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Note The following memorization cards are a compilation of various topics you will need to know for the CFP Exam. The cards cover the calculator, economics, and investment topics. You will want to use this format to add topics you need to memorize for the exam. Using the Formulas Assume a client wants to know the Future Value of an investment of $500 in an investment with an interest rate of 6%, which they will sell in 4 years. 1. First what is the Multiplication Factor? 2. What is the Future Value? FV = PV (1+i )n Using the (yx) Key 1.06  yx 4 =, you will see the factors is: 1.2625 If you multiply the $500 by the factor you get the following answer: $500 x 1.2625 = $631.25 You can check it with your calculator: 500 +/- PV, 4 n, 6 i, FV = $632.2385 Using TVM Tables Assume a client wants to know the Future Value of an investment of $500 in an investment with an interest rate of 6%, which they will sell in 4 years. First what is the Multiplication Factor? What is the Future Value? Future Value Table Interest Rate n 0 1 2 3 4 6 8 10 1 1.0000 1.0100 1.0200 1.0300 1.0400 1.0600 1.0800 1.1000 2 1.0000 1.0201 1.0404 1.0609 1.0816 1.1236 1.1664 1.2100 3 1.0000 1.0303 1.0612 1.0927 1.1249 1.1910 1.2597 1.3310 4 1.0000 1.0406 1.0824 1.1255 1.1699 1.2625 1.3605 1.4641 5 1.0000 1.0510 1.1041 1.1593 1.2167 1.3382 1.4693 1.6105 First remember to use the correct table. There are different tables for different types of problems. Here if you cross-reference the 6% and the 4 periods, you will see the factors is: 1.2625 If you multiply the $500 by the factor you get the following answer, $500 x 1.2625 = $631.25 You can check it with your calculator: 500 +/- PV, 4 n, 6 i, FV = $632.2385 Setting Up Your HP-10BII Calculator Setting the number of Decimals (to 4 places) SHIFT DISP 4 Setting the Compounding Periods Per Year To 1 1 SHIFT P/YR Setting Your Calculator to END Mode (for an Ordinary Annuity) SHIFT BEG/END Clearing the Memory SHIFT CLEAR ALL Using Your Financial Calculator Only think in terms of Number of Periods (Not years or quarters) You only need to take a small number of different factors into consideration from each TVM Problem, and plug them into your calculator: PV FV PMT n (Remember, this is not necessarily the number of years) i (Also, this is not necessarily the annual rate) Begin Cash Flow Keys Include (note that these keys are not used with the others and vice versa): CFj Nj NPV IRR For both problems you will need the: +/-, This key tells the calculator that money is going INTO the problem. The easy way to remember this is to: Always use the +/- key when you are taking money out of your pocket and putting it into the problem! Serial Interest Rate: (1 + Growth Rate ÷ 1 + Inflation Rate) – 1 x 100 = Things to REMBER!!! When Using Your Financial Calculator Always Clear Your Calculator before and after doing each problem! Pay attention to when cash flows are happening. Are they Annuity Due or Ordinary Annuity Problems? Then always set your calculator back to Ordinary Annuity when finished. For Semi-Annual, Quarterly, Monthly and DAILY problems you must adjust both the Number of Periods and the Interest Rate! All Bond problems (including Zero Coupon Bonds) are Semi-Annual based on $1,000 Par Value, unless told otherwise! Remember to correctly use the +/- key FV Single Sum Today, Bill purchased a large ring for $50,000. He expects it to increase in value at a rate of 15% compound Annually for the next 5 years. How much will his ring be worth at the end of the 5th year? Clear Your Calculator 50,000 +/- PV 15 i 5 n FV $100,567.86 Future Value of a Single Sum $1,000 is invested at 8% compounded annually for 3 years. What will its value be? Clear Your Calculator 1,000 +/- PV 8 I 3 n FV $1,259.71 Present Value of a Single Sum Client will receive $1,000 in 3 years. What will it be worth today if the opportunity cost is 8%. Clear Your Calculator 1,000 FV 8 i 3 n PV -793.83 Future Value Today Bob Jones purchased an investment grade gold coin for $50,000. He expects the coin to increase in value at a rate of 12% compounded annually for the next 5 years. How much will the coin be worth at the end of the fifth year if his expectations are correct? a. $89,792.82 b. $6691 1.28 c. $88,117.08 d. $89,542.38 e. None of the above 50,000 +/- PV 5 n 12 i 0 PMT FV = $88,117.08 Future Value A client invested $10,000 in an interest-bearing promissory note earning an 11% annual rate of interest compounded monthly. How much will the note be worth at the end of 7 years assuming all interest is reinvested at the 11% rate? a. $13,788.43 b. $20,762.60 c. $21,048.52 d. $21,522.04 e. None of the above 10,000 +/- PV 11 12 = 0.91666 i 7 x 12 = 84 n 0 PMT FV = $21,522.04 Future Value Bill Barrett purchased $60,000 worth of silver coins 8 years ago. The coins have appreciated 7.5% compounded annually over the last 8 years. How much are the coins worth today? a. $107,008.67 b. $102,829.46 c. $99,719.03 d. $99,542.95 e. None of the above 60,000 +/- PV 8 n 7.5 i 0 PMT FV = $107,008.67 Present Value Sarah Attaya wants to give her daughter $25,000 in 8 years to start her own business. How much should she invest today at an annual interest rate of 8% compounded annually to have $25,000 in 8 years? a. $12,802.95 b. $13,506.72 c. $13,347.70 d. $13,210.34 e. None of the above 25,000 +/- FV 8 n 8 i 0 PMT PV = $13,506.72 Present Value Cassie expects to receive $75,000 from a trust fund in 6 years. What is the current value of this fund if it is discounted at 9% compounded semiannually? a. $57,592.18 b. $44,720.05 c. $44,224.79 d. $42,794.31 e. None of the above 75,000 +/- FV 9 2 = 4.5 i 6 x 2 = 12 n 0 PMT PV = $44,224.79 Present Value Bill McDowell expects to receive $75,000 in 5 years. His opportunity cost is 10% compounded monthly. What is this sum worth to Bill today? a. $45,584.14 b. $46,043.49 c. $46,569.10 d. $48,542.09 e. None of the above 75,000 +/- FV 10 12 = 0.8333 i 5 x 12 = 60 n 0 PMT PV = $45,584.14 Present Value Mary Sue wants to accumulate $57,000 in 8.5 years to purchase a boat. She expects an annual rate of return of 10.5% compounded quarterly. How much does Mary Sue need to invest today to meet her goal? a. $23,529.87 b. $23,619.30 c. $23,883.56 d. $24,364.33 e. None of the above 57,000 +/- FV 10.5 4 = 2.625 i 8.5 x 4 = 34 n 0 PMT PV = $23,619.30 Present Value of a Single Sum (more frequent compounding) Client will receive $1,000 in 5 years. What will it be worth today, if the opportunity cost is 8% compounded monthly. Clear Your Calculator 1,000 FV 8 ÷ 12 = i 5 x 12 = n PV $671.21 Future Value Your Client found $12,000 on the sidewalk and wants to invest it. He can get 10% compounded annually on his money for the first 4 years, 12% for the next 3 years and 15% for the last 5 years. How much will Client have after 4 years, then 7 years, and last 12 years? Using TVM Tables Table (1.46410) x 12,000 Table (1.46410) x 12,000 Table (1.40493) x 17,569 = 24,683 Table (1.46410) x 12,000 Table (1.40493) x 17,569 = 24,683 Table (2.01136) x 24,683 = 49,646.398 Using a Financial Calculator Clear Your Calculator 12,000 +/- PV 10 i 4 n FV $17,569.20 17,569 +/- PV 12 i 3 n FV $24,683 24,683 +/- PV 15 i 5 n FV $49,646.33 Future Value of Annuities (more frequent compounding) Your Client Barney Phife invests $500 at the END of each 6 month period for 3 years. He can get 8% compound semi-annually. What will be the value 3 years? Clear Your Calculator (Not BGN) 500 +/- PMT 3 x 2 = n 8 ÷ 2 = i FV $3,316.49 FV of Single Sums and Annuities An investor deposits $20,000 into a fund. Also another $2,500, each year there-after. What will be the value in 8 years at 9% annually? Clear Your Calculator 20,000 +/- PV 2,500 +/- PMT 9 i 8 n FV $67,422.44 The initial deposit is treated as a Single Sum, then annual payments are treated as an Annuity. Future Value of an Annuity Client invests $1,000 at the Beginning of each of the next 3 years, and can earn 8% annually. What will be the value in 3 years? Clear Your Calculator 1,000 +/- PMT 8 I 3 n FV $3,506.11 PV of Single Sums and Annuities A client would like to have $300,000 in 10 years. He can invest $10,000 at the END of each year, in an account at 8% annually. What initial lump sum is required additionally now, to attain his goal? Clear Your Calculator 300,000 FV 10,000 +/- PMT 8 i 10 n PV $71,857.23 Present Value of an Annuity Client expects payments of $1,000 at the End of each of the next 3 years, if opportunity costs are 8% annually. What is the Annuity worth today? Clear Your Calculator (Not BGN) 1,000 PMT 8 I 3 n PV $-2577.10 Future Value of an Ordinary Annuity Client Invests $100 at the end of each year for 5 years, with a 10% interest rate. TVM Table: (6.10510) x 100 = $610.51 100 +/- PMT 10 i 5 n FV $610.51 Future Value of an Annuity Client Invests $100 at the Beginning of each year for 5 years, with a 10% interest rate. TVM Table: (6.71561) x 100 = $671.56 Set Calculator to: BGN 100 +/- PMT 10 i 5 n FV $671.56 Compounding Periods of Single Sums/Annuities A client wants to save $125,000. Has $26,000 to invest now, and can save $10,000 at the END of each year. He can get 10% annually. How many years will he have to save? Clear Your Calculator 125,000 FV 26,000 +/- PV 10,000 +/- PMT 10 i n 6.08 years Number of Compounding Periods Client has $1000 to invest. He wants $3670. He can get 8%, how many years will it take. 1,000 +/- PV 3670 FV 8 i n 16.89 years Number of Compounding Periods (More Frequent Compounding) Client has $1000 to invest. He wants $3670. He can get 8% compounded semi-annually, how many years will it take. 1,000 +/- PV 3,670 FV 8 ÷ 2 = i n 33.15 ÷ 2 16.58 years Number of Compounding Periods Joe purchased 10 shares of an aggressive growth mutual fund at $90 per share 7 years ago. Today he sold all 10 shares for $4,500. What was his average annual compound rate of return on this investment before tax? a. 17.46% b. 19.58% c. 21 .73% d. 25.85% e. None of the above 900 +/- PV 4,500 FV 7 n 0 PMT i = 25.8499% Number of Compounding Periods John borrowed $800 from his father to purchase a mountain bike. John paid back $1200 to his father at the end of 5 years. What was the average annual compound rate of interest on John’s loan from his father? a. 11.5646% b. 8.4472% c. 7.7892% d. 5.1990% e. None of the above B 800 +/- PV 1,200 FV 5 n 0 PMT i = 8.4472% Number of Compounding Periods Susan Jones purchased a zero-coupon bond 6.5 years ago for $525. If the bond matures today and the face value is $1,000, what is the average annual compound rate of return (calculated semiannually) that Susan realized on her investment? a. 11.3372% b. 10.5713% c. 10.400% d. 10.163% e. None of the above 525 +/- PV 1,000 FV 6.5 x 2 = 13 n 0 PMT i = 5.0815 Annual Rate of Return = 5.0815 x 2 = 10.163% Present Value of a Serial Payment Client wants to receive an equivalent of $10,000 in today’s dollars at the BEGINNING of each of the next 4 years. Inflation will average 5%, and he can get 8% compounded annually after tax return. He wants to invest a lump sum today to fund this need and dissipate the funds at the beginning of the 4th year, to maintain a constant standard of living. Clear Your Calculator BGN 1.08 ÷ 1.05 - 1 x 100 = i 10,000 PMT 4 n PV $38,363.98 NPV Your clients want to have $10,000 at the end of each of the next 2 years and $25,000 at the end of the 3rd year to provide for travel. Assume that the clients will use lump-sum assets to achieve this goal. What is the amount that must be deposited in an investment returning 7.5% annually to have $10,000 available at the end of each of the next 2 years and $25,000 available at the end of the third year. 0 CF0 10,000 CFj 10,000 CFj 25,000 CFj 7.5 i NPV $38,079.66 The rate of return provided is on an after-tax basis. Unless otherwise noted, both principal and earnings are used to achieve financial goals. NPV of Unequal Cash Flows What is the Present Value of an investment, for which the following cash flows are expected assuming the clients required annual rate of return for an investment at this level of risk is 10.5%? Cash Inflow Cash Outflow End of year 1: $100 0 End of year 2: 0 $50 +/- End of year 3: 0 $50 +/- End of year 4: 0 $50 +/- End of year 5: 0 0 End of year 6: $300 0 Clear Your Calculator 0 CF0 100 CFj 50 +/- CFj 50 +/- CFj 50 +/- CFj 0 CFj 300 CFj 10.5 i NPV Present Value, or the price that will allow a 10.5% return on this investment, is $143.75 Uneven Cash Flows Your client is considering purchasing a real estate rental property. Her Required Rate of Return for this investment is 10.5% per year. (She can invest her money elsewhere, at a equal level of risk, and earn 10.5%). So, she wants to know how much the property should cost for her to earn an average annual compound return of 10.5%. She predicts the following net cash flows. If those cash flows occur, what should your client pay for the property (NPV) to earn a 10.5% average annual compounded return IRR? 0 CF0 15,000 +/- CFi 0 CFj 0 CFj 0 CFj 15,000 + 175,000 = CFi 10.5 i NPV 101,755.31778 or $101,755.32 Your client is still considering purchasing the real estate rental property. She submitted a bid of $100,000 based on the results of the last calculation. The seller, however, did not accept and countered with an offer to sell at $110,000. If your client pays $110,000 for the property and expects the same cash flows, What will be the IRR for this investment? 110,000 +/- CF0 15,000 +/- CFj 0 CFj 0 CFj 0 CFj 15,000 + 175,000 = CFj IRR 8.9595 or 8.95% Price (Or Intrinsic Value) Of A Bond What is the price (or Intrinsic Value) of a bond with $1,000 face value, a 10% coupon, and 3 years to maturity, if comparable bonds of the same maturity and grade are yielding 11.5%? Coupon: [1,000 x .10] 2 = 50 0 CF0 50 CFj 50 CFj 50 CFj 50 CFj 50 CFj 1,000 + 50 = CFi 11.5 ÷ 2 = i NPV 962.8286 or 962.83 NPV What is the PV of an investment, for which the following cash flows are expected assuming the client's required annual rate of return for an investment at this level of risk is 11%? Cash Inflow Cash Outflow End of year 1: $50 0 End of year 2: $60 0 End of year 3: 0 $100 End of year 4: 0 0 End of year 5: $600 0 0 CF0 50 CFj 60 CFj 100 +/- CFj 0 CFj 600 CFj 11 i NPV 376.69 Present Value Your client's goal is to have $200,000 in 7 years to buy a partnership interest in her father's veterinary clinic. One plan your client is considering is to use lump-sum assets only and invest in 2 different securities that have different rates of return. If she deposits $100,000 into an investment returning 7% annually, what is the amount of the additional lump-sum deposit that would be required in an investment returning 9% annually to accumulate a total of $200,000 in 7 years? 7 n 7 i 100,000 +/- PV FV - 200000 = +/- FV 9 i PV = 21,565 The rate of return provided is on an after-tax basis. Unless otherwise noted, both principal and earnings are used to achieve financial goals. Annuity Due Your client's goal is to have $200,000 in 7 years to buy a partnership interest in her father's veterinary clinic. One plan your client is considering to achieve the goal is to invest $11,000 at the beginning of each of the next 7 years, starting today, in an investment returning 7% annually. If your client decides to make these annual deposits, what is the size of the additional annual payments that would be required, starting today, in an investment returning 9% to accumulate a total of $200,000 in 7 years? Clear Your Calculator BGN 11000 +/- PMT 7 n 7 i FV - 200000 = FV 7 n 9 i PMT = $9,786.35 The rate of return provided is on an after-tax basis. Unless otherwise noted, both principal and earnings are used to achieve financial goals. Lump Sum with a Annuity Due Your client decides to use both a lump-sum deposit and periodic payments to achieve her goal of $200,000 in 7 years. She will use a onetime lump-sum amount of $66,900, and, in addition make annual payments, starting today, to achieve her goal. What annual deposit will she need to make in an investment with an annual return of 8.5%? Clear Your Calculator BGN Long Method Short Method 66,900 +/- PV 7 n 8.5 i FV = $118,422.52 118,422.52 - 200000 = FV 0 PV 7 n 8.5 i PMT = $8,298 66,900 +/- PV 7 n 8.5 i 200,000 FV PMT = $8,298 The rate of return provided is on an after-tax basis. Unless otherwise noted, both principal and earnings are used to achieve financial goals. 0 1 2 3 4 5 6 200,000 7 66,900 118,422 Present Value Assume your clients would consider receiving $6,800 every 6 months during the 3 years, with the 1st payment to be received 6 months from today. Use a 6% annual return in calculating the amount that must be deposited today to provide for these cash flows. 0 CF0 6,800 CFj 6,800 CFj 6,800 CFj 6,800 CFj 6,800 CFj 6,800 CFj 6 2 = i NPV 6,800 PMT 3 x 2 = n 6 2 = i PV = $36,836.90 Annuity Due Your client wants to have $90,000 in 5 years to buy a vacation condominium. If he deposits $5,000 at the beginning of each of the next 5 years, starting today, into an investment returning 8% annually, what is the size of the additional annual payments that would be required into an investment returning 7% annually to reach his goal? Clear Your Calculator BGN 5000 +/- PMT 5 n 8 i FV - 90000 = FV 7 i PMT = $9,478 Present Value Your client's goal is to accumulate $200,000 in 5 years to build a new home. In addition, he wants to retire in 4 years and receive $2,400 at the beginning of each month for 1 year. At the end of that year, he will begin receiving pension benefits and no longer will need the $2,400 monthly payments. Assuming a 7% rate of return, what lump sum must he deposit today to meet these goals? Illustration of cash flows: 12 PMT’s 2,400 $200,000 0 1 2 3 1 4 2 3 4 5 6 7 8 9 10 11 12 5 200,000 FV 5 n 7 i PV = 142,597 BGN 2,400 PMT 12 n 7 12 = I PV = 27,899 27,899 FV 4 n 7 i PV = 21,284 142,597 + 21,284 = $163,881 IRR What is the IRR earned on a 2-year investment in a mutual fund that paid $25 at the end of each quarter for the 1st 4 quarters; then paid $30 at the end of each quarter for the 2nd year. If the initial investment was $7,000, and the account value at the time of final quarterly distribution was $10,500? (The quarterly dividends were NOT reinvested) 25 25 25 25 30 30 30 30 10,500 30 0 7,000 1 2 3 4 5 6 7 8 7,000 +/- CF0 25 CFj 25 CFj 25 CFj 25 CFj 30 CFj 30 CFj 30 CFj 10,500 + 30 = CFj IRR x 4 = 22.1088 or 22.11% Rate of Return Assume your clients can invest $36,000 today to meet their goal of $10,000 at the end of each of the next 2 years and $25,000 at the end of the 3rd year. What average annual rate of return would they have to earn on an investment to achieve their cash flow requirements? 36,000 +/- CF0 10,000 CFi 10,000 CFi 25,000 CFi IRR = 10.1860 or 10.19% The rate of return provided is on an after-tax basis. Unless otherwise noted, both principal and earnings are used to achieve financial goals. After-Tax Rate of Return A Certificate of Deposit (CD), currently valued at $4,000 is expected to earn an interest rate of 6% annually. The client will pay a 28% tax on the reinvested earnings each year. What is the After-Tax Rate for this problem? (1 - Tax Rate) x Rate of Return (1 - .28) x 6% (.72) x 6 = 4.32% What will its FV be in 31 years? 4,000 +/- PV 4.32 i 31 n FV = $14,840.718 After-Tax Rate of Return To convert a Taxable Rate to a Non-Taxable Rate (After-Tax Rate of Return): Non-Taxable Equivalent = (1 - Tax Rate) x Rate of Return To convert a Non-Taxable Rate of Return to a Taxable Rate of Return? Taxable Equivalent = Rate of Return (1 - Tax Rate) Rate of Return of Single Sums/Annuities 6 years ago, a client invested $5,000 in a fund. He made additional investments of $300 at the END of each year. Yesterday the client had a balance of $8,500. What was his rate of return? 5,000 $300 $300 $300 $300 $300 $300 1 2 3 4 5 6 8,500 5,000 +/- PV 300 +/- PMT 8,500 FV 6 n i 4.44% IRR of Unequal Cash Flows What is the average compound rate of return earned from investing an antique chair that was bought 6 years ago for $300, was then repaired at the end of the 2nd year at a cost of $150, then just sold for $850? 300 +/- 150 +/- 1 2 3 4 5 6 850 300 +/- CF0 0 CFj 150 +/- CFj 0 CFj 0 CFj 0 CFj 850 CFj IRR 12.54% IRR of Unequal Cash Flows What is the IRR earned on a 3 year fund that pays quarterly distributions. Distributions are not reinvested back into the fund. The initial investment was $12,000 and the value of the fund at the time of the last quarterly distribution was $16,500? 12,000 1 Q1 50 Q2 50 Q3 50 Q4 50 2 Q1 57 Q2 57 Q3 57 Q4 57 3 Q1 60 Q2 60 Q3 60 Q4 60 16,500 12,000 +/- CF0 50 CFj 4 Nj 57 CFj 4 Nj 60 CFj 3 Nj 16,500 + 60 Cfj IRR x 4 = 12.36% Note: Multiple Cash Flows are illustrated on the HP 10B Interest Rate Client has $1000, he wants it to be $1470 in 5 years. What annual rate will be needed. 1,000 +/- PV 1,470 FV 5 n i 8.01% Client has $1000, he wants it to be $1470 in 5 years. What annual rate will be needed, if it is compounded quarterly? (More Frequent Compounding) 1,000 +/- PV 1,470 FV 5 x 4 = n i (1.94) x 4 = 7.78 Rate of Return An investor bought a stock for $28 and sold it for $48 after 4 years. What is the stock's Holding Period Return? 48 - 28 = 20 28 = .7142 HPR= 20 = .7142 = 71.42% 28 HPR= Sales Price + Income - Purchase Price Purchase Price What is the stock's Average Annual Compound Rate of Return? IRR = 14.43% 28 +/- CF0 0 CFj 0 CFj 0 CFj 48 CFj IRR 14.4249% 28 +/- PV 48 FV 4 n i 14.4249% Rate of Return Assume an investor purchased a stock for $30, sold it for $45 after 6 years, and collected an annual dividend of $1.75 during the 6-year period. What was the HPR and IRR on this investment? HPR= Sales Price + Income - Purchase Price Purchase Price HPR= 45 + 10.50 - 30 30 25.50 30 = .85 or 85% 30 +/- CF0 1.75 CFj 5 Nj 45 + 1.75 = CFj IRR 11.99 or 12% Rate of Return Your client invested $12,000 in the Achievement Mutual Fund 5 years ago. All dividends and disbursements paid to the client from the fund have been reinvested directly back into the fund. The client instructed the fund to reinvest all payments, so they were never sent to the client. If this mutual fund investment is completely liquidated today for $19,000, What was the internal rate of return on this investment? 12,000 +/- CF0 0 CFj 0 CFj 0 CFj 0 CFj 19,000 CFj IRR = 9.63% (or) 12,000 +/- PV 19,000 FV 5 n i = 9.63% Rate of Return A bond has a market price of $875. The bond pays 12% coupon interest semiannually. The bond will mature in 7 years and will pay a face value of $1,000. What is the yield to maturity or internal rate of return for this bond? 875 +/- CF0 60 CFj 13 Nj 1000 + 60 = CFj IRR 7.4698 x 2 = 14.939 or 14.94% (or) 7 x 2 = n 875 +/- PV 1,000 FV x .12 2 = PMT i x 2 = 14.94% IRR Your client has invested in a mutual fund by using a Dollar-cost Averaging Plan. Purchases of $2,000 each have been made at the Beginning of each year for 5 years. The fund is now (at the end of the 5th year) worth $13,000. What is the IRR for this Investment? BGN 2,000 +/- CFj 2,000 +/- CFj 2,000 +/- CFj 2,000 +/- CFj 2,000 +/- CFj 13,000 CFj IRR 8.8768 or 8.88% IRR is the average annual compound return. Some years could have earned more than 8.88% & some could have earned less. IRR Investments do not always have equal periodic payments. For example, an investor wants to know what average annual return can be expected for a real estate investment. The cash flows that are expected for each year that the property will be owned have been estimated. Negative cash flows, such as maintenance, insurance, & taxes, have been subtracted from positive cash flows, such as rent, for each of 5 years to get a net amount for each year. The purchase price of the property is $125,000 & the client expects that the property could be sold at the end of 5 years for $175,000. Net cash flows for each year are as follows: End of Year 1 - 15,000 End of Year 2 - 7,000 End of Year 3 + 5,000 End of Year 4 + 12,000 End of Year 5 + 15,000 Note: The last cash flow occurs at the same time that the client predicts that the property could be sold for $175,000. Therefore, the total cash flow for the end of Year 5 is $175,000 + $15,000 = $190,000. If cash flows occur as expected, What would the IRR be for this investment? 125,000 +/- CFi 15,000 +/- CFi 7,000 +/- CFi 5,000 CFi 12,000 CFi 175,000 + 15,000 = CFi IRR 7.5544 or 7.55% IRR or Yield To Maturity What is the IRR (or yield to maturity) earned on an investment in a bond with a $1,000 face value, a price of $966, a 10% coupon, and 3 years to maturity? 966 +/- 1 50 2 50 3 50 4 50 5 50 6 50 1,000 Coupon: 1,000 x .10 = 100 2 = 50 966 +/- CF0 50 CFj 50 CFj 50 CFj 50 CFj 50 CFj 1,000 + 50 = CFj IRR x 2 = 11.369 or 11.37% IRR (or Yield To Maturity) What is the IRR (or Yield to Maturity) earned on an investment in a Zero-coupon bond with a $1,000 face value, a price of $746 and 3 years to maturity? Note: Zero-Coupon bonds have no coupon interest payments. However, semiannual compounding is still used. 746 +/- CF0 0 CFj 0 CFj 0 CFj 0 CFj 0 CFj 1,000 CFj IRR 5.0051 x 2 = 10.01% 746 +/- PV 1,000 FV 3 n i Intrinsic Value (or price) of a Zero-Coupon Bond What is the Intrinsic Value (or price) of a Zero-Coupon Bond with a $1,000 face value, yield to maturity of 10.01% and 3 years to maturity? Note: Zero-Coupon bonds have no coupon interest payments. However, semiannual compounding is still used. CF0 0 CFj 0 CFj 0 CFj 0 CFj 0 CFj 1,000 CFj 10.01 ÷ 2 = i NPV 746.0022 or $746.00 (or) 1,000 FV 3 x 2 = n 10.01 2 = i PV IRR What is the IRR that has been earned from investing in a coin collection that was purchased for $1,200 6 years ago, was expanded at the end of the 3rd year at a cost of $400, and has just sold for $2,500? $2500 0 $1200 1 2 3 $400 4 5 6 1,200 +/- CF0 0 CFj 0 CFj 400 +/- CFj 0 CFj 0 CFj 2,500 CFi IRR 8.7545 or 8.75% Periodic Payments of Singles Sums/Annuities A client wants $90,000 in 7 years. She can invest $32,000 today at 11% annually. She plans to make additional payments at the END of each year. What periodic payment will be needed to meet her goal? Clear Your Calculator 90,000 FV 32,000 +/- PV 7 n 11 i PMT $2,408.49 Serial Payment for a Future Sum Client wants to retire in 5 years. In today’s dollars he will need $100,000 in 5 years. He assumes inflation will be 4% and he can get 7% on after-tax investments. What series of payments will add up to $121,665.29 in 5 years, ($121,665.29 = FV of $100,000 today)? Clear Your Calculator 1.07 ÷ 1.04 - 1 x 100 = i 100,000 FV 5 n PMT 18,878.96 x 1.04 = $19,634.11 Periodic Payment or Receipt Client wants to buy a $10,000 auto, financed at 12% annually for 4 years. What payment is required at the END of each of the 4 years? Clear Your Calculator 10,000 PV 4 n 12 i PMT $-3292.34 Periodic Payment or Receipt (more frequent compounding) Client borrows $10,000. The loan is repaid over 4 years at 12% annually compounded monthly. What are the monthly payments? Clear Your Calculator 10,000 PV 12 ÷ 12 = i 4 x 12 = n PMT $-263.34 Periodic Payment/Receipt (frequent compounding) Client wants $10,000 in 4 years. He can earn 12% annual compounded monthly. He wants to put money away at the BEGINNING of each month to meet his goal. What monthly payment is required? Clear Your Calculator BGN 10,000 FV 12 x 12 = i 4 x 12 = n PMT $-161.72 Mortgage Payment John Johnson recently purchased a house for $350,000. He made a down payment of 20% and financed the balance over 30 years at 7%. How much is John’s monthly payment? Clear Your Calculator 350,000 x .8 = PV 30 x 12 = N 7 12 = I/YR 0 FV PMT $-1,862.847 Mortgage Payment Nathan McCoy made an offered of $370,000 to purchased a house. He made a down payment of 5% and financed the balance over 15 years at 5.5%. How much is John’s monthly payment? Clear Your Calculator 370,000 x .95 = PV 15 x 12 = N 5.5 12 = I/YR 0 FV PMT $-2,872.05 TVM Calculation Jennie Phillips had a goal of buying a cabin in Wisconsin when she retires. The size and type of cabin she wants on 2 acres of land costs $85,000 today. She has graduate from a highly esteemed college today with a 4.0 GPA, therefore she believes she can get a good job and achieve her goal. If inflation averages 3% and she will retire in 40 years, how much will this cabin cost her in 40 years? Clear Your Calculator 85,000 PV 40 = N 3 = I/YR FV $-493,829 TVM Calculation Blake Millers grandfather has just retired from farming the fall of 2002 after harvesting his last crop, he gave Blake his entire farm because Blake has been such a great grandson. Blake’s grandfather paid $7,500 for the farm in 1941. Today the gift was valued at 350,000 by the IRS. Blake wonders what his grandfather’s rate of return was on his original investment of $7,500? Clear Your Calculator 7,500 PV 61 = N 350,000 = FV I/YR 6.5% TVM Calculation David Schnorr, a very intelligent young man who has just become Mr. Minnesota. Coincidentally 5 young ladies have asked him to be their husband. While he is smart enough to wait for Ms. Right to come along later who loves him for his wonderful personality, he knows the most affluent young lady Darci has a net worth of $700,000 and invests expecting 8% over the long term. On the other hand, one of the others Tanya has a net worth of only $550,000 but invests more aggressively and should receive a market return of 10%. He wonders, which of the 2 ladies will have the highest net worth simply based on today’s information, in 40 years? While he thinks about this very often, he says it has nothing to do with agreeing to the offers. (at that’s his story and he’s sticking to it) Clear Your Calculator Darci Tanya 700,000 +/- PV 40 N 8 I/YR FV $15,207,165 550,000 +/- PV 40 N 10 I/YR FV $24,892,590 David is Still Thinking! Continuous Compounding FV State Bank offers compounding daily at 6% and National Bank offers continuos compounding at 5.9%. You deposit $1,000 into each bank. After 2 years, you withdraw the funds. What is the difference in the amount you get from each bank? State Bank National Bank 1000 +/- PV 6 365 = i 2 x 365 = n FV = 1,127.49 0.059 x 2 = ex x 1000 = 1,125.24 1,127.49 - 1,125.24 = 2 Continuous Compounding PV In 6 years, a client will receive $100,000. If the account earns a 9% rate compounded continuously, how much is that account worth today? 0.09 x 6 = ex = 1.7160 100,000 1.7160 = $58,275.06 Mike Kibley purchased an Oriental rug for $8,000. Today, he sold the rug for $15,000. Mike determined the average annual compound rate of return on the rug was 12%. Approximately how many years did Mike own the rug? (rounded to the nearest .0000) a. 6.8452 b. 5.5468 c. 4.5337 d. 5.8451 e. 6.0000 8,000 +/- PV 15,000 FV 12 i 0 PMT n = 5.5468 Note 1: Anytime you calculate for N (term) using a HPI2C you may need to find the answer by trial and error. The HPI2C calculator rounds to the nearest integer when calculating N, and therefore, your answer is not always precise when calculating the term. You must then take what you have and find the exact answer by trial and error methods. The HP Will give you 5.533. Note 2: It you are using an HPI2C and use correct N of 5.5468 the F’! will be $15,023.84, which, of course, looks incorrect. The error is in the way the HP works. )f you are using a HPIOB, HPI7BII, Sharp EL-733A, or TIBAII Plus you will get 5.5468 (the correct N). You can mathematically prove this answer by taking 1.12 raised to the 5.5468 power and then multiply by $8,000 to get $15,000.04. Today, Raul put all of his cash into an account earning an annual interest rate of 9% compounded monthly. Assuming he makes no withdrawals or additions into this account, approximately how many years must Raul wait to double his money? (rounded to the nearest .00) a. 7.75 b. 8.25 c. 8.75 d. 7.25 e. 8.00 1 +/- PV 2 FV 9 12 = 0.75 i 0 PMT n 12 = 7.75 HP12C = 7.73 Other Calculators Clarence Cushman has been investing $1,000 at the end of each year for the past 15 years. How much has accumulated assuming he has earned 10.5% compounded annually on his investment? a. $20,303.72 b. $23,349.28 c. $33,060.04 d. $36,531.34 e. None of the above 0 PV PMTOA +/- 1,000 10.5 i 15 n FVOA = $33,060.04 Christine Valico has been dollar-cost averaging into a mutual fund by investing $2,000 at the end of every quarter for the past 7 years. She has been earning an average annual compound return of 11% compounded quarterly on this investment How much is the fund worth today? a. $78,266.19 b. $81,170.29 c. $82,721.95 d. $84,996.80 e. $86,875.47 0 PV PMTOA +/- 2,000 11 / 4 = i 7 x 4 = n FVOA = $82,721.95 Bill Russell has been investing $3,000 at the beginning of each year for the past 15 years. How much has accumulated assuming he has earned 8% compounded annually on his investment? a. $91,896.04 b. $87,972.85 c. $84,696.81 d. $81,456.34 e. None of the above 0 PV PMTAD +/- 3,000 8 i 15 n FVAD = $87,972.85 Chrissy Nables has been Dollar-Cost Averaging in a mutual fund by investing $2,000 at the beginning of every quarter for the past 7 years. She has been earning an average annual compound return of 11% compounded quarterly on this investment. How much is the fund worth today? a. $82,721.95 b. $93,902.42 c. $91,389.22 d. $84,996.80 e. None of the above Begin 0 PV PMTAD +/- 2,000 11 4 = i 7 x 4 = n FVAD = $84,996.80 Stuart Wood expects to receive $5,000 at the end of each of the next 4 years. His opportunity cost is 14% compounded annually. What is this sum worth to Stuart today? a. $14,568.56 b. $16,608.16 c. $19,568.56 d. $17,165.41 e. None of the above PMTOA 5,000 14 i 4 n FV 0 PVOA ($14,568.56) Tim, injured in an automobile accident, won a judgment that provides him $1,500 at the end of each 6-month period over the next 6 years. If the escrow account that holds Tim's settlement award earns an average annual rate of 11% compounded semiannually, how much was the defendant initially required to pay Tim to compensate him for his injuries? a. $6,345.81 b. $7,043.85 c. $12,927.78 d. $13,638.80 e. None of the above PMTOA 1,500 11 12 = i 6 x 2 = n FV = 0 PVOA = ($12,927.78) Jane wants to withdraw $4,000 at the beginning of each year for the next 7 years. She expects to earn 10.5% compounded annually on her investment. What lump sum should Jane deposit today? a. $19,157.21 b. $18,667.20 c. $20,627.25 d. $21,168.72 e. None of the above PMTOA 4,000 10.5 i 7 n FV 0 PVOA ($21,168.72) Connie wants to withdraw $1,200 at the beginning of each month for the next 5 years. She expects to earn 10% compounded monthly on her investments. What lump sum should Connie deposit today? a. $56,478.44 b. $56,949.10 c. $58,630.51 d. $59,119.10 e. None of the above PMTAD 1,200 10 12 = i 5 x 12 = n FV = 0 PVAD = ($56,949.10) Gary received an inheritance of $200,000. He wants to withdraw equal periodic payments at the beginning of each month for the next 5 years. He expects to earn 12% annual interest, compounded monthly on his investments. How much can he receive each month? a. $4,404.84 b. $4,448.89 c. $49,537.45 d. $55,481.95 e. None of the above PV = 200,000 12 12 = i 5 x 12 = n FV = 0 PMTAD = ($4,404.84) Eugene wants to purchase a fishing camp in 5 years for $60,000. What periodic payment should he invest at the beginning of each quarter to attain the goal if he can earn 10.5% annual interest, compounded quarterly on investments? a. $2,319.42 b. $2,260.09 c. $8,805.91 d. $9,730.53 e. None of the above FV = 60,000 10.5 4 = i 5 x 20 = n PV = 0 PMTAD = ($2,260.09) Tina wants to purchase a home 6 years from now. She anticipates spending $150,000. To attain this goal, how much should Tine invest at the end of each 6-month period if she expects to earn a 12% annual compound rate of return, compounded semiannually, on her investments? a. $18,483.86 b. $16,503.44 c. $8,891.55 d. $8,388.26 e. None of the above FV = 150,000 15 2 = i 6 x 2 = n PV = 0 PMTOA = ($8,891.55) Janet purchased a car for $19,500. She is financing the auto at 11% annual interest rate, compounded monthly for 3 years. What payment is required at the end of each month to finance Janet’s car? a. $606.71 b. $638.40 c. $632.61 d. $684.97 e. None of the above. PV = 19,500 11 12 = i 3 x 12 = n FV = 0 PMTOA = ($638.40) Shane estimates his opportunity cost on investments at 10.5% compounded annually. Which one of the following is the best investment opportunity for Shane? a. To receive $45,000 today b. To receive $120,000 at the end of 10 years c. To receive $5,500 at the beginning of each year for 15 years d. To receive $5,500 at the end of each year for 19 years e. To receive $5,750 at the end of each year for 17 years A Option A Option B Option C Option D Option E PV = $45,000 FV = 120,000 10.5 = i 10 = n 0 PMT PV = $44,213.86 PMTAD 5,500 10.5 = i 15 = n FV = 0 PVAD ($44,935.97) PMTOA 5,500 10.5 = i 19 = n FV = 0 PVOA ($44,523.35) PMTOA 5,750 10.5 = i 17 = n FV = 0 PVOA ($44,731.47) Richard estimates his opportunity cost on investments at 9% compounded annually, which one of the following is the best investment opportunity? a. To receive $100,000 today b. To receive $310,000 at the end of 15 years c. To receive $1,200 at the end of each month for 11 years compounded monthly d. To receive $65,000 in 5 years and $125,000 5 years later e. To receive $65,000 in 5 years and $200,000 10 years later C Option A Option B Option C Option D Option E PV = $100,000 FV = 310,000 9 = i 15 = n 0 PMT PV = $85,106.79 PMT = 1,200 9 / 12 = i 11 x 12 = n FV = 0 PVOA ($100,327.70) FV 65,000 9 = i 5 = n PMT = 0 PV ($42,245.54) FV 125,000 9 = i 5 = n PMT = 0 PV ($52,801.35) FV 65,000 9 = i 5 = n PMT = 0 PV ($42,245.54) 15 = n 9 = i FV 200,000 PMT = 0 PV ($54,907.61) D) 42,245.54 + 52,801.35 = 95,046.54 E) 54,907.61 + 42,245.54 = 97,153.15 Judy Martin estimates her opportunity cost on investments to be 12% compounded annually. Which one of the following is the best investment opportunity? a. To receive $50,000 today b. To receive $250,000 at the end of 14 years c. To receive $40,000 at the end of 4 years and $120,000 8 years later at the end of the year d. To receive $5,000 at the beginning of each 6-month period for 9 years compounded semiannually e. To receive $60,000 at the end of 3 years D Option A Option B Option C Option D Option E PV = $50,000 FV = 250,000 12 = i 14 = n 0 PMT PV = $51,154.95 FV 40,000 12 = i 4 = n PMT = 0 PV ($25,420.72) FV 120,000 12 = i 12 = n PMT = 0 PV ($30,801.01) PMT = 5,000 12 / 2 = i 9 x 2 = n FV = 0 PVAD ($57,386.30) FV = 60,000 12 = i 3 = n 0 PMT PV = $42,706.81 C) 25,420.72 + 30,801.01 = 56,221.73 Morris and Jo Ann Simpson are ready to retire. They want to receive the equivalent of $25,000 in today's dollars at the beginning of each year for the next 20 years. They assume inflation will average 4% over the long run, and they can earn an 8% compound annual after-tax return on investments. What lump sum do Morris and Jo Ann need to invest today to attain their goal? a. $265,089.98 b. $339,758.16 c. $353,348.49 d. $357,681.56 e. None of the above PMT 25,000 1.08 1.04 – 1 x 100 = i 20 = n FV = 0 PVAD = ($357,681.56) Stuart needs an income stream equivalent to $50,000 in today's dollars at the beginning of each year for the next 12 years to maintain his standard of living. He assumes inflation will average 4.5% over the long run, and he can earn a 9% compound annual after-tax return on investments. What lump sum does Stuart need to invest today to fund his needs? a. $480,878.04 b. $455,929.00 c. $476,445.85 d. $461,025.81 e. None of the above PMT 50,000 1.09 1.045 – 1 x 100 = i 12 = n FV = 0 PVAD = ($480,878.04) Clark Roberts wants to retire in 9 years. He needs an additional $300,000 (today's $) in 9 years to have sufficient funds to finance this objective. He assumes inflation will average 5.0% over the long run, and he can earn a 4.0% compound annual after-tax return on investments. What serial payment should Clark invest at the END of the first year to attain his objective? a. $34,623.42 b. $34,689.00 c. $36,354.60 d. $36,423.45 e. None of the above 300,000 FV 1.04 1.05 – 1 x 100 = (0.95238)* = i 9 = n PV = 0 PMTOA = ($34,623.42) x 1.05 = ($36,354.60) Change Sign *The interest rate is negative because the inflation rate exceeds the return. Judy Danos wants to retire in 9 years. She needs an additional $300,000 (today's $) in 9 years to have sufficient funds to finance this objective. She assumes inflation will average 5.0% over the long run, and she can earn a 4.0% compound annual after-tax return on investments. What will be Judy's payment at the end of the second year? a. $38,244.62 b. $38,172.33 c. $36,354.60 d. $34,623.42 e. None of the above B 300,000 FV 1.04 1.05 – 1 x 100 = (0.95238)* = i *The interest rate is negative because the inflation rate exceeds the return. 9 = n PV = 0 PMTOA = ($34,623.42) x 1.05 = ($36,354.60) Change Sign 36,354.60* x 1.05 = $38,172.33 John wants to start his own business in 6 years. He needs to accumulate $200,000 (today's $) in 6 years to sufficiently finance his business. He assumes inflation will average 4%, and he can earn a 9% compound annual after-tax return on investments. What serial payment should John invest at the end of the first year to attain his goal? a. $29,546.11 b. $30,727.95 c. $28,190.78 d. $29,318.41 e. None of the above PMT 200,000 1.09 1.04 – 1 x 100 = i 6 = n FV = 0 PMTOA = $29,546.11 x 1.04 = ($30,727.95) Change Sign Sarah wants to start her own business in 6 years. She needs to accumulate $200,000 (today's $) in 6 years to sufficiently finance her business. She assumes inflation will average 4%, and she can earn a 9% compound annual after-tax return on investments. What will be Sarah's payment at the end of the second year? a. $28,190.78 b. $30,727.95 c. $30,491.00 d. $31,957.07 e. None of the above D 200,000 FV 1.09 1.04 – 1 x 100 = i 6 = n PMTOA = $29,546.11 x 1.04 = ($30,727.95) 30,727.95 x 1.04 = $31,957.07 Change Sign Determine the future value of a periodic deposit of $6,100 made at the beginning of each year for10 years to a mutual fund expected to earn 11.5% compounded annually during the projection period. Calculate the future value rounded to the nearest dollar. a. $104,493 b. $116,510 c. $113,040 d. $124,344 e. $39,229 The question specifies that the deposits are made at the beginning of each year; therefore, the student is required to calculate the future value of an annuity due. Answer A is the future value of deposits made at the end of the year. Answer C is incorrect because the calculation is based on the future value of the deposits made at the end of the year at 10% for 11.5 years, a reversal of the term and the interest rate. Answer D is similar to C except the calculation is based on an annuity due. Answer E is the present value of an annuity due instead of the future value of an annuity due. The keystrokes used with a financial calculator are: PMTAD = ($6,100) i = 11.5 N = 10 PV = $0 FVAD = $116,510 Determine the future value of a periodic deposit of $6,100 made at the beginning of each year for 10 years to a mutual fund expected to earn 11.5% compounded quarterly during the projection period. Calculate the future value rounded to the nearest dollar. a. $447,130 b. $116,510 C. $119,931 d. $107,076 e. $459,985 Step 1 Step 2 ($1) PV 4 i 11 4 = n 0 PMT FV = 1.120055 Therefore i = 12.0055 0 PV (6.100) PMTAD 12.0055 i 10 n FV = 119,931 Answer A calculates the future value of a $6,100 deposit made at the end of each quarter for 40 quarters using i = 2.875 (11.5 + 4). This is incorrect because the question specifies an annual deposit and not a quarterly deposit. Answer E calculates the future value of an annuity due of a $6,100 deposit made at the beginning of each quarter for 40 quarters using i = 2.875 (11.5 + 4). Finally, answer B calculates the future value of an annuity due of a $6,100 deposit made annually for 10 years at i = 11.5. A client is to receive $650 per month for 5 years beginning one year from today at the beginning of the month. What is the present value of all payments (rounded to the nearest dollar) assuming an annual discount rate of 9%? a. $33,070 b. $28,943 c. $30,339 d. $31,548 e. $28,728 B, There are two steps in solving this question. Step 1: calculate the present value of an annuity of $650 per month for 60 months at a discount rate of 9%. Financial Calculations: Begin, PMT = $650, i = .75 (9 + 12), n = 60 (5*12) and solve for PV1 = $31,548 This provides the present value of an annuity one-year from now. Step 2: This amount is further discounted to the present, one year. Financial Calculation: Begin, FV = $31,548, i = 9, n =1 and solve for PV = $28,943 Answer A is the present value of an annuity due of $7,800 (650 * 12) received for five years at a discount rate of 9%. Answer C is the present value of answer A discounted for one year at 9%. Answer D is the first part of the correct calculation. Finally, answer E is the present value of an ordinary annuity instead of an annuity due. The rate which produces a Net Present Value of a series of discounted cash flows equal to zero is called the: a. Return on investment (ROI) b. Internal rate of return (IRR) c. Average rate of return d. Cost of capital e. Inflation rate B The question presented is the definition of Internal Rate of Return. If the net present value of a series of discounted cash flows is greater than zero, one could interpret that: 1. The discounted cash flows exceed the investment outlay. 2. The rate of return is higher than the cost of capital. 3. The return on investment is lower than the internal rate of return. 4. The internal rate of return was the discount rate used. a. 1 only b. 1 and 4 C. 1, 2, 3, and 4 d. 2 and 3 e. 2 only A A positive net present value of a series of discounted cash flows means that the discounted cash flows exceed the investment outlay. Statements 2 and 3 cannot be correct because the question does not provide appropriate information. Statement 4 is not correct because if the internal rate of return were the rate used, the net present value amount would be equal to zero. If the net present value of a series of discounted cash flows is equal to zero, one could interpret that 1. The discounted cash flows equal the investment outlay. 2. The rate of return is lower than the cost of capital. 3. The return on investment is lower than the internal rate of return. 4. The internal rate of return was the discount rate used. a. 1 only b. 1 and 4 c. 1, 2, 3,and 4 d. 2 and 3 e. 2 only B Statements 1 and 4 are correct A net present value of a series of discounted cash flows equal to zero means the discounted cash flows are equal to the investment outlay. If the net present value of a series of discounted cash flows is less than zero, one could interpret that: 1. The discounted cash flows are lower than the investment outlay. 2. The rate of return is lower than the cost of capital. 3. The return on investment is higher than the internal rate of return. 4. The internal rate of return was the discount rate used. a. 1 only b. 1 and 4 c. 1, 2, 3, and 4 d. 2 and 3 e. 2 only A A negative net present value of a series of discounted cash flows means the investment outlay exceeds the discounted cash flows. What is the monthly payment made at the end of each month required to accumulate a balance of $150,000 in 10 years at an assumed interest rate of 11% compounded monthly and a beginning savings balance of $2,500? a. $684.97 b. $691.25 c. $656.81 d. $650.85 e. $712.14 C There are two steps to solving this question. The first step is to compute the future value of the beginning savings balance. PV = $2,500, i = .92 (11 / 12), N = 120 (10 * 12) and solve for PV = $7,472.87. This amount is subtracted from the required balance of $150,000 to arrive at the amount that needs to be funded of $142,527.13. Solving for this amount is as follows: P4 = $142,527.13, i = .92 (11 + 12), N = 120 (10 * 12) and solve for PMTOA = $656.81. Answer D has the correct inputs except the answer is the calculation of an annuity due. Answer A calculates the annuity due assuming no beginning savings balance. Answer B calculates the payment required assuming no beginning savings balance. Answer E calculates the annual payment required assuming a beginning balance and divides that number by 12. Joe wants to buy a business in 10 years. He estimates he will need $150,000 at that time. He currently has a zero-coupon bond with a market value of $1,157.98 that he will use as part of the required amount. The zero-coupon bond has a face value of $2,500 and will mature in 10 years. The bond has a semiannual effective interest rate of 3.923%. In addition to the bond, he wants to save a monthly amount to reach his goal. What is Joe's required monthly payment made at the beginning of each month in order to accumulate the $150,000, including the zero-coupon bond, at an assumed interest rate of 11%? a. $676.10 b. $673.56 c. $669.96 d. $679.73 e. $800.91 B The amount to be funded is $147,500, the required amount of $150,000 less the face amount of the bond of $2,500. PV = $147,500, i =.92 (11 + 12), N = 120 (10 * 12) and solve for PMTAD = $673.56. Answer A is incorrect because the payment is calculated as if the present value of the bond is projected at 11%, the assumed rate of return. It is unnecessary to project the present amount since the face value at the end is known. Answer C is the same as A except the payment is solved as an annuity due. Answer D calculates the future value correctly ($147,500) except as a regular payment and not an annuity due. Answer E calculates the annuity due of $147,500 except at an interest rate of 8%, which is the implicit rate of the bond. The Financial Planning Process Benefits of Financial Planning Integrates the Financial Mission, Financial Goals, and Financial Objectives into one Comprehensive Cohesive Plan. Identifies and Plans for Goals, making them more likely to be achieved. Identifies Risk Exposures. Gives more control over Financial Destiny. Allows for better Strategic Choices. Creates a framework for Feedback, Evaluation, and Control. Establishes Measurable Goals and Expectations. Develops an improved Awareness of Financial Choices, and of how the internal and external environments affect those choices. Establishes Rationality and Reality and purges the client of “pie in the sky” ideas and wishful thinking. Brings Financial Order and Discipline to clients. Instills Confidence that goals will be achieved. Identifies the Changes in Actions and Behaviors necessary to accomplish financial goals. Provides a forum for rationalizing the need for change. The Financial Planning Process Financial Planning is about making Financial Choices and Allocating Scarce Resources. Personal Utility Curves Economic Curves that describe the Satisfaction that an individual receives from selecting a thing and/or additional units of that thing. Opportunity Costs The highest valued alternative not chosen. That is to say what is given up in order to have another choice. The Financial Planning Process Lifecycle Phases & Characteristics The Financial Planning Process Lifecycle Phases & Characteristics As clients move through the various phases of life, their goals and objectives will change: Asset Allocation Phase Usually in the 25 to 50 age range Young clients start out with more debt, less cash and net worth Conservation/Protection Phase Usually in the 35 to retirement age range Clients have accumulated assets due to greater cash flow, now may become slightly more risk adverse. Distribution/Gifting Phase Begins when they realize they have the money to do what they want. Clients have little or no debt, and relatively high net worth. The Financial Planning Process 6 Steps of the Financial Planning Process (EG ADIM) 1. Establishing Client Planner Relationship Explain Issues and Concepts, Explain Services Provided, 2. Gathering Data Collect Qualitative (subjective) and Quantitative (measurable or factual) Information, Establishing and Quantifying Goals (specific dollar amount & time frame), Prioritizing or Ranking Goals in order of importance, Determine Clients “Time Horizons” and “Risk Tolerance” 3. Analyzing and Processing Information Identify Strengths and Weaknesses, Consider Options and Strategies for Achievement of Goals 4. Develop and Present a Comprehensive Financial Plan Prepare Financial Statements Develop a Budget and a Schedule for Implementation, Write the Plan and Explain the Plan, Collaborate with the client to ensure they are comfortable with the plan 5. Implement the Plan Assist client as needed with products, and working with other professionals 6. Monitoring the Plan Periodically Review Plan for continued appropriateness, continued progress on goals. Gathering Data Whatever the sequence of interviews might be, the financial planner collects Quantitative and Qualitative Data such as that outlined below, depending upon the client’s goals. Quantitative Data (See Practice Standard 200-2 In Appendix B.) General Family Profile including: names, addresses, and telephone numbers of financial advisors Assets and Liabilities, as well as Cash Inflows and Outflows (Financial Statements) Insurance Policy Information Employee Benefit and Pension Plan information Tax Returns for the last three years Details on Current Investments Retirement Benefits Available Information about any client-owned businesses Copies of Wills and Trusts Lifetime Gifting programs Qualitative Data (subjective, not exactly measurable) Goals and Objectives (dreams and desires) Health Status of client and family members (heredity issues as well) Interests and Hobbies Expectations about Employment Risk Tolerance Level Anticipated Changes in current or future lifestyle Steps to the Budgeting Process 1. Gather the Previous Years Bank, Credit Card and Relevant Statements, Prepare a spread sheet, or Use a computer program such as Quicken or MS Money, Create Categories of expenses (such as: dinning out, utilities, insurance) 2. Identify the Various Categories of Expenses, and The Totals As a Percentage of Gross (total) Income 3. Identify the Various Categories of Expenses As: Fixed Discretionary, and Inflation Sensitive 4. Forecast Next Years Monthly Income 5. Determine Next Years Monthly Expenses Remember to account for the non-monthly expenses 6. Project the Monthly Expenses (Budget) for the Next 12 Months That is, reconcile steps 4 and 5 7. Compare Past Actual Monthly Expenses to the Projections Adjust the following monthly expenses accordingly 8. Continue To Analyze the Budget Monthly, Examples of expenses which can be controlled: Pick out the specific discretionary expenses you can control, Utilities, Long Distance telephone calls and Dining Out Other Budgeting Tips Remember to include an expense item for: The Emergency Fund should be between 3 to 6 months of expenses. Scheduled Expenses Investment Savings Families with Highly Variable Incomes or Expenses should prepare 2 budgets: 1. A “Worst Case Budget” based on the lowest income and highest expenses 2. A “Average Case Budget” based on “reasonably expectations” of expenses Liquidity vs. Marketability Liquidity The ability to sell an asset quickly at a competitive price, with no loss of principal and little price concession. Marketability The ability of an investor to find a ready market where the investor may sell their investment. Emergency Fund (All Financial Plans Need A Base) The Emergency Fund is that base: Should be Liquid Savings and Money that can be accessed without delay, penalty, or incurring debt. How Much Individuals need to retain a sufficient amount of Liquid Assets at all times to handle emergencies so they will not have to borrow money or liquidate investments at a potentially inopportune time. However, because investments with the greatest liquidity tend to have the lowest earnings, it is important that the amount that is held out for an Emergency Fund is not excessive. A good rule of thumb is that the client should have the equivalent of 3 to 6 Months of Fixed and Variable Expenses in liquid accounts. This would exclude the expense of Income-related Taxes and Contributions to savings and investments. Appropriate Assets for an Emergency Fund are Cash and/or Cash Equivalents such as: Checking Accounts (excluding funds to be utilized for normal expenses, which from a practical standpoint means that you should reserve an amount equal to one month's expenses, and can use any remaining checking amounts), Savings Accounts Money Market Accounts or Funds, which all can be converted to cash quickly. A Certificate of Deposit may be appropriate if it matures in the near term (<90 Days) CDs with maturity dates of more than 90 days are not appropriate for emergency use because of the typical Early Withdrawal Penalties Emergency Fund (Flexability) Rules of Thumb are not for everyone: Clients with Extremely Stable Sources of Income may need less than 3 months of funds. A client may have several sources of income (from rental real estate), both spouses may have extremely stable employers (government jobs) For these clients smaller Emergency Funds may be required. Clients with Very Unstable Sources of Income, may require more than 6 months of funds. Some clients may have very unpredictable incomes (real estate sales people) For these clients Larger Emergency Funds may be required. Some financial planners also recommend that clients set up "Opportunity Funds," which are: Liquid or Semi-liquid Accounts available for large purchases of a non-emergency nature that the client may wish to make, such as jewelry, furniture, or travel. Such funds would prevent the client from having to borrow to attain these items. Some planners use Opportunity Funds for investing purposes, ensuring that clients have liquid funds available to take advantage of investment opportunities that may arise. Financial Statements Statement of Financial Position (Balance Sheet) See examples in your books 1. Assets and Liabilities should be presented at Fair Market Value (FMV) 2. Statement needs to be Appropriately Dated 3. Net Worth should be indicated 4. Footnotes should be utilized to describe details of both Assets and Liabilities 5. Property should be identified with owner (e.g., JTWROS, or H for husband, W for wife, etc.) 6. Categories of Assets - Depends on Type and Use of Asset Cash and Cash Equivalents INVESTED ASSETS (INVESTMENT portfolio) Use Assets (Residence, Furniture, and Autos) Assets should be Listed In Order of Liquidity (the ability to convert to cash quickly) 7. Liabilities should be categorized according to Maturity Date Current Liabilities - due within 1 - year Long-Term Liabilities - generally Mortgages and Notes (beyond a yaer) 8. Net Worth = Assets - Liabilities Financial Statements Statement of Recurring Cash Flows (For Past Year and Pro Forma For Next Year) See examples in your books 1. Indicate period covered 2. INFLOWS: Gross Salaries Dividend Income Refunds Due (Tax) Alimony Received Interest Income Rental Income Other Incoming Cash Flows 3. OUTFLOWS: Savings and Investment - by item Fixed outflows – (Non-Discretionary) House Payments Auto Payments Taxes Fixed Outflows – (Discretionary) Club Dues Utilities (a portion may be a variable outflow) Variable Outflows – (Non-Discretionary) Food Variable Outflows – (Discretionary) Vacations Entertainment 4. Net Discretionary Cash Flow = Inflows - Outflows 5. Footnotes should be used to explain details of Income and Expenses Ratio Analysis Ratio Analysis will give the planner a good idea or starting point in analyzing the client's financial situation. Liquidity Ratio = Liquid Assets ÷ Monthly Expenses Most planners suggest 3 to 6 months’ coverage of Fixed and Variable Outflows. Housing Payment Ratio All Monthly Non-Executory Housing Costs* + Monthly Gross Income < 28% *Includes Principal, Interest, Taxes, Insurance, and any Condominium Fee if a renter, then the ratio is: Rent + Insurance ÷ Monthly Gross Income < 28% Total Payments Ratio All Monthly Payments and Housing Costs (i.e. Housing Payment Ratio) ÷ Gross Monthly Income < 36% The 28% and 36% are common mortgage lender standards and are healthy targets for most clients. Solvency Ratio = Total Assets ÷ Total Debt > 1.1 Savings Ratio = Savings Per Year + Gross Income The Savings Ratio should be 8% - 25% Depending on Age For example, a savings ratio of 8% or more for a younger individual may be appropriate, while a person in their late 50’s 25% may be more appropriate. Debt