3403 FIN - Exam 1 Topic Review - Fall 2008 Page 1
FIN 3403 - Exam 1 Topic Review - Fall 2008 Basically, the exam covers Chapters 1, 2, 5 (markets and institutions), but may also include other items that we have discussed in class as well as questions from the syllabus and the exam instructions (front page of the exam). The exam consists of 28 questions: 1 administrative, 10 true/false, and 15 problem-oriented. Section 1 - Administrative - 5 Points 1. Select the statement that is most correct. * A. I am in the correct room, and I have correctly filled in my Name, UF ID#, Group Number, and have signed the front of this exam, and I have correctly filled in and bubbled in my Name, UF ID# (left justified in the space marked either UF ID or SSN), Exam Code (Test Form Code), and Group Number (right justified in the space for Section Number: e.g., Group 3 = 0003; Group 25 = 0025, etc.) on my scantron sheet. Therefore I should receive 5 points. B. I am not in the correct room, and/or I have failed to correctly fill in my Name, UF ID#, Group Number, and sign the front of this exam, and/or I have failed to correctly fill in and bubble in my Name, UF ID# (left justified in the space marked either UF ID or SSN), Exam Code (Test Form Code), and/or Group Number (right justified in the space for Section Number: e.g., Group 3 = 0003; Group 25 = 0025, etc.) on my scantron sheet. Therefore I should not receive 5 points. This is the first question on all exams: remember that you must know your group number. Please make sure that you fill out the first page (cover) of your exam correctly, and make sure you bubble in Name, UF ID# (8 digits, left-justified), Exam Code (Form Code), and Group Number (right-justified in the space for Section Number) correctly. You also need to bubble in well and to erase well. Also note that room assignments for on-campus students are by Group number. You must go the room assigned to your group. If you do not go to the correct room, your exam will not be graded. Section 2 - True/False - 1 Point Each Students will get the same questions, but the order may change for each exam code. The general material to be covered is as follows:
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2. General question from the syllabus: exam dates. Monday, 9/15 Thursday, 10/16 Monday, 11/10 Monday, 12/15 at 8:00 P.M. 3. General question from the syllabus: rounding course grades 4. General question from the syllabus: how to contact the instructor/coordinator. [e-mail] 5. General question about exam instructions: stopping work when time is called. You must immediately stop or your exam will not be graded. Continue even longer, and you will be referred to Student Judicial Affairs. 6. General question about exam instructions: asking proctors to verify correctness of what you put on the front page of your exam or bubbled in on your scantron. See Items 8 and 9 on the front page of the exam.
7. The three ways to transfer capital. 8. Definition of different types of markets. 9. Closely held versus publicly owned corporations. 10. Partnerships versus proprietorships. 11. Agency problems / agency costs. Section 3 - Problems - 5 Points Each Some of the problems are rather straightforward, but you are reminded that I often switch equations around and ask you to solve for a different variable. Although a couple of these problems are challenging, I have covered the material required for each problem in class.
Note: You should take all calculations out to at least 6-9 decimal places and then round at the end as needed.
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12. Present value, and nominal rates versus periodic rates versus effective rates. iNOM = stated or quoted rate iPER = periodic rate = iNOM / m EAR = (1 + iPER)m - 1.0 iPER = (1 + EAR)1/m - 1.0 iNOM = (iPER)*(m) If m = 1, then iPER = iNOM = EAR If m > 1, then iPER < iNOM < EAR Make sure that you understand that the time period for the "effective" rate has to match the time period of the cash flows (the periodicity of the interest rate must match the periodicity of the cash flows). If the nominal rate is 8%, but compounding is quarterly, then the periodic rate is equal to the "effective quarterly rate". Other effective rates would include the following:
Timing of Cash Flow Calculation Rate Every 3 Months (1.02)1 - 1.0 2.00% Every 6 Months (1.02)2 - 1.0 4.40% Every 9 Months (1.02)3 - 1.0 6.12% Every 12 Months (1.02)4 - 1.0 8.24% Every 15 Months (1.02)5 - 1.0 10.41% Every 18 Months (1.02)6 - 1.0 12.62% Every 21 Months (1.02)7 - 1.0 14.87% Every 24 Months (1.02)8 - 1.0 17.17%
iNOM = stated or quoted rate iPER = periodic rate = iNOM / m Effective Rate for Cash Flow Period = (1 + iPER)n - 1.0 Where "n" is the number of periods between cash flows, not the number of compounding period per year. Continuous Compounding: EAR = e(r)*(t) - 1.0 PV = (FV) / (e(r)*(t)) = (FV)*e-(r)*(t)
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FV = (PV)*e(r)*(t) 13. Future value, and nominal rates versus periodic rates versus effective rates. See #12 above. 14. Time value of money, future value, ordinary annuities versus annuities due, and
effective interest rates. The top row of your calculator has buttons for 5 different variables. If you know the value of any 4 of these variables, the calculator will solve for the fifth.
Inputs Outputs
N I/YR PV PMT FV
One of the cash flows (either input or output) will be negative: one way to think of this is, as just one example, depositing money (a negative or outflow) getting versus cash back (a positive or inflow). __________ To find the present or future value of an annuity due, simply take the present or future value of an ordinary (regular) annuity and compound it forward one period. $100 $100 $100 $100 PVA FVA PVAD FVAD PVAD = PVA(1+i) FVAD = FVA(1+i) Regular annuities: PV is one period before the first payment. FV is as of the last payment Annuities Due: PV is as of the first payment FV is one period after the last payment
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These are the only 4 points in time that your calculator can solve for the value of an annuity. What determines whether you use BEGIN or END is when you want to determine the value, not whether you call it an ordinary annuity or an annuity due. Once you have calculated one of these four values, you can also then discount or compound to any other point in time. Keep in mind that when dealing with annuities you can also solve for N, I/YR, PV, PMT, or FV 15. Time value of money, present value, ordinary annuities versus annuities due, and effective interest rates. See Problem # 14 above. 16. Time value of money and the valuation of perpetuities. (1) P0 = D0(1+g)1/(1+r)1 + D0(1+g)2/(1+r)2 + ... + D0(1+g)-1/(1+r)-1 + D0(1+g)/(1+r) Now multiply both sides of Equation 1 by (1+r)/(1+g) to get Equation 2: (2) P0(1+r)/(1+g) = D0 + D0(1+g)1/(1+r)1 + ... + D0(1+g)-2/(1+r)-2 + D0(1+g)-1/(1+r)-1 Now subtract Equation 1 from Equation 2 P0(1+r)/(1+g) - P0 = D0 - D0(1+g)/(1+r) If we assume that the discount rate is greater than the growth rate, then the last term approaches 0 in the limit and can be discarded, which leaves us with: P0(1+r)/(1+g) - P0 = D0 Multiplying through we can rearrange terms as follows: P0(1+r) - P0(1+g) = D0(1+g) P0 - P0 + P0r -P0g = D0(1+g) = P0(r-g)
P0 = D0(1+g)/(r-g) = D1/(r-g) __________
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Note that if growth is zero, then D1 = D for all time periods and this reduces down to the equation for a perpetuity: P0 = D/r
__________
When using the perpetuity equation, we always find the value of the perpetuity one period before the first cash flow. Thus, if our first cash flow is at Year 13, we will find the value at Year 12: V12 = CF13 / r On the other hand, if our first cash flow takes place at Year 54, we will find the value at Year 53, etc.: V53 = CF54 / r Where "r" is the appropriate discount rate to apply to the cash flows. 17. Value of a perpetuity versus constant growth cash flow. See #16 above, especially P0 = D0(1+g)/(r-g) = D1/(r-g) 18. Installment loans and effective versus nominal rates of return. See #12 above. 19. Installment loans, loan amortization, and the loan amortization function on your calculator. See the PowerPoint slides at the end of Module 1 - Chapter 2. 20. Effective versus nominal rates of return. See #12 above. 21. Time value of money, installment loans, solving for payments, and solving for number of payments. 22. Non-annual cash flows and periodic versus effective versus nominal rates.
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See #12 above. 23. Complex cash flows. Make sure that you know how to use the Nj key when using the cash flow (CFj) registers on your calculator. There are only 14 CFj registers and the Nj key can be used to input like values without using multiple registers. An example: suppose you have cash flows of $100 in Years 1-3, nothing in Years 4-8, $200 in Years 9-12, an interest rate of 10 percent, and you want to find the value at Year 0. CFj 0 (place holder; must have single cash flow to start) CFj $100 (Year 1) Nj 3 (Year 1 through Year 3) CFj 0 (place holder: Year 4) Nj 5 (Year 4 through Year 8) CFj $200 (Year 9) Nj 4 (Year 9 through Year 12) I/YR 10 Solve for NPV = $544.44 __________
Once you have found PV it is then a simple process to convert to FV. As an example, assume that you wanted to find the value of the cash flows above as of Year 15: N = 15; I/YR = 10; PV = -544.44; Solve for FV = $2,274.26 24. Annuities as differences of perpetuities. Perpetuity 2 Perpetuity 1 0 1 N N+1 A/i A/i
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Assume that we have 2 perpetuities: Perpetuity 1 has payments in Periods 1 through , while Perpetuity 2 has payments in Periods N+1 through . If I subtract Perpetuity 2 from Perpetuity 1, I am left with an N-Period annuity. If both perpetuities are evaluated as of Period 0: A/i - (A/i)*(1/(1+i)N) = A [ 1/i - 1/i(1+i)N ] where [ 1/i - 1/i(1+i)N ] is the PVIFAi%,N Then what I have is the present value of an N-Period annuity evaluated as of Period 0. If both perpetuities are evaluate as of Period N: (A/i)*(1+i)N - A/i = A [ ((1+i)N - 1)/i ] where [ ((1+i)N - 1)/i ] is the FVIFAi%,N Then what I have is the future value of an N-Period annuity evaluated as of Period N. 25. Security valuation. The price that you should be willing to pay for a security is nothing more than the present value of the cash flows to be received. 26. Net present value and complex cash flows. See Problem #23 above. 27. Birthday problem and annuities. Note: The amount put in has to be equal to the amount taken out, as long as both are measured at the same point in time. Also, see Problems #14 and #23 above. 28. Birthday problem, annuities, and effective interest rates. Note: The amount put in has to be equal to the amount taken out, as long as both are measured at the same point in time. Also note that the time period for your effective interest rate must equal the time period for your cash flows. Also see Problems #12, #14, and #23 above.