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COMM 121 Finance Midterm Exam Review

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Queen's University
COMM 121
Kory Salli

Finance Midterm Exam Review Shannon Bailey Oct 2013 Chapter 1 / Lecture 1 & 2 Finance – the study of how and under what terms savings (money) is allocated between lenders and borrower Capital budgeting (capital expenditure) – the process of making and managing expenditures on long lived assets Capital structure – represents the proportions of the firm’s financing from current and long term debt and equity (think of the firm like a pie, composed of debt and equity) Creditors – the persons or institutions that buy debt from the firm Shareholders – the holders of equity shares Value of the firm = debt + equity -the shareholders’ claim on firm value at the end of the period is the amount that remains after the debtholders are paid – they get nothing if the firm’s value is equal to or less than the amount promised to debtholders, or they get the residual of the firm’s value over the amount promised to debtholders if the firm’s value is greater than the amount promised to debtholders -debt and equity are contingent claims on the total firm value Arbitrage – exploiting price differences to earn riskless profit. There must be an absence of arbitrage – as soon as different interest rates are offered for essentially the same risk free loans, arbitrageurs will take advantage of the situation by borrowing at the low rate and lending at the high rate. The gap between both rates will be closed quickly. i.e. Seinfeld video in class – travelling across state border to get more money for beer cans Sole proprietorship – a business owned by one person -cheapest to own, no corporate income taxes, unlimited liability, the life extends over the length of the sole proprietor, equity money limited to proprietor’s personal wealth Partnerships: General partnership – business in which any two or more partners agree to provide some fraction of the work and cash to share the profits and losses. Each partner liable for debts Limited partnership – permit the liability of some of the partners to be limited to the amount of cash each has contributed to the partnership. -partnerships are inexpensive & easy to form, have life the length of any general partner, taxed as personal income, difficult to raise large amounts of cash Corporation – a business that is a distinct legal entity that can issue stocks, does not hold any shareholder personally liable, has a perpetual life, and has corporately taxed income Agency costs – the costs of resolving the conflicts of interest between managers and shareholders Direct agency costs – costs of things like job perks (corporate jet), monitoring – you are spending $$ Indirect agency costs – costs of a missed opportunity i.e. management buys the CEO an expensive painting, missing the opportunity of a profitable investment -managerial goals are different from those as shareholders – the principal hires the agent (management) to represent his interest, but agents have a tendency to be motivated by their expenses (like company cars, company dinners etc) which definitely don’t maximize shareholder wealth -shareholder wealth maximization is considered the most appropriate goal to guide agents (NOT accounting profit maximization, since it changes with depreciation and ignores timing) -shareholders (owners) don’t necessarily control managers; depends on the costs of monitoring management, the costs of implementing control devices, and the benefits of control How can you address the conflict of interest? a) Compensation plans – i.e. stock options b) Have a board of directors – chosen by shareholders, choose the management team c) Market discipline – i.e. lay-off, hostile takeover Financial Institutions – facilitate flows of funds from savers to borrowers i.e. banks, insurance companies, etc. Financial Markets – markets where you can trade financial instruments (or claims/securities) - short-term debt securities are bought and sold in money markets - long-term debt and shares of stock are sold in capital markets Primary markets – refer to the original sale of securities by governments and corporations (i.e. an IPO) Secondary markets – markets where these securities are bought and sold after the original sale, either in an exchange or over the counter in a dealer market Foreign exchange market – the market where one country’s currency is traded for another Direct financing involves financial intermediaries, whereas indirect financing does not 2 Major Categories of Financial Securities Debt Instruments Equity Instruments Commerical Paper Common stock T-bills and notes Preferred stock Mortgage loans Bonds Chapter 4/Lecture 2 Financial intermediaries – institutions that match borrowers and lenders (traders) Market clearing – the total amount of people who wish to lend to the market must equal the total amount of people that wish to borrow from the market. If lenders wish to lend more than the borrowers wish to borrow, the interest rate is too high, and vice versa. The interest rate that clears the market is the equilibrium rate of interest. Investment Rule – Basic Principle – an investment must be at least as desirable as the opportunities available in the financial markets (i.e. you won’t take on an investment whose return is 5% if the interest rate in the markets is 7%) A Competitive market has three qualities: 1) trading is costless 2) information about borrowing and lending opportunities is readily available to all market participants 3) there are many traders, and no individual can move market prices (price takers) Example 1. A person has an income of $50 000 this year and $60 000 next year. The interest rate r = 10%. The figure shows all possible consumption opportunities open to the person through borrowing and lending Point A represents consuming nothing this year (lending $50,000), and everything (second year income & proceeds from the loan) next year: A = 60,000 + 50,000 (1 + .10) Point B represents spending everything this year, including taking out a loan to spend next year’s income: B = 50,000 + 60,000/1.10 Point C represents spending $40,000 of this year’s income this year and saving $10,000 -next year you would be able to spend $60,000 + 10,000(1.10) The line has a slope of –(1+r), so that for each additional dollar spent today, (1+r) less dollars can be spent next year Example 2. A person has income of 50k this year and 60k next year when the interest rate r = 10%. The person has the chance to undertake an investment that will require a 30k outlay of cash and will return 40k to the investor next year At point B, the person has decided to undertake the investment decision, where the person can consume 20k (50,000-30,000) this year and 100k (60,000+40,000) next year. B is on the new line because there are new possibilities available with the investment. The lines are parallel since the interest rate is constant The total amount available to consume today without the investment is: =$50,000 + $60,000/1.1 = $104,545 The total amount available to consume today with the investment is: =$50,000 - $30,000 + ($60,000+$40,000)/(1+.01) =$20,000 + $100,000/1.10 = $110,909 The difference between these amounts, $110,909-$104,545 = $6364 = the Net Present Value (NPV) It can also be calculated by converting all consumption values to the present, on a standalone basis from the investment itself: -$30,000 + $40,000/1.1 = $6364 -if the NPV is positive, the investment is worth taking on Fisher Separation theorem – all investors will want to accept or reject the same investment projects by using the NPV rule, regardless of their personal preferences, -same for shareholder’s and the firm’s NPV decisions -so investment decision making is separated from the owners and handled by the managers -an individual’s preference for consumption will not impact an NPV decision Chapter 5 / Lectures 3 & 4 Present Value of Investment = PV = C1 1 + r where C 1s the cash flow at date 1 and r is the interest rate Net present value (NPV) – the value of the investment after stating all the benefits and all the costs as of date 0 Compounding – the process of leaving money in the capital market and lending it for another year -compounding may not make a big difference in the short run, but can make a huge difference over a long period of time -involves interest on interest (i.e. r , exponential growth) [versus simple interest over two years, 2 x r] Future value of an investment = FV = C x (0 + r) T Where C i0 the cash to be invested at date 0, r is the interest rate, and T is the number of periods over which the cash is invested Discounting – the process of calculating the present value of a future cash flow – is the opposite of compounding Present value factor – the factor used to calculate the present value of a future cash T flow (the 1/(1+r) part) Compounding an investment m times over one year provides end of year wealth of: m C o1 + r/m) -where r is the stated annual interest rate (or annual percentage rate) Annual percentage rate (APR) – the stated or quoted annual rate that gnored the effects of compounding. It is computed by simply multiplying the periodic rate by the number of periods in a year i.e. an investment pay 3% per quarter with quarterly compounding. The APR will be 3 x 4 = 12% whereas the EAR will be 12.5509% Effective annual interest rate (EAR) – the annual rate of return. Due to compounding, the EAR will be greater than the stated rate EAR = (1 + r/m) – 1 i.e. if the stated annual rate of interest, 8%, is compounded quarterly, what is the EAR? EAR = (1 + .08/4) – 1 = 0.0824 = 8.24% Future Value with Compounding = FV = C (1 + r/m) mT 0 -where m is the number of times per year the investment is compounded, and T is the number of years r T Continuous Compounding Present Value = C x e 0 -remember than e ln(= x -if looking to solve for T, you made need to take the ln of both sides of an equation Perpetuity – a constant stream of cash flows without end i.e. consols PV perpetuityC r i.e. consider a perpetuity paying $100 a year. If the interest rate = 0.08, what is the value of the consol? PV = 100/0.08 = $1250 Growing perpetuity – a constant, growing stream of cash flows that will grow indefinitely PV growing perpetuityC , r – g -note that the numerator is the cash flow one period hence, not at date zero -the interest rate must be greater than the growth rate, otherwise the denominator gets infinitesimally small and the PV grows infinitely large; the PV will be undefined when r is less than g -assumes a regular and discrete pattern of cash flow Annuity – a level stream of regular payments that lasts for a fixed number of periods i.e. leases, mortgages, pension plans Present Value of an annuity = PV = C [ 1 – 1 ] r (1 + r) -where C is the payment at date 1 T (the FV would be the PV of an annuity times (1 + r) i.e. a lady wins the lottery that pays $50k a year from now each year for 20 years. If the interest rate is 8%, what is the true value of the lottery? PV = 50000/0.08 (1 – (1/(1.08) ))20 PV = $490 905 Annuity factor – the term we used to compute the value of the stream of level payments, denoted as A Tr A = [ 1 – 1 ] r T r r(1 + r) Mortgages – a common example of an annuity with monthly payments. Keep in mind that although payments are monthly, mortgage rates are typically quotes with semiannual compounding. You must convert the stated semi-annual rate to the EAR, and then to the effective monthly rate. i.e. a bank is offering a $100 000 25 year mortgage at a stated rate of 6%. What is the monthly mortgage payment? 2 EAR = (1 + 0.06/2) - 1 EAR = 6.09% Effective monthly rate = EMR = (EAR + 1) 1/m – 1 1/12 = (1.0609) – 1 = 0.49% PV = $100,000 = C [ 1 – 1 ] = C [1 - 1 ] r (1 + r) .0049 (1.0049) 300 = $636.99 *note that T = 300 payments come from 25 years x 12 payments per year Delayed annuities – if an annuity begins on a date many periods into the future (say, date n), you must calculate the annuity at date n – 1 and then discount the present value at date n – 1 to date 0 using the simple present value formula Annuity due – if the annuity begins at date zero, you can calculate the present value by either using the same formula and then compounding it for one year, or by calculating the value of the annuity for T – 1 years, and adding today’s payment to that value without any discounting whatsoever i.e. using the same example as before, the lady receives the lottery of $50 000 a year for 20 years, but is given the first payment immediately. The present value is: 19 $50 000 + $50 000 x A 0.08 payment at date 0 19 – year annuity (not 20!) it could also be calculated as follows: 20 $50 000 x A 0.08= $490 905  as a 20 year annuity beginning at date 1 $490 905(1.08) = $530 177  compounded forward by one year Infrequent annuities – determine the interest rate over the period the annuity is payable i.e. An annuity is $450 payable once every two years, over the next 20 years. The first payment occurs at date 2, two years from today. The annual interest rate is 6%. Determine the interest rate over a two year period: = (1.06 x 1.06) – 1 = 12.36% Now we want the value of an annuity over 10 periods, with an r = .1236 = $450/.1236 [1 - 1 ] = $2,505.57 (1.1236) 10 Equating the present values of two annuities i.e. Two parents are saving for the university education of their baby. They estimate school will cost $30k per year when she enters uni in 18 years. The annual return on their investment account will be 14%. How much money should they deposit in their bank each year so that they can withdraw tuition money each year beginning on her 18 birthday. They will make equal deposits on each of her first 17 birthdays, but no deposit at date 0. 1. Calculate the present value of the four years at university at date 17. PV 17= $30000/.14 [1 - 1 ] = $87,411 (1.14) 4 2. Calculate the present value of the four years at university as of date 0 PV 0 87,411 = $9,422.91 (1.14) 17 3. Calculate an annual deposit that will yield a present value of all the the deposits of $9,422.91 9,422.91 = C /.14 [1 - 1 ] (1.14)17 C = $1478.59 Growing Annuity – a finite number of growing cash flows PV growing annuity ( ) Chapter 6 145-151 / Lecture 5 Bond – a certificate showing that a borrower owes a specified sum. In order to repay the money, the borrower makes interest and principal payments on designated dates - less than one year – Bills or papers i.e. treasury bills, commercial papers - 1 year < maturity < 10 years – Notes - Maturity > 10 years – Bonds Treasury Bills – short term government debt obligations which mature within a year. They are ALWAYS issued at a discount and mature at face value. They are generally regarded as risk free Price of a T-bill = Where BEY = bond equivalent yield = x Where P = market price of the t-bill, F = face value of the T-bill, and n = number of days until maturity i.e. What is the price of a $1 000 000 Canadian T-bill with 80 days to maturity and a BEY of 4.5%? Price = 1000000/(1.045(80/365)) = $990 233.33 Pure discount bonds/zero-coupon bonds – a bond that promises to make a single payment at a fixed future date. The holder receives no cash payments until maturity. Issued at a discount and matures at par/face value. Has no reinvestment rate risk (since no coupons to be reinvested) Maturity date – the date when the issuer of the bond makes the last payment Face value – the payment at maturity Value/Price of a zero-coupon bond = P = F , (1 + r)T where F is the face value that is paid in T years i.e. What is the market price of a $50000 zero coupon bond with 25 years to maturity that is currently yielding 6%? PZCB = = $11 650 Coupons – cash payments offered by bonds at regular times before maturity Level coupon bond – a bond that pays a coupon annually (or semi-annually) until maturity when the face value is paid Value of a level-coupon bond = PV = + -in the above equation, the first term is the PV of the annuity of all the coupon payments, and the second term is the PV of the lump sum face value payment i.e. What is the market price of a 10 year, $1000 bond with a 5% annual coupon if the bond’s YTM is 6%? Coupon = .05 x 1000 = $50 Price = + = $926.39 For semi-annual coupons: - Size of the coupon payment – divide by 2 - Number of periods – multiply by 2 - YTM – divide by 2 i.e. Suppose you want to value a five-year, $1000 bond with a 4% coupon in semi- annual payments with a YTM of 6%? Coupon = .04/2 = .02 x 1000 = $20 YTM = .06 / 2 = .03 Five years  10 years Price = +
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