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IRV-P11
PGDM 2011-13: Term-III

IRV: Introduction to Risk and Valuation

PGDM: XIMB 2011-2012
Banikanta Mishra

Course Content: The objective of the financial-manager of a firm is to create wealth for the firm’s stakeholders. S/he does so by identifying and investing in projects where the current worth of cash-flows exceeds the current cost of the required investments. This worth is measured by value.

This course revolves around the central theme of finance: valuation. It will start by introducing you to concepts of valuation and their measurements. You will then use this knowledge to value the two most basic securities: stock and bond. You would learn that value depends upon two variables: cash-flows and discount-rate.

Discount-rate is typically the more difficult variable to tackle. When valuing stocks and bonds, you would have initially taken the discount-rate as given. But, later in the course, you will analyze how these discount-rates are determined. The first thing that you will learn in this regard is that risk of an instrument influences its discount-rate. Then, you will ferret out the different sources of risk for a bondholder. In this context, you will learn about the term-structure-of-interest-rates, which explains why riskless - and even similarly risky - bonds of different maturities command different yields.

Determination of discount-rate for stocks is perforce a more complicated task. This will necessitate your understanding the risk-return framework in which individuals make their portfolio-selection choices. You will learn how risk is defined and measured for a stock. That will introduce you to the concept of “beta”, which measures a stock’s risk.

Course Materials: I do not refer to any specific book. The Indicative Schedule at the end refers to the pages of Fundamentals of Corporate Finance by Ross et al, TMH (Tata McGraw-Hill). But, books by Bodie & Merton, Grinblatt & Titman, and Brealey & Myers are also good ones (possibly in that order). You may scan The Wall Street Journal Guide to Understanding Money and Investing by Kenneth Morrris and Allen Siegel (Lightbulb Press); Wall Street is the Dalal Street of USA and the Wall Street Journal its Economic Times. Three not-to-be-graded assignments are also enclosed in the course-pack.

Examinations: There will be only one final examination accounting for 80% of the course-grade. This closed-book examination (you will be allowed to carry only the Formula Sheet provided by me) will typically have conceptual questions and numerical problems (short, medium, long). There will be no make-up examination

Assignments: The course-pack contains three assignments. You should not submit their solutions to me. I would hand you over the answers to the questions in an assignment only after all the topics relating to that assignment have been covered and you have had a few days to work on the problems. Answers to cases, if any, would not be handed over, though they would be discussed in class. The COC (Group) Project is somewhat different and requires your group to determine and analyze the cost-of-capital of a company. Your group may be provided with the name of a company or asked to choose one for itself.

Grade: Your grade would depend on your performance in the final examination (80%), class participation (10%), and your group-report on the COC Project (10%); a group should have maximum six students. Unless there is an official grade distribution of the Institute, your QPI would be calculated as equal to (P-N)/10, where P is your overall percentage-score and N is between 0 and 10 (usually 10).

Class Participation: All students are expected to take an active part in class discussions; it also carries a 10% weight. Class participation is an integral component of the learning process. Therefore, I would urge you to come well-prepared to the class, to answer questions when called upon to do so, and to raise interesting issues for discussion. Besides, you must attend every class. You are allowed to miss up to two classes only if you or someone in your family is seriously ill or there is a death in your family (God forbid!). If you miss any class in violation of this rule, 0.2 would be deducted from your QPI for every class thus missed. This penalty would be in addition to a low or zero score for you in the CP component.

Some Basic Examination Rules: You would be given either a question-cum-answer paper or a question paper with the answer-paper attached. In the former case, you would be given a specific amount of space following each question for writing your answer. In the latter, you would be given a specific total number of pages to write your answers; you should use both sides of each sheet and show your answers in ascending order (answer to Q.1 first, followed by answer to Q2 and so on), leaving half-inch gap between your answers. In all cases, leave half-inch margin on both left and right side. Read instructions, if any, on the question/question-cum-answer book; if an instruction therein conflicts with one given here, then it overrides the one given here. If not specifically asked to use a pen, you may use either pen or pencil. Write legibly; if I cannot read what you have written, I will not give you any points for the relevant portion. Unless merely asked to tick the right answer, explain clearly all your derivations and answers; if no explanation is given, no credit will be given for merely ticking or jotting down the correct answer. Be precise; clumsy writing and imprecise or unnecessarily lengthy answers will be penalized. You are not allowed to seek any clarifications from anyone (not even your instructor) during examinations; if a question is wrong or unclear, just state why the question is wrong/unclear and, if possible, make an assumption and answer the question. If you are found to be justified doing what you did, you will get full points; or else, you would receive less (even zero).

Formula Sheet and PV-FV Tables: I have provided a 4-page Formula Sheet and 4-page PV-FV Tables. You must bring these to every class. You should bring these to all examinations also. No other sheet would be allowed or provided by me for the examinations.

Code of Ethics: You must abide yourself by the (unwritten) Code of Ethics for Students. For individual (group) assignments/examinations/projects, it is unethical to seek any direct help from others (other groups), whether or not you make use of the help. Besides, other forms of dishonesty (like plagiarism) would also invite severe punishment. Moreover, for a group assignment, all members of the group should contribute to the preparation of the report (no free-riders), and no direct help should be sought or taken from persons outside the group. Discussion among individual students and groups (except in the examination hall or class-room) is, of course, always encouraged. But, the final report or solution should be totally in your (your group’s) own style and language; any form of copying from another student (or group) or from any outside source is a serious offense. Moreover, you (or, wherever relevant, each member of your group) must fully and clearly understand every word and every step written in your (your group’s) report. Your basic purpose should be to learn, without resorting to any unfair means for getting a higher score/grade. If you resort to any unfair means, including, but not limited to, the ones mentioned above, you would receive an F in the course; I may also recommend to the Institute for your expulsion.

‘Hide Thy Name’ Policy: In all your solutions / reports / examinations, please mention only your Roll Number(s) on the last page. Never mention your name(s) anywhere, not even in the examination-answer-sheets. This ensures that the person grading your assignment/examination does not know your identity. If you mention your name, up to 40 points would be deducted from your assignment (examination / report / case solutions). If you are anywhere directed to write your name, it shall be deemed to be a mistake and to be overwritten by the ‘Hide Thy Name’ Policy mentioned here.

Contact Details: If you want a meeting, please get an appointment in advance. You can reach me by e-mail at banikant@ximb.ac.in OR banikanta@hotmail.com (the former is preferred).

Feedback: Feedback is always useful, even for the most seasoned veteran. In that spirit (but, of course, without claiming to be either seasoned or a veteran), I would request you to give me continuous “informal” feedback. Toward this, the class may like to form a “focus group” that continuously interacts with the students and informs me about their problems, if any, with the course. I would also request you to submit the midterm-evaluation on the day/date mentioned at the top of the midterm-evaluation-form (included). The final evaluation-form, which is different from the "official" one you would receive from the Dean's Office, asks some specific questions regarding topics and cases (which are not touched upon by the official form). I would be thankful if you submit it to me on the day of the final examination (just after the exam).

Complaints: If you have problems with the course, please report to me first. You can push in printed slips under my office-door or talk to me face to face. If for some reason, you do not feel like talking to me or are not satisfied after talking to me, you can report to the Area Coordinator, Accounting & Finance (currently Professor BP Mishra, Office Extension: 767). If still not satisfied, you should contact the Dean (Academics). I do sincerely respect your right to complain.

Indicative Schedule: The Indicative Schedule on the next page gives you an idea about the chronological sequence of topics I plan to cover and the amount of time I plan to spend on each topic. It is by no means binding. I would try my best to ensure that you understand a topic well before moving on to the next topic. Based on my past experience, I, of course, believe that we shall be able to cover most, if not all, the topics mentioned in the Indicative Schedule.

I hope that I live up to your expectation (of teaching quality) and you up to mine (of sincerity).
I also hope that you enjoy the course and get the value of your time and money spent on it.




Indicative Schedule



Session
Topics Covered
Chapter(s)
1-4
Time Value of Money and Discounted Cash Flows
5, 6
5-7
Security Valuation – Bonds and Stocks
7, 8
8-10
Risk and Return, CAPM
13


Do not submit answers to the instructor; solutions would be provided in 5th session

IRV Practice Assignment - 1 Banikanta Mishra

1. If the rate is 21%, what is the PV of Rs.550 to be received after six months?

2. Bank Banque claims to double your money in 70 months. What rate is it offering?

3. A bank which follows quarterly compounding has an annual rate of 12.55%. How much need you deposit to get back Rs.212.18 from the bank at the end of six months?

4. If the rate is 8% per period, what is the PV of a security that pays Rs.100 at the end of the first period, collects Rs.200 at the end of the second year, and pays Rs.300 at the end of the third?

5. You have to repay a loan of Rs.10,373 taken at @1.20% per month in monthly installments over the next two years. What is the installment?

6. What is the PV of a security paying Rs.420 at the end of every two years up to the end of the tenth year, if the rate is 10% per year?

7. A scheme requires you to deposit Rs.200 every alternative year starting at the end of the first year and receive Rs.260 every alternative year starting at the end of the second year. If you have 13 withdrawals and 13 receipts, what is the PV of the scheme? FV? Assume discount rate is 5%.

8. You have taken a loan of Rs.15,000 @7%. If you can repay at most Rs.300 per month (starting at the end of this month), at least how many months will it take for the loan to be fully paid off? What if the rate is 1.7% per quarter?

9. Bank A doubles your money in 12 years, while Bank B gives you 1.5% per quarter. Who is offering a better rate?

10. If, staring at the end of the quarter, you deposit Rs.200 a quarter in a scheme paying 2% per quarter, how many years will it take you to accumulate Rs.6000?

11. You have taken a loan of Rs.10,000 @19.6%. It has to be paid off in Equal Monthly Installments over two years (with the first payment starting at the end of the month). What will be your installment?

12. A scheme requires you to pay, starting at the end of the second year, Rs.420 every alternate year (t=2, t=4, t=6, and so on for ever); you receive Rs.420 every alternate year starting at the end of the year (t=1, t=3, t=5, and so on for ever). What is the PV of this scheme if RRR is 10%?

13. A bank claims to quadruple your money in 180 months. Is it offering a better rate than a bank that gives you Rs.6 at the end of 20 years for every Rs.1 deposited today?

14. You can pay Rs.5000 up front or, starting at the end of the month, Rs.100 a month for the next five years, says the VCR-seller. What rate is she implicitly charging for the installment option? If you get 8.0% on your bank-deposit, would you prefer the lump-sum option or the installment one?

15. You have decided to deposit, starting at t=1, Rs.1000 per year in a scheme that pays 5% EAR. But, your brother is going to withdraw Rs.500 per year from the third year (t=3) onwards. How many years will it take for you to accumulate Rs.15,000?

16. You have taken a loan of Rs.20,000 @10%. The principal has to be repaid in four equal annual installments (EAIs) of Rs.5000. What then would be the interest-payment streams? What would be the payment/installment streams?

17. If, starting at the end of the month, you deposit Rs.500 per month in a scheme paying 0.75% monthly, how many years will it take for you to accumulate Rs.20,000?

18. You have taken a loan of Rs.17,900 @ 19.56%. If you pay Rs.1000 per month, how many years will it take you to repay the loan?

19. You have borrowed Rs.11,111 @19.56% to be paid off in 120 equal-monthly-installments. What should be your installment? Would you prefer to pay Rs.2,500 per year?

Do not submit answers to the instructor; solutions would be provided in 9th session

IRV Practice Assignment - 2 Banikanta Mishra

1. Mr. A and Ms. B want to buy a five-year Rs.1000-par bond paying 11% coupon annually. Mr. A would sell it at the end of the year, while Ms. B would sell it at the end of the second year. If kd = 11%, what price would A and B respectively offer for the bond (work it out without using the standard bond-valuation formula)? What if kd = 12%? What if kd = 10%? Who is pricing it higher and why?

2. Take the question above. Suppose that kd = 11% and both Mr. A and Ms. B bought the bond at the prices derived above. What will happen to realized-returns of Mr. A and Ms. B if kd at t=1 (end of the year) falls to 10%? What happens if kd at t=1 (end of the year) increases to 12%?

3. If kd = 11%, would an 11%-coupon-rate bond with semiannual interest-payments sell below, at, or above par? Why?

4. Consider two bonds with 15% coupon-rate, Rs.1000 face-value, 16% kd, but different maturities. Which of the two bonds would have a higher price? What if the shorter-maturity bond has a coupon-rate of 15.5%?

5. If a bond that pays 12% coupon is selling 20% above par, what best can you tell about its kd? What if it is selling 4% below par?

6. A firm's bond is rated AA, requiring a risk-premium of say 2%. Currently, investors are expecting inflation to be around 5% per year. What best can you tell about the required yield on this bond?

7. Two bonds having the same coupon-rate and the same discount-rate but different-maturities are selling for almost the same price. How is that possible?

8. A 12% coupon-rate bond with five years to maturity is selling for Rs.1,018.25. What is its kd? If you buy the above bond now and sell it after one year, what will be your current-yield, capital-gains-yield, and total yield?

9. What is the duration of a three-year 11% coupon bond that has a Rs.1,000 face-value? What is the meaning of this number? What is the convexity of this bond? What does this number mean? Is this bond more or less interest-rate-sensitive than a two-year 15% bond with the same face-value? Assume that both the bonds have a yield of 12%.

10. Consider two bonds that are identical in all respects, except that Bond A has double the maturity of Bond B. Interest-rate just went up by 0.1% and the price of Bond B just went down by 0.5%. What best can you tell about the change in the price of Bond A?

11. Which has a higher duration: a three-year zero-coupon-bond or a five-year amortizing loan that pays off a loan in five equal-annual-installments?

12. What is the duration of a bond that pays Rs.22 a year forever, if its yield now is 10%? Show that this number actually measures the interest-rate-sensitivity of this bond.

13. If two equally-priced assets have the same duration and one has a lower convexity than the other, which one would be more attractive? Why?

14. Consider two bonds having the same maturity and face-value. One of them has a 12% coupon-rate, while the other has a 10% coupon-rate. If the two bonds have the same kd, which one would be more interest-rate sensitive?

15. The two-year zero-coupon treasury-security (which only pays Rs.100 at t=2) is selling for Rs.89.00, while the three-year zero-coupon treasury-security is selling for Rs.80.50. What does this data tell you about the market's expectation regarding the one-year rate two years down the line (the forward rate)?

16. The two-year zero-coupon treasury-security (which only pays Rs.100 at t=2) is selling for Rs.89.00, while the one-year zero-coupon treasury-security is selling for Rs.93.24. What does this data tell you about the market's expectation regarding the one-year rate one year down the line (the forward rate)?

17. If you can buy # at $1.50 now and deposit it @5%, and the banks are willing to buy # from you at the end of the year at $1.53, what must be your $-borrowing-interest-rate to discourage you from indulging in CIA (covered-interest-arbitrage)?

18. Assume that, at present, rRs = 13.4%, r$ = 5%, and S (Rs per $) = Rs.45.00. If interest-rate-parity holds, what should be the forward-rate (for transactions at the end of the year)? What does your result tell you about the expected appreciation/depreciation of Rs vis-à-vis $? Would you in this case prefer to put your money in a Rs deposit or $ deposit?

19. Assume that inflation in India is 15.5%, while that in USA is 10%. If $1=Rs.40 at present, what is the expected exchange-rate at the end of one year from now?

20. The Indian banks have quoted the following rates: $ Spot: Buy=30.00, Sell=30.25, $ Forward: Buy=32.40, Sell=32.67, $ Lending Rate=5.0%, $ Borrowing Rate=4.0%, Re Lending Rate=13.4%, Re Borrowing Rate=11.8%. Is arbitrage possible?

Do not submit answers to the instructor; solutions would be provided in 13th session

IRV Practice Assignment - 3 Banikanta Mishra

A stock is expected to pay Rs.10 dividend next year, Rs.11 the year after, Rs.12.10 the year after that and so on. What is its PV if k=15%? What is its value at the end of the year?

A stock's dividends for the three recent years (-2, -1, 0) has been as follows: Rs.10.00, Rs.9.90, Rs.10.10 (with the last dividend to be paid today shortly). Its k=10%. What should be its price now? What will be the price just after the dividend is paid today? What will be its price at the year-end?

A stock selling for Rs.220 now is not expected to pay any dividend in the short run. If its growth-rate in prices has been 10%, what should the share sell for next year?

A stock is expected to pay Rs.10 at the year-end, Rs.11 the next year, Rs.12.10 the year after, Rs.13.31 at the end of the following year, and Rs.15 per year from the fifth year onwards. What is its PV if k=15%?

A share is expected to pay Rs.30 dividends at the year-end, Rs.28.50 the year after, Rs.27.075 the next year, and so on. What is its PV if k=10%? What is its expected value at the year-end?

Take the share in Question 1 above. If you buy the share now and sell it at the end of the year, what is your ERR and what is its breakdown? Repeat using data for questions 2 to 5.

A stock is expected to give a dividend of Rs.12 at the end of the year (t=1) and the dividend is expected to grow at the rate of 5% per year. The ks for this stock is 10%. If you buy the stock today, planning to sell it at the end of the year, what are your dividend-yield and capital-gains-yield?

A stock paid Rs.5.00 dividend a year ago, just paid Rs.5.50 toward its dividend for this year, and is expected to pay Rs.6.05 next year (at the end of one year from now). If the stock's current price is Rs.110, what is its ERR?

A company is faced with a dilemma. It can pay Rs.8 dividends per share now and continue to keep it constant at that level, as it has been doing for long. Alternatively, to finance some excellent investment opportunities it has come up with, it can cut down the dividend to Rs.6 now, increasing it by 10% per year; it strongly feels that it can sustain this increase for ever. What should it do, if its ks = 25%?

A firm has 500 shares with a current market-value of Rs.12,000. Its share has been paying dividend, which has been growing annually at a rate of 20%. It has just paid a dividend of Rs.2.00. What must be its ks?

You are contemplating to purchase a few shares in a company which has been set up purely for a high-way project. You will not receive any dividends till the project completes at the end of the fifth year (t=5). From the end of the sixth year (t=6) onwards, you expect to receive Rs.15 per year for 10 years (to be financed by the toll receipts), after which the project would be handed over to the local government. How much would you pay for these shares, if you require a 20% return on such investments?


12. The three following assets give perpetual cash-flows. The probability-distributions of cash-flow to the assets is the same every year. They are given below (each state has a probability of 1/3.)

If their RRR is the same and the prices of 1, 2, and 3 are Rs.110, Rs.80, and Rs.320 respectively, is there a strategy to make money? If no, why not? If yes, what is the strategy?

13. The following table gives the distribution of future return on A and B based on historical data.

State Ret on A Ret on B
1 0.20 0.15
2 -0.04 0.00
3 0.17 0.07
4 0.11 0.22

If you are asked to put your money only in ONE stock, what will be the return and risk of your optimal portfolio? What if you are allowed to put your money in ALL stocks?

14. Humors Company has two divisions: Joke and Laughter. Joke is in a highly risky business; its beta is 1.2. Laughter is in a comparatively low risk (from the point of market risk) operation; its beta is 0.8. Around 50% of Humor's assets are invested in the Laughter division.

Humors uses 100% equity financing. If the current expected return on the market portfolio is 12%, what is Humors's cost of capital?

Determine the NPV of the following project the Joke division is contemplating about. The project cost is Rs.50,000 and it is expected to provide perpetual cash flows of Rs.6,000 per year. Should Humors accept the project?

Due in my office: Any time before the commencement of the final examination (exam hall okay)

IRV COC Project Banikanta Mishra
Answer all questions. All questions carry equal points. Total is 25 points.

You have chosen or been provided the name of a company ("your company"). Find out some financial data pertaining to this firm (on a recent date: last 31 December is acceptable) and answer the following questions.

1. What is the rating, if any, of your company's bonds?

2. What is the cost of debt of your company? How did you arrive at this figure?

3. How much debt does your company have?

4. What is the market-value of equity of your company?

5. What is the Debt/Equity percentage (ratio) of your company?

6. What is the Debt/Equity percentage of your company's competitors?

7. How does your company's Return on Assets compare with those of its competitors?

8. How does your company's Interest Coverage compare with those of its competitors?

9. Would your company's bonds be rated better or worse than an average competitor? Why?

10. What is the company's P/E Ratio? Is it higher or lower than that of its competitors? Why?

11. What has been the dividend-yield of your company's shares?

12. What has been the capital-gains-yield on your company's shares?

13. What has been the average growth in annual dividends during the last five years or so?

14. What has been the average growth in annual EPS during the last five years or so?

15. What has been the company's average Payout Ratio during the last five years or so?

16. What has been the company's reported book Return on Equity (ROE)?

17. What is the company's cost-of-equity (COE) as per the DDM (dividend discount model)?

18. Is the DDM-COE obtained above higher or lower than earnings-yield (inverse of the P/E ratio)? Why?

19. Is the DDM-COE obtained above same as the reported (book) ROE? Should it be?

20. What is the bs of your company?

21. Is the company's bs higher or lower than that of its competitors? Why so?

22. Based on your company's bs, what is your company's CAPM-COE?

23. How does your estimate of the CAPM-COE compare with your estimate of the DDM-COE?

24. What is the WACC of your company? Which cash flows do you discount at this rate?

25. What is the Adjusted COC of your company? When do you use this?

Banikanta Mishra Concepts Covered IRV
(somewhat in chronological order)


1. The Market-Value Balance-Sheet
2. Finance Manager as a Link between the Capital Market and the Real-Assets Market
3. Real Rate and the (Nominal) Risk-Free Rate
4. Future Value (FV) after One Period
5. Expected Rate of Return
6. Risky Investment: Risk Adjusted Discount Rate
7. FV after Multiple Periods: Reinvestment at a Different Rate
8. FV after Multiple Periods: Reinvestment at the Same Rate
9. Term Structure of Interest Rates
10. FV after Multiperiods
11. Compounding
12. Effective Annual Rate
13. Effective Annual Rate (EAR) and Annual Percentage Rate (APR)
14. Effective T-period Rate from Effective One-period Rate
15. Effective One-period Rate from Effective T-period Rate
16. Concept of Internal Rate of Return (IRR)
17. Concept of Required Rate of Return (RRR)
18. Making Investment Decision: Compare IRR and RRR
19. Making Investment Decision: Compare Ending CFs
20. Making Investment Decision: Compare Required Investment-> Concept of Present Value
21. Time Value of Money
22. Why Discount?
23. NPV Rule and IRR Rule
24. Informationally Efficient Capital Market
25. Computing the Present Value (PV) of a Distant Cash Flows
26. PV of a Future Cash-Flow Stream: the Value Additivity Principle
27. PV of an Annuity
28. The Concept of Equivalent Annuity (EA)
29. Solving for the Equal Periodic Installment (EPI) for an Amortizing Loan
30. Verifying the EPI for an Amortizing Loan
31. PV of a Perpetuity, the Perpetual Annuity
32. FV of an Annuity
33. Bond Valuation Principle
34. Bond Characteristics
35. Coupon Rate (CR) versus kd : Premium, Par, and Discount Bonds
36. Interest Rate Sensitivity of Bond Price
37. Duration and Convexity
38. Expected Rate of Return on a Bond
39. Relationship between CR, kd, and Current Yield
40. Realized Rate of Return versus ERR
41. Concept of Yield to Maturity (YTM)
42. The Approximate-Yield Formula
43. Yield to Call
44. Term Structure of Interest Rates
45. Using the Yield Curve to Set kd
46. Variables Affecting Corporate Credit-Rating
47. Interest-Rate Parity (IRP) Condition: CIA -> Covered Interest Arbitrage
48. Purchasing-Power Parity (PPP) Condition
49. Market Efficiency
50. The Generic Dividend Discount Model (DDM) of Equity Valuation
51. The Two Special Cases of DDM
52. Non-Dividend Paying Stocks
53. Stocks with Changing Dividend-Growth-Rate
54. Return on a Stock
55. Determining the Expected Growth Rate
56. On P-E Ratio
57. Cash Flow versus Return
58. Stochastic Dominance
59. The Individual Portfolio-Selection Problem
60. Defining Risk-Aversion
61. The Risk-Averse Investor's Decision Rules
62. Uncertainty and Risk: Definition
63. Measuring Risk: Probability, LPM, and Variance
64. The Mean-Variance Selection Rules
65. Diversification through Portfolio Formation
66. Portfolio Mean and Variance
67. Sources of Risk: Why Diversification Usually Pays?
68. How Diversification Works
69. The Concept of Optimal Portfolio
70. Determining the Asset Weights for the Optimal Portfolio: Case of Two Assets
71. The Minimum-Variance Frontier and the Capital Market Line (CML)
72. Asset Risk as its Contribution to Portfolio Risk
73. The Two Conditions that Asset-Risk-Measure should Satisfy
74. Non-standardized and Standardized Risk
75. Covariance and Correlation
76. Capital Asset Pricing Model (CAPM) and the Beta
77. Some Implications of the Linear CAPM
78. Using the CAPM in the Real World
79. Beta of New High-Risk Firms
80. Cost of Debt, Cost of Equity, and the Weighted Average Cost of Capital (WACC)
81. What Determines the Equity-Beta?

FORMULAE

Banikanta Mishra FM
1. FVT = PV (1 + r)T [r = discount-rate per period; T = number of periods]

2. PV =

3. FVIFAr,T =
4. PVIFAr,T = = ; PVIFAr,T for T = (a perpetuity) becomes
5. Per Period Rate of Return =
(where T = Number of Periods)

6. Annual Percentage Rate (APR) = Rate per Period x Number of Periods in a Year (e.g. rm x 12)
which implies that, Rate-per Period = APR / Number of Periods in a Year (e.g. rq = APR / 4)

7. Given 1-period rate r, get the T-period-rate rT = (1 + r)T - 1 => (1 + r)T = 1 + rT
For example, given monthly-rate rm, get Effective Annual Rate or EAR = (1 + rm)12 - 1

Otherwise, given APR, get EAR = , which, for , becomes
[N is the number of compoundings in a year; Annual Compounding => N=1; Semiannual => N=2; Quarterly => N=4; Monthly => N=12; Daily => N=360 or 365; Continuous => .]

8. Given the T-period-rate rT, get 1-period-rate r = (1 + rT)1/T - 1 => (1 + rT)1/T = 1 + r
For example, given quarterly-rate rq, get monthly-rate rm = (1 + rq)1/3 - 1
Or, given the EAR, get the monthly-rate as follows: rm = (1 + EAR)1/12 - 1

Otherwise, given EAR, get APR = , which, for , is ln (1 + EAR)

9. Given PVIFA, get T as equal to

10. Given FVIFA, get T as equal to

11. If roT is the EAR on a T-year risk-less zero-coupon bond and rot is the EAR on a similar t-year bond, then Expectation Hypothesis would imply that (1 + r0T)T = (1 + r0t)t x (1 + rtT)T-t
[The rtT is called the forward rate; specifically, the T-t period forward-rate at t.]
For example: (1 + r05)5 = (1 + r03)3 x (1 + r35)2 [where r35 is the two-year forward-rate at t=3]
Similarly: (1 + r02)2 = (1 + r01) x (1 + r12) [where r12 is the one-year forward-rate at year-end]
12. General Bond Valuation Formula: PV = [ Int x PVIFAkd,T ] + [ ],
where T is the number of periods to maturity, Par is the par-value paid at the maturity, Int is the coupon-payment (in $) per period, and kd is the discount-rate per period

13. If Coupon-Rate > = < kd, then bond's PV > = < Par [where Coupon-Rate = Int / Par ]

14. All else being same, price of a longer-maturity bond changes (rises / falls) more than that of a shorter-maturity bond, for a given change in interest-rate

15. When interest-rate rises, bond value falls at a falling-rate; and when interest-rate falls, bond value increases at an increasing rate.

16. Approximate Yield on Bond =
where P0 is current price, Ann Int is annual interest-payment, other variables as defined above

17. ERR0 on a Bond = Current Yield + Capital Gains Yield =
ERR0 is Expected Rate of Return, P0 is price now, P1 is price on next interest-payment date.
If next interest-payment date is less than a year away, this return should be annualized (EAR).

18. kd > = < Current Yield > = < Coupon-Rate

19. General Stock Valuation Formula:
where D1 is the Dividend at the end of the period (at t=1), kS is the discount-rate or RRR,
g is the growth-rate of dividends, T is the life of the stock

20. When T = , we obtain that P0 =

21. Thus, kS = + g,
And, ERR on a Stock = Dividend Yield + Capital Gains Yield =
[D1 is next dividend expected, P0 is current price, and P1 price on next dividend-payment date]
If next dividend-payment date is less than one year away, the return should be annualized

In any case, if the share is fairly priced, ks = ERR, as required for equilibrium

22. For a share which will not pay any dividend in the short-run, PV =
where DT is the dividend expected at some distant future date T;
for such a stock, ERR = g

23. F / S0 = (1+ r1) / (1 + r2) [F and S are in currency of Country 1 per currency of Country 2; S is the current exchange-rate, F is the (agreed upon) forward-rate, and ri is the interest-rate of Country i] // For example, if S is $ per # and F is also $ per #, then F / S0 = (1+ r$) / (1 + r#)

24. Interest-Rate Parity:
[F and S are in domestic-currency per foreign-currency; S is the current exchange-rate, F is the forward-rate, and r is the interest-rate with d denoting domestic and f foreign]
For example, if S is $ per # and F is also $ per #, then F / S0 = (1+ r$) / (1 + r#)
[Here, r is the interest-rate between now and the maturity-date of the forward contract. So, if F matures at the quarter-end, then r is the quarterly-rate,
while, if F matures at the end of three years, r is the three-yearly rate = (1 + EAR)3 - 1]
This condition is the same as [( F - S0) / S0] = [ (1+ rd) / (1 + rf)] - 1
where the LHS is referred to as the forward-premium

25. If F / S0 > (1+ rd) / (1 + rf) then borrow domestic currency, convert it into foreign-currency, and deposit/lend it and vice versa [i.e. prefer borrowing domestic currency and lending foreign] This condition [Covered Interest Arbitrage] is same as [( F - S0) / S0] > [ (1+ rd) / (1 + rf)] - 1

When forward-price F is not available or not used, [(S1 - S0) / S0] > [ (1+ rd) / (1 + rf) ] - 1
implies Uncovered Interest Arbitrage; this is the same condition as: S1 / S0 > (1+ rd) / (1 + rf)

26. Relative Purchasing Power Parity:
[S1 and S0 are in domestic-currency per foreign-currency, S1 is the expected exchange-rate at time 1, S0 is the exchange-rate now at time 0, and i is expected inflation-rate with d denoting domestic and f foreign]
For example: if S1 and S0 are in $ per #, then S1 / S0 = (1 + iUSA) / (1 + iUK)
[Here, i is qualified the way r is qualified above.]


27. Real Exchange Rate (RER) at time t = = St-1 if Relative PPP holds
Specifically, RER1 = S1 x [ (1 + if) / (1 + id) ] = S0, if Relative PPP holds
[Here RER and S are defined in terms of domestic currency per foreign-currency]

28. = wi2 si2 + wj2 sj2 + 2 wi wj si sj rij
where si (sj) is the standard-deviation of i (j), and rij is the correlation between i and j

29. bi =
30. Optimal Weight on Asset j when Asset i & j have same mean =
31. kS = + ( - kd) [similar equation for the b]

32. ITS = Interest x t

33. PVITS = D x t (for perpetual debt)

34. Levered CF (CFL) = Unlevered CF (CFU) + ITS

35. Value of Levered firm (VL) = Value of Unlevered firm (VU) + PVITS

36. WACC =

37. Adjusted COC =

38. VL = OR Alternatively VL =

39. = (also called the "asset beta")

40. brev=


Created By: Debasis Mohanty on 12/08/2011 at 08:55 AM
Category: PGP-I Doctype: Document

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