Close
CID-R11
(PGDM-RM 2011-13 : Term-III)

CID: Capital Investment Decisions

PGDM-RM: 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.

You would have learnt the basics of valuation and risk in IRV (Introduction to Risk and Valuation). This course would build on that.

This course will teach you how to evaluate – or value - a capital-investment opportunity using various rules, especially NPV (Net Present Value) and IRR (Internal rate of Return). It would thus familiarize you with the nuances of determination of cash-flows for a project, in particular the effect of tax-shields, opportunity costs, externalities, and unequal lives. It would also tell you ho to determine cost-of-capital and what effect debt-equity ratio and other factors have on the cost-of-capital. You may also get a glimpse of "real options", options that arise in capital-budgeting problems.

After having gone through the course, you should be able to evaluate an investment opportunity or, by extension, even value a firm.

Course Materials: I do not refer to any specific book. The Indicative Schedule at the end refers to the pages of Fundamentals of Financial Management by Prasanna Chandra, TMH (Tata McGraw-Hill), latest edition used here at XIMB. But, books by Ross et al, 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. Two 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

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).

Assignments: The course-pack contains two 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 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.

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.

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.

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.

Contact Details: Though I am usually always available in my office (Room 227 Admin Block) between 11:00 a.m. and 6:00 p.m. (except lunch break) on weekdays (and at random hours on weekends), I may not always be free to talk to you. So, if you want a meeting, please get an appointment in advance. You can reach me in my office at extension 827 or at home (only between 10:00-1:00 and 5:00-9:00, please) at 864; in case my home extension does not work, you may call me in my direct number at 230-2727 during the same hours. My secretary, Mr. Bijay Raut, can be reached at extension 842. You can, of course, always reach me by e-mail at banikant@ximb.ac.in OR banikanta@hotmail.com (the former is preferred).

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
1
Recap: Deriving Cash Flows
2
Cost of Capital
3-4
Capital Budgeting: Competing Criteria
5-7
Capital Budgeting Under Certainty
8-9
Capital Structure and Project Value
10
Special Topics in Capital Budgeting

Do not submit answers to the instructor; solutions would be provided in 7th session

CID Practice Assignment - 1 Banikanta Mishra

1. A firm has an EBIT of Rs.50 million. It pays tax at the rate of 30%. Its Kfu=14%. Suppose it decides to issue Rs.100 million debt at a rate of 8%. If the interest-payments are NOT tax-deductible, then, after the debt-issue, what will be its Ks? What will happen to the total market value of its shares and its debt-equity ratio? What will be its Kf after the debt-issue? What will become the value of the firm? If the firm has 50 million shares outstanding before the debt-issue, how many shares will be outstanding after the debt-issue?

2. Construe of an efficient capital market without taxes (or, in which interest payments are not tax-deductible). The following data shows the current position of ABC International, Incorporated: RRRD=8%, RRRS=12%, D/S=1.0. The expected cash flow to the firm is Rs.100 million per year till infinity. Derive the market values of ABC's debt and stock. Is the debt issued by ABC risk free? Suppose the realized cash flow in a given year is Rs.35 million. How much would the debt holders receive? Now suppose the realized cash flow is Rs.45 million. How much would the debt-holders receive?

3. A firm has an EBIT of Rs.72 million. Its corporate tax-rate is 40%. It has a Kfu of 12%. It has just decided to issue debt at 7% to push up its D/S from 0 to 1/3. What will happen to its Ks? What will be its new Kf and firm-value?

4. A firm's EBIT is Rs.45 and its tax-rate is 40%. It is given that RF=6% and kM = 11%. If its bu is 1.5, what must be the price of each of its 40 outstanding shares, given that it has no debt?

5. You plan to start a toy manufacturing company in Ann Arbor and want to raise some capital by issuing 10,000 shares. You estimate that you can pay a constant dividend of around Rs.3.21 per share and are wondering at what price you can sell your shares. To help you in your task, you have collected the following data for three toy-manufacturing firms in similar townships. You plan to have very low D/S (0.25), so as to enable you to issue risk-free debt. Your planned FC/CF is 0.40. Your corporate tax-rate is going to be 40%. You have also found out from the WSJ that the current yield on one-year TB is 8%; your analysis of the historical data shows that the average spread between the market and treasury has been around 5%. What is the best estimate of your bs?

(a) 1.30 (b) 1.265 (c) 1.40 (d) 1.61 (e) None of these

6. Take the data in question above. What is the "fair price" of your shares?


7. A firm pays out all its earnings as dividends, and its total earnings has remained - and expected to remain - at Rs.30. The ks of its shares is 10%, and there are 50 shares outstanding. It has Rs.60 cash in hand, and it is wondering what use to put it to. If it uses the cash to pay dividends to existing shareholders, what would happen to the stock price after the dividend has been paid?

8. Take the data in question above. If the firm decides to use the cash for share-repurchase instead, how many shares would be outstanding after the share-repurchase?

9. Take the data in the question preceding the one above. Assume that corporate tax-rate is 10% and that interest-payments are tax-deductible. Suppose also that the firm decided to pay out the excess cash in dividends (as in 20). But, after that, the firm decided to issue debt and use the proceeds to repurchase 20 shares. How much debt would the firm need to issue?
10. Firm T has 50 million shares outstanding, of which managers hold 20%. T’s outstanding debt is Rs.225 million; its cost is 13.5%. T pays corporate-tax at the rate of 40%. Given its current investment opportunities, every dollar invested in T generates perpetual after-tax cash-flow of 18.5 cents per year, without taking into account the interest-tax-shield (ITS). ITS adds a further 3% of the D/S ratio to the return to shareholders. T's target D/S ratio is 0.5. Based on the investment it has already made so far, T’s annual earnings are expected to be Rs.70 million. It has no non-cash-charges. T typically pays out all its earnings in dividends. Currently, T has cash-in-hand of Rs.100 million. If T desires, it can invest this money in projects that would yield fair rates of return.

Firm B believes that, even without making any additional investment, it can increase T’s annual earnings to Rs.79.4 million, thus reducing D/S to 0.45 and the concomitant RRR to 19.85%. B makes the highest possible public offer it should make (how much should it be?) and T’s stock-price goes up (to what?).

In the light of this, evaluate three choices T has to make use of its Rs.100 million cash-in-hand: (a) pay out dividends, (b) invest in projects, (c) buy back its own shares. What happens to the managers’ stake in the company and its value in each of these three cases? What if managers try to increase their stake through an open-market purchase? What about a debt-financed share-repurchase?

11. (From the Course Text: Principles of Corporate Finance, By Richard Brealey & Stewart Myers; McGraw Hill, 1999) The current price of the shares of Charles River Mining Corporation is Rs.50. Next year's earnings and dividends-per-share are Rs.4 and Rs.2, respectively. Investors expect perpetual growth at 8 percent per year. The expected rate of return demanded by investors is r=12 percent. What should be the price of the share?

Do not submit answers to the instructor; solutions would be provided in last (10th) session

CID Practice Assignment - 2 Banikanta Mishra

1. If two projects A and B have the same IRR, do they also have the same NPV?

2. A company is debating whether to replace its existing machine with a new model that costs Rs.80,000 and has a ten-year life. (If desired, it can be sold for Rs.40,000 after six years.) The new machine will increase revenue from Rs.45,000 to Rs.60,000, while the variable-cost would remain at one-third of the revenue. Fixed cost will go up by Rs.5,000. The existing machine was bought 15 years back for Rs.105,000 and lasts for 21 years. Its current market-value is Rs.20,000. The corporation’s tax-rate is 40%, and its cost-of-capital is 10%. Should it replace the machine?

3. A project requires an investment now of Rs.10,000 and is expected to generate unlevered cash-flow of Rs.1,500 per year from t=1 forever. If the project's WACC is 15%, should you accept the project?

4. A project requires outlays of Rs.1000 per month this year (from t=1, the end of the first month, to t=12) and is expected to generate Rs.1200 per month the next year (from t=13 to t=24). What is the project's IRR?

5. A project requires an investment of Rs.56,500 and is expected to generate Rs.10,000 per year for the next ten years (t=1 onwards). What is its IRR?

6. A project requires an investment of Rs.20,000 now and is expected to generate Rs.2,000 for the next nine years (from t=1 onwards) and Rs.22,000 at the end of the tenth year (t=10). What is its IRR?

7. Project X has a three-year life and an NPV of Rs.30,000, while Project X has a two-year life and an NPV of Rs.20,000. Which project is more attractive?

8. A company's cost of equity is 15%, while its cost of debt is 10%. Interest payment is tax-deductible, and the corporate tax-rate is 40%. The firm has retained-earnings of Rs.20,000; it wants to raise Rs.40,000 in debt. Then it wants to put all the above money in a project that generates perpetual cash flow of Rs.X per year from t=1 onwards. What must be X for the project to be acceptable?

9. You can produce light-bulbs at a cost of Rs.30 per bulb and can sell it for Rs.40. Manufacturing these bulbs would require the purchase of a machine costing Rs.50,000. The machine would have a ten-year life, and would require maintenance expenses of Rs.2,000 per year. If the firm's tax-rate is 40% and cost-of-capital is 15%, what is the breakeven point?

10. Two projects with equal lives have the same IRR and the same NPV, even though they have different cash flows. How is that possible?

11. XYZ Corporation is contemplating whether to lease a lathe machine or buy one. The machine costs Rs.200,000 and has a 20-year life, after which it has no salvage-value. In case the machine is to be gotten rid of before the end of its life, it can be sold for Rs.50,000 at the end of the 10th year and Rs.30,000 at the end of the 15th. The machine requires annual maintenance of Rs.5,000. If XYZ leases the machine, it would need to pay Rs.35,000 per year for ten years, after which it has to return the machine. The maintenance would be done by the lessor during the ten years. If XYZ desires, however, it can continue making the lease payment for five more years, after which it would be allowed to buy the machine for Rs.25,000; but, in this case, the lessor would not do the maintenance for these five years. XYZ's corporate tax-rate is 40%. Its borrowing-rate is 10%, while its overall cost-of-capital is 16%. Suggest the best course of action for XYZ.


12. Chemlab Corporation sells chemical mixtures. Mixing chemicals is not a simple process. It requires a mechanical mixer. Different chemicals in different proportions are processed through the mixer. This stage involves some wastage. After the output from this stage is obtained, it undergoes some manual operations. The final purified mix is sold in packages through retail outlets. Chemlab’s tax-rate is 40% and cost-of-capital 15%.

Chemlab buys chemicals from Unique Chemical Supplies, which delivers them at Chemlab's warehouse. Unique charges Chemlab Rs.20 per pound for all types of chemicals.

Chemlab processes the chemicals through the existing Mix-in-a-Minute chemical mixer. This 5000-pound-capacity (input capacity) mixer has a 20% wastage rate; that is, if one pound of chemical A is mixed with two pounds of chemical B, the final output from processing the three pounds of chemicals is 2.4 pounds [= 3 pounds x (1.00 - 0.20)]. Labor expenses are currently 15% of sales. Last year, Chemlab sold 4,000 pounds of mixtures in the market, and it expects to continue the same performance for the next five years if it stays with the existing Mix-in-a-Minute. It also expects to maintain its selling price at the current level, which is Rs.40 per pound. Of course, at this price, Chemlab can sell up to 10,300 pounds of mixture per year, if it has the capacity.

Chemlab bought the existing Mix-in-a-Minute mixer 10 years at back at a price of Rs.120,000. It has a remaining life of five years. Its current market value is a paltry Rs.20,000, partly due to the competing modern mixers available in the market.

The mechanical mixer requires an electric motor. The current motor, which has a total life of 10 years, was purchased five years back for Rs.50,000. Market value of this motor now is only Rs.15,000, since it is almost useless to support any big operations by itself. However, if Rs.10,000 is spent on overhauling this motor now, it can be made to generate 15 horse-power (HP) for the next five years, after which it will be worthless. Note that the overhauling cost is an investment.

But, the problem is that, due to an increase in the utilization of the mixer, Mix-in-a-Minute needs a motor with 25 HP. Price quotations has been obtained by Chemlab for new motors with 25 HP. The best one has a cost of Rs.60,000. This would last for five years. Chemlab has to decide whether to go for this new motor or not.

But, what makes the above problem complicated is that Chemlab also has to decide now if it would replace Mix-in-a-Minute by the modern, fancy mixer called "Mixomatic". Mixomatic costs Rs.90,000 and has a five-year life. Mixomatic has a built-in motor of 10 HP; therefore, it would need only 15 HP from the external motor, which can be provided by Chemlab's existing motor if it is overhauled now.

The 10,000-pound-capacity Mixomatic is quite efficient. But, because of its fully automatic nature, wastage rate would increase to 30%. Moreover, because of the same reason, labor costs are going to decrease to 10% of sales. What should Chemlab do?



13. (COMPREHENSIVE) ABC Corporation is planning to raise capital to invest in a project requiring an outlay of Rs.25 million. The project is expected to generate perpetual after-tax-earnings of Rs.3 million per year, which is calculated on the basis of Rs.10 million revenue, 40% variable costs, Rs.1 million fixed operating costs, and a 40% corporate tax-rate.
The company intends to issue 10,000 ten-year 11%-annual-coupon bonds of Rs.1000 face-value. The bonds are expected to be rated AA, as were the 11% twenty-year bonds it issued seven years back. A similar company yesterday issued its ten-year AA bonds of Rs.5000 face-value and Rs.150 quarterly-coupon for Rs.5428.40. The firm also considered issuing 15-year bonds, but dropped the idea due to higher costs. At present, on a linearly increasing yield-curve, 15-year TBs are offering 9.8% vis-à-vis 9.5% for 10-year treasuries.
The company will raise the residual capital with the help of equity. It expects to give no dividends for the first five years. At the end of the sixth year, it expects to pay Rs.9 in dividends, increasing it by 10% every year and stabilizing it at Rs.14.50 after it reaches at or just below that level. A similar-risk stock, whose dividends have historically grown by an average of 12% per year to reach Rs.7.50 this year (just paid today), is now selling for Rs.336. The company has come up with a novel idea to market its shares. An investor can buy the share up-front or pay five equal annual installments of Rs.12.19 each. Some local banks are also willing to lend money to investors @12% to buy the shares; the investors need only pay Rs.7.84 per year till the loan is paid off.

a. Should the firm accept the project? Show your work step by step.
b. If an investor plans to buy the bond at the end of the third year, how much does it need to deposit per month (starting at the month-end) in an account giving 1% per month?
c. If an investor buys the bond today and sells it at the end of the year, what will be her current yield and capital-gains yield?
d. Will the newly issued bonds be more or less interest-rate-sensitive than the company’s existing bonds? Why?
e. You are planning to buy a five-year TB at the end of the tenth year from now. What price would you pay for this Rs.1000-par security, and what would be your ERR?
f. If an investor chooses the company’s installment-plan to buy the company’s shares, what rate would she be implicitly charged by the company?
g. If an investor opts for the loan option offered by the local banks to buy the firm’s shares, how much time would he take to pay off the loan? Is this option better or worse than the company’s installment-payment plan?
h. If you buy the stock today and sell it at the end of the year, what will be your (expected) dividend-yield and capital-gains-yield?


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

CID 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 FM
(somewhat in chronological order)


1. Divisional Cost of Capital and Corporate Cost of Capital
2. Cost of Debt, Cost of Equity, and the Weighted Average Cost of Capital (WACC)
3. Should WACC Account for Cost of Short-Term Debt?
4. What Determines the Equity-Beta?
5. Effect of Debt-Ratio on Firm Value and Equity Beta in a World Without Taxes
6. Effect of Debt-Ratio on Firm Value and Equity Beta in a World With Taxes
7. Computing Values when D is Given or when D/S Fraction is Given
8. Adjusted Cost-of-Capital (ACOC)
9. Beta of an Unlevered Firm, Beta of a Levered Firm, RRR of an Unlevered Firm, etc.
10. Capital Structure and Firm Value when there are Reorganization/Bankruptcy Costs
11. What Determines Beta of an Unlevered Firm? : The Role of Operating Leverage
12. Finding the Equity-Beta of a New Firm: Pricing an IPO
13. Effect of Dividend Policy on Equity Value
14. Alternatives to Dividend Payment: Share Repurchase et al
15. Two Issues for Capital Investment Decision: Project Acceptance and Comparison
16. NPV Rule for Project Comparison
17. IRR Rule for Project Comparison
18. NPV versus IRR in Project Acceptance Decision: Recap
19. NPV versus IRR in Project Preference Decision
20. Differences and Compatibility between NPV and IRR Rules
21. Determining the (Net) Cash Flow: Alternative Approaches
22. Interest and Other Tax Shields
23. Cash Flow Table
24. Incremental CF and Incremental NPV
25. Accounting for Sunk Cost
26. Accounting for Foregone Cash Flows
27. Accounting for Externalities
28. Accounting for Opportunity Cost
29. To Each, His Own: Using the Proper Discount Rate
30. A Capital Budgeting Problem: To Replace or Not?
31. Equivalent Annuity: Breakeven Point
32. Equivalent Annuity: Projects with Unequal Lives
33. Real Option: Option to Enter a Future Market
34. Real Option: Option to Abandon

FORMULAE

Banikanta Mishra CID
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: Hemanta Ranjan Deo on 12/12/2011 at 10:26 AM
Category: PGPRM-II Doctype: Document

...........................