loan type, meaning money is received at the beginning and paid out over the life of the project, then the IRR is really a borrowing rate and lower is better. If cash flows change sign more than once, then you will have multiple internal rates of return. This is problematic for the IRR rule, however, the NPV rule still works fine. Mutually exclusive investment decisions – taking one project means another cannot be taken Redeeming Qualities of the IRR ‐People seem to prefer talking about rates of return to dollars of value ‐NPV requires a market discount rate, IRR relies only on the project cash flows The Profitability Index Profitability index – present value of the future cash flows divided by the initial investment (both numerator and denominator are positive). This definition assumes no negative cash flows after year zero. Technically, PI = PV of inflows / PV of outflows, thus a nonconventional project’s PI will have a PV in both the numerator and the denominator. If a project has a positive NPV, then the PI will be greater than 1. 30B Finance review for ETS 11/10/08 8 The Practice of Capital Budgeting It is common among large firms to employ a discounted cash flow technique such as IRR or NPV along with payback period or average accounting return. It is suggested that this is one way to resolve the considerable uncertainty over future events that surrounds the estimation of NPV. 31B Finance review for ETS 11/10/08 9 Working Capital Management 5B Float and Cash Management Reasons for Holding Cash Speculative motive – take advantage of unexpected opportunities Precautionary motive – cash for emergencies Transaction motive – day‐to‐day cash requirements to meet expenses Costs of Holding Cash – The opportunity cost of holding cash is the return that could be earned by investing the cash in other assets. However, there is also a cost to convert between cash and other assets. The optimal cash balance will balance these costs to minimize the overall cost of holding cash. Understanding Float Book balance – the amount of cash recorded in the accounting records of the firm Available balance – the amount of cash the bank says is available to be withdrawn from the account (may not be the same as the amount of checks deposited minus amount of checks paid, because deposits are not normally available immediately) Float = Available balance – book balance Negative float implies that checkshave been deposited that are not yet available. The firm needs to be careful that it does not write checks over the available balance, or the checks may bounce. Positive float implies that checks have been written that have not yet cleared. The company needs to make be sure to adjust the available balance so it does not think that there is more money to spend than there actually is. Disbursement float – generated by checks the firm has written that have not yet cleared the bank; arrangements can be made so that this money is invested in marketable securities until needed to cover the checks. Collection float – generated by checks that have been received by the firm but are not yet included in the available balance at the bank Managers need to be more concerned with net float and available balances than with the book balance. 32B The three components of float are: ‐Mail float – the time the check is in the mail ‐Processing float – handling time between receipt and deposit Finance review for ETS 11/10/08 10 ‐Availability float – time to clear the banking system Float management – speeding up collections (reducing collection float) and slowing down disbursements (increasing disbursement float) Cash Management: Collection, Disbursement, and Investment Cash Collection and Concentration Collection Time = mailing time + processing delay + availability delay Cash collection policies depend on the nature of the business. Firms can choose to have checks mailed to one location, or many locations (reduces mailing time), or allow preauthorized payments. Many firms also accept online payments either with a credit card or with authorization to request the funds directly from your bank. 3B Lockboxes – special post office boxes that allow banks to process the incoming checks and then send the information on account payment to the firm; that reduces processing time and often reduces mail time because several regional lockboxes can be used. Cash concentration is the practice of moving cash from multiple banks into the firm’s main accounts. This is a common practice that is used in conjunction with lockboxes. Managing Cash Disbursements Increasing disbursement float – slowing payments by increasing mail delay, processing time, or collection time. May not want to do this from both an ethical standpoint and a valuation standpoint. Slowing payment could cause a company to forgo discounts on its accounts payable. As we will see later in the chapter, the cost of forgoing discounts can be extremely high. Controlling disbursements – minimize liquidity needs by keeping a tight rein on disbursements through any ethical means possible. Zero‐balance accounts – maintain several sub‐accounts at regional banks and one master account. Funds are transferred from the master account when checks are presented for payment at one of the regional accounts. This reduces the firm’s liquidity needs. Controlled disbursement accounts – the firm is notified on a daily basis how much cash is required to meet that day’s disbursements and the firm wires the necessary funds. Investing Idle Cash Temporary cash surpluses: ‐seasonal or cyclical activities Finance review for ETS 11/10/08 11 ‐planned or possible expenditures The goal is to invest temporary cash surpluses in liquid assets with short maturities, low default risk, and high marketability Credit and Receivables Components of Credit Policy ‐Terms of sale – defines credit period and any available discounts ‐Credit analysis – estimating probability of default for individual customers to determine who receives credit and at what terms ‐Collection policy – what steps will be taken to collect on receivables, particularly when customers are late with their payment Terms of the Sale ‐Credit period – amount of time allowed for payment ‐Cash discount and discount period – percent of discount allowed if payment is made during the discount period ‐Type of credit instrument Basic form: 2/10 net 60 means 2% discount if paid in 10 days; total amount is due in 60 days if the discount is not taken. In this example, the 60 days is the net credit period, the 10 days is the discount period and the 2% is the cash discount amount. The invoice date is the date for which the credit period starts. This is normally the shipping date, but some companies may post‐date the invoice to encourage customers to order early. 34B Length of the credit period depends on: ‐Buyer’s inventory and credit cycle ‐Perishability and collateral value ‐Consumer demand ‐Cost, profitability, and standardization ‐Credit risk ‐Size of the account ‐Competition ‐Customer type Cash discounts – offered by sellers to induce early payment. Not taking the discount involves a cost of credit for the purchaser. Finance review for ETS 11/10/08 12 Cost of credit – the cost of not taking discounts offered (this is a benefit to the company granting credit) Periodic rate = (discount %) / (100% – discount %) Number of periods per year = m = 365 / (net credit period – discount period) APR = m(periodic rate) EAR = (1 + periodic rate)m – 1 Example: Consider terms of 1/15 net 45 (assume payment is made on time in 45 days when the discount is forgone) Periodic rate = 1/99 = .0101 Number of periods per year = m = 365 / (45 – 15) = 12.166667 APR = 12.166667(.0101) = 12.288% EAR = (1.0101)12.166667 – 1 = 13.01% Offering discounts generally reduces the average collection period and thus the cash cycle. This reduces the amount of financing required, but the company loses sales in the amount of the discount taken. Consequently, the firm needs to look at the size and timing of the expected cash flows to determine what, if any, discount should be offered. Credit instruments – evidence of indebtedness ‐Open account – invoice only ‐Promissory note – basic IOU, may be used when the order is large or the purchasing firm has a history of late payments ‐Commercial draft – request for funds sent directly to the purchaser’s bank ‐Sight draft – payable immediately ‐Time draft – payment required by some future date ‐Trade acceptance – buyer accepts draft with agreement to pay in the future ‐Bankers’ acceptance – bank accepts draft and guarantees payment Optimal Credit Policy An optimal credit policy is one in which the incremental cash flows from sales are equal to the incremental costs of carrying the increased investment in accounts receivable. The cost of granting credit is described by the total credit cost curve, which depicts the trade‐off between two kinds of costs: Carrying costs – required return on receivables, losses from bad debts, costs of managing credit and collections Opportunity costs – potential profit from credit sales that is lost Credit Analysis Finance review for ETS 11/10/08 13 Credit information: ‐Financial statements ‐Credit reports (i.e., Dun and Bradstreet) ‐Banks ‐Customer’s payment history Credit evaluation – trying to estimate probability of default Five...
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