Finance Notes Dr. Andrew Spieler
1
FIN 101, 110, 160 COURSE PACKET
Hofstra University
Frank G. Zarb School of Business
Dr. Andrew C. Spieler, CFA, FRM, CAIA
Andrew.C.Spieler@hofstra.edu
Updated: 03/26/2015
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FIN 101, 110, 160 COURSE PACKET
Hofstra University
Frank G. Zarb School of Business
Dr. Andrew C. Spieler, CFA, FRM, CAIA
Andrew.C.Spieler@hofstra.edu
Updated: 03/26/
Table of Contents
1. INTRODUCTORY NOTES
Most important Ideas Time Value of Money Risk and Return Recognizing/understanding options and game theory (economics of information)
3 Branches of Finance
1. Corporate
Capital budgeting Project selection NPV, IRR, PI, etc.
Raising capital Debt Public debt: bonds
Private debt: bank loan (origination or renewal) Convertibles & warrants
Callable Puttable Equity
IPO SEO Stock split / stock dividend
Preferred stock Capital structure Investment banking
Dividend policy / share repurchase Mergers & Acquisitions
LBOs and MBOs Conglomerates Cash vs. stock exchange
Corporate governance
2. Investments
Traditional Investments
Asset pricing i.e. valuation Bonds Preferred stock
Stock Derivatives Options
Puts Calls Real options??
Futures Forwards Swaps
Swaptions Credit default swap (CDS) Securitization
MBS CMBS CDOs, CLOs
PO vs. IO (which is more expensive security?) Sequential pay tranches
Indices and benchmarking DJIA S&P 500
Case-Shiller Factor models
CAPM, Fama-French, multi-factor models, APT
Structure Products PPN, CLN
Commodity-linked notes Step-up, step-down Alternative Investments
Hedge funds Real estate Private equity
Venture capital Angel financing Commodities
Infrastructure Life settlements
3. Financial Markets and Institutions
What do banks do? Institutional investors Mutual funds
Pension funds Life insurance companies Non-life insurance companies
Endowments / foundations / not-for-profits Market structure
Auction markets Broker-dealer markets Market design
International markets / regional exchanges
Yield curves / term structure of interest rates
Behavioral Finance
Investor rationality? Is this a good assumption?
Risk aversion Risk neutral Risk taker
Loss aversion / prospect theory See article Psychology and Behavioral Finance
**** Game theory and information economics ****
Pervades all of finance and many other situations
Moral hazard vs. adverse selection
Classic examples o SH-Manager conflict o SH-BH conflict o Bankers as directors
Prisoner’s dilemma example
Solution concepts Method of elimination of Dominated Strategies o Nash Equilibrium o Separating vs. Pooling equilibrium
Applications to finance:
Stock vs. cash offer Incentive compensation Insurance and risk sharing
Dividend policy / share repurchases o Issuing and rationing of IPO o Collusion on NASDAQ
6. EAR vs. APR o APR = nominal (“quoted”) interest rate on ANNUAL basis o 𝐴𝑃𝑅 = 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒𝑝𝑒𝑟𝑖𝑜𝑑 ∗ # 𝑝𝑒𝑟𝑖𝑜𝑑𝑠𝑦𝑒𝑎𝑟
o EAR = effective annual rate o 𝐸𝐴𝑅 = (1 + 𝐴𝑃𝑅𝑚 )𝑚^ − 1
7. Continuous compounding o EAR with ∞ periods (m is infinite) (1 + 𝐴𝑃𝑅𝑚 )𝑚^ = 𝑒𝐴𝑃𝑅 o Compounding every instant in time, i.e. dt from stochastic calculus o PV: (Lump sum)×e-rt o FV: (Lump sum)×ert Excel Calculations of APR and EAR i = (%) m i/period APR EAR 2% (^1) 2.0000000% 2% 2.00000% 2% (^2) 1.0000000% 2% 2.01000% 2% (^4) 0.5000000% 2% 2.01505% 2% (^12) 0.1666667% 2% 2.01844% 2% (^24) 0.0833333% 2% 2.01928% 2% (^100) 0.0200000% 2% 2.01993% 2% (^365) 0.0054795% 2% 2.02008% 2% (^1000) 0.0020000% 2% 2.02011% 2% (^100000) 0.0000200% 2% 2.02013%
6% (^1) 6.0000000% 6% 6.00000% 6% (^2) 3.0000000% 6% 6.09000% 6% (^4) 1.5000000% 6% 6.13636% 6% (^12) 0.5000000% 6% 6.16778% 6% (^24) 0.2500000% 6% 6.17570% 6% (^100) 0.0600000% 6% 6.18174% 6% (^365) 0.0164384% 6% 6.18313% 6% (^1000) 0.0060000% 6% 6.18346% 6% (^100000) 0.0000600% 6% 6.18365%
12% (^1) 12.0000000% 12% 12.00000% 12% (^2) 6.0000000% 12% 12.36000% 12% (^4) 3.0000000% 12% 12.55088% 12% (^12) 1.0000000% 12% 12.68250% 12% (^24) 0.5000000% 12% 12.71598% 12% (^100) 0.1200000% 12% 12.74157% 12% (^365) 0.0328767% 12% 12.74746% 12% (^1000) 0.0120000% 12% 12.74887% 12% (^100000) 0.0001200% 12% 12.74968%
8. Example Handouts: mortgages, college funding, retirement
3. CALCULATOR NOTES (For TI – BAII / BAII Plus / Professional)
First, you must realize the calculator is stupid – it doesn’t know what you want to do – you must tell it EXACTLY what to do.
For simplicity, let us examine the CFs associated with an ordinary annuity. Using uneven CFs follows the same principle.
One source of confusion involves the interpretation and entering positive and negative CFs. So, let’s start with a simple example, one that is in the slide workbook.
QUESTION #1:
Calculate the PV of a 3-period ordinary annuity with 10% discount rate.
PMT = 200 N = 3 I/Y = 10 (remember calculator reads this as % so do NOT enter .10 – that would be 0.1%) FV = 0 (no terminal CF) PV = ?? = -
Notice the final answer is -497. The economic interpretation is clear $497 is equivalent to the present value of a 3 period stream of $200. So, why is the answer negative? The calculator has an internal algorithm that “balances” the inflows and outflows so the sum = 0.
Let’s calculate the same PV entering -200 for PMT
PMT = - N = 3 I/Y = 10 FV = 0 (no terminal CF) PV = ?? = 497
4. TIME VALUE OF MONEY PRACTICE PROBLEMS
Question 1 Suppose the Hempstead Savings Bank is offering 6% on all deposits and your initial deposit is $10,000.
(i) What is the balance in your savings account after 1 year? (ii) What is the balance in your savings account after 5 years? (iii) How much interest has accumulated after 10 years? (iv) How much do you have in your savings account after 6 months?
Question 2 Suppose the Uniondale Savings Bank is offering 5% on all deposits and your initial deposit is $10,000.
(i) What is your balance after 5 years? (ii) What is your balance after 8 years? (iii) What is your balance after 5 years if the bank only offers simple interest?
Question 3 Suppose you are expected to receive $10,000 in exactly 10 years. Find the present value under the following conditions. Assume the APR = 12%
(i) Annual compounding (ii) Semi-annual compounding (iii) Monthly compounding
Question 4 You just graduated Hofstra University. Instead of saving for your retirement, you decide to purchase a new sports car for $40,000. Assume your first payment is one month from now and the loan is for 5 years.
(i) If the APR is 2.9%, what are your monthly payments? What is the EAR? (ii) If the APR is 9.9%, what are your monthly payments? What is the EAR?
Question 5 Suppose the Bloomington Savings Bank is offering 6% on all savings deposits. Your initial deposit is $10,000.
(i) What is your balance after one year assuming annual compounding? (ii) What is your balance after one year assuming semi-annual compounding? (iii) What is your balance after one year assuming monthly compounding? (iv) What is your balance after one year assuming daily compounding?
5. TIME VALUE OF MONEY ADVANCED PROBLEMS
Question 1 (mortgage problem) (Try to work this question WITHOUT using Excel) You purchase a house that costs $625,000 with a 8%, 30-year mortgage. In order to avoid PMI insurance, you decide to follow a conforming mortgage by making a down payment of 20%.
- What is your monthly payment?
- Amortize the first and second payments.
- What is the mortgage balance after 5 years?
- What percentage of the principal is paid off after 5 years?
- Suppose after 5 years you refinance at 6% the remaining balance at a cost of $10,000, for 30 years. What is your new monthly payment?
- Further, suppose you maintain the same payments as in (1), i.e. pre-pay on the principal, how many YEARS until you pay off the mortgage?
Question 2 (2nd mortgage problem) You are considering the purchase of a $500,000 home. You plan to take a 30-year fixed mortgage after making a 20% downpayment to avoid PMI. Payments are to be made monthly (at the end of the month) and the APR is 8%.
- What is the monthly payment?
- During what month does the principal portion first exceed the interest portion? Are you surprised by your answer?
- How long does it take to pay off your mortgage if you pay an additional $300 towards principal each payment?
- How long does it take to pay off your mortgage if you pay an additional amount each month equal to the current month’s principal?
Question 3 (College planning) Your child was just born and you are planning for his/her college education. Based on your wonderful experience in Financial Economics you decide to send your child to Hofstra University as well. You anticipate the annual tuition to be $60,000 per year for the four years of college. You plan on making equal deposits on your child’s birthday every year starting today, the day of your child’s birth. No deposits will be made after starting college. The first tuition payment is due in exactly 18 years from today (the day your child turns 18 – no deposit required, i.e. last deposit is on 17th birthday). Assume the annual expected return on your investments is 10% over this period.
- Calculate the annual deposit. FV (deposits) = PV (tuition payments)
- Calculate the amount needed if only equal annual deposits are made on birthday’s 5-10 inclusive. FV (deposits) = PV (tuition payments as lump sum)
- Calculate the amount needed if two equal annual deposits are made on birthday’s 5 and 13.
- Answer part (i), now assume tuition rises 10% per year.
- Answer part (i) assuming first deposit will be made on your child’s 1st birthday. All other information is the same. What is the annual tuition payment? How does it compare to part (i)? Is your answer surprising?
6. RISK AND RETURN BASICS
Risk and Return and Time Value of Money are the most important concepts in all of finance We need to be able to quantify the relationship between risk and return than simply the intuitively state “more risk, more return” o In fact, very simply by adding the work “Expected” as in Expected Return adds a lot more depth to the subject. This incorporates the element of uncertainty which is inherent in virtually all our decision-making.
How do we measure Risk and Return? Truly a question for the ages and one that has puzzled many a Nobel Prize winner! First, how do we define Risk? How do we define Return? ⇒which is more difficult? Think about this before moving on.
Start with return since it is easier. Technically the relationship is based on EXPECTED return. o A good example is flipping coins.
Ex: Flip 100 coins EXPECT 50 heads but ACTUAL number of heads will most likely differ. (ex-ante expectations and ex-post realizations are almost always NOT equal)
Therefore, we base our expectations on 50 heads.
Same with stocks and other securities. How do we form our “expectations”? One method is to use historical data. Another is to use probabilistic data, i.e. our best guess of what is to occur. Mathematical example later in this handout will make the distinction clear.
Measuring Risk Now, risk. How do we measure risk? There are many ways. Some are: (1) Range of data, that is, highest return – lowest return. (2) Standard deviation of historical returns (daily, annual, etc.) called VOLATILITY (3) Beta – measure of systematic risk
Comparison (1) Range is too simple (2) Standard deviation makes sense intuitively but has limitations because SD measures TOTAL RISK. (3) TOTAL RISK = SYSTEMATIC RISK + UNSYSTEMATIC RISK = UNDIVERSIFIABLE RISK + DIVERSIFIABLE RISK = MARKET RISK + FIRM-SPECIFIC RISK = β + ε
Since it is possible to diversify (when number of securities =30 or more) unsystematic risk away (by forming portfolios), market only bases EXPECTED RETURNS on SYSTEMATIC RISK. Therefore, if you hold an asset in isolation, you are bearing more risk (total risk) than you are compensated for (systematic risk)
This idea led to the concept of diversified portfolios and efficient frontiers of Markowitz (1959) for which he won the Nobel Prize. We will cover these ideas in class.
This train of thought also led to the development of the CAPM (capital asset pricing model), which is an equilibrium pricing relationship. In English: you tell me the SYSTEMATIC RISK and I will tell you the REQUIRED RETURN for that asset. Note: this is for any asset, not just a stock. The CAPM equation is:
𝑅𝑖 = 𝑅𝐹 + 𝛽(𝐸(𝑅𝑀) − 𝑅𝐹),
where Ri is the REQUIRED RETURN for the specific security based on its level of SYSTEMATIC RISK, RM = market return (usually proxied by broad index such as S&P500) RF = risk-free rate (proxied by ST, i.e. .3-month T-Bill)
Last idea to think about is correlation (or equivalently covariance, remember our statistics?)
Correlation is the mathematical representation of how TWO variables are related. Do they TEND to move together, apart or independent of one another?
What correlation would you like for the assets in your portfolio (taken two at a time)? In other words, would you like your portfolio to have a high variance (or equivalently standard deviation) or a low variance?
Case 2: Historical Returns
Year IBM Return (%) ATT Return (%) Portfolio Return (%) Here’s the reason!! 1995 30 40 1996 40 60 1997 10 - 1998 -20 30
- Calculate the Expected Return of IBM and ATT.
- Calculate the Variance of IBM and ATT.
- Calculate the Standard Deviation of IBM and ATT.
Assume you have a portfolio of 25% IBM and 75% ATT.
- Calculate the Expected Return of the portfolio.
- Calculate the Variance of the portfolio.
- Calculate the Standard Deviation of the portfolio
8. DIVIDEND PRACTICE PROBLEMS
Assume ks = 10% for problems 1 – 6.
- Perpetuity The XYZ Corp. pays a $3 dividend every year. If the first dividend is due one year from now, what is the current price of XYZ?
- Delayed perpetuity The XYZ Corp. pays a $3 dividend every year. If the first dividend is due three years from now, what is the current price of XYZ?
- Growing perpetuity The XYZ Corp. expects to pay a $3 dividend next year. If the growth rate is 5%, what is the current price of XYZ?
- Delayed Growing perpetuity The XYZ Corp. expects to pay its first dividend of $3 in 4 years. If the growth rate is 5%, what is the current price of XYZ?
- Delayed Growing Perpetuity with Additional Dividends The XYZ Corporation expects to issue the following dividends: $1 – 1 year from now;$2 – 2 years from now; and $3 – 3 years from now. Dividends are then expected to grow at 6% forever beginning with the 4th dividend. What is the current price?
- Supernormal Growth and Delayed Growing Perpetuity The XYZ Corp. paid a $2 dividend YESTERDAY. The company expects dividends to increase by 50% for the next 2 years and then by 4% forever. What is the current stock price?
- Supernormal Growth, Delayed Growing Perpetuity and Changing Discount Rate The XYZ Company paid a $3 dividend yesterday. The company expects dividends to grow at 50% for the first two years and then 5% forever. The discount rate during the supernormal period will be 18% and then drop to 12% during the constant dividend period as the company enters the mature phase of its life-cycle. Determine the current stock price.
- Verify ks = % ∆price change + dividend yield for Question 3
- Verify ks = % ∆price change + dividend yield for Question 6
4. Delayed Growing Perpetuity P 0 =? P 3 = 60. 3.00 3.
g = 5%→ 0 1 2 3 4 5 Using the Gordon Growth model, we can find the value of constantly growing stock at t=
𝑃 3 =
(𝑘𝑠 − 𝑔) 𝑃^0 =^
Now that we have the price of the stock at t=3, we can discount it to t=0 to find the present value of the stock
𝑃 0 =
( 1. 1 )^3
5. Delayed Growing Perpetuity with Additional Dividends P 0 =? P 3 = 79. 1.00 2.00 3.00 3.
g = 6%→ 0 1 2 3 4 5 D 1 = 1. D 2 = 2. D 3 = 3. D 4 = D 3 × (1+g) = 3.00 × (1.06) = 3.
The dividend will grow at a constant rate starting from t = 3. Using the Gordon Growth Model, we find the following:
𝑃 3 =
Next we find the present value of dividends 1, 2, and 3 as well as the present value of the constant growth stock at t=
𝑃 0 =
( 1. 1 )^1
( 1. 1 )^2
( 1. 1 )^3
( 1. 1 )^3
6. Supernormal Growth and Delayed Growing Perpetuity P 0 =? P 2 = 78. 2.00* 3.00 4.50 4.
g = 50%→ g = 4%→ 0 1 2 3 4 5 *Note: first dividend going forward will be considered being paid one period from now (t=1). The gap at t=1 and the time the dividend is actually paid will be considered negligible
D 1 = 2.00 × (1.5) = 3. D 2 = 2.00 × (1.5)^2 = 4.50 or D 2 = D 1 × (1.5) = 3.00 × (1.5) = 4. D 3 = D 2 × (1.04) = 4.50 × (1.04) = 4.
Step 1 : Find the value of the stock when the dividends begin constant growth. Therefore, the PV of D 3 , D 4 , D 5 , … , Dn is captured in the PV of the stock at t = 2
(𝑘𝑠 − 𝑔) 𝑃^2 =^
Step 2 : Sum the present value of all the dividends paid prior to the constant growth, that is, PV of all supernormal growth dividends PLUS the PV of the stock at t = 2