FIN practice questions

Suppose a stock had an initial price of $80 per share, paid a dividend of $.60 per share during the year, and had an ending share price of $88. What was the dividend yield and the capital gains yield? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Dividend yield % Capital gains yield %

Ch 12 # 2 The dividend yield is the dividend divided by the beginning of the period price, so: Dividend yield = $.60 / $80 Dividend yield = .0075, or .75% And the capital gains yield is the increase in price divided by the initial price, so: Capital gains yield = ($88 - 80) / $80 Capital gains yield = .1000, or 10.00%

Suppose you bought a bond with an annual coupon rate of 7.4 percent one year ago for $900. The bond sells for $940 today. a. Assuming a $1,000 face value, what was your total dollar return on this investment over the past year? Total dollar return $ b. What was your total nominal rate of return on this investment over the past year? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Nominal rate of return % c. If the inflation rate last year was 2 percent, what was your total real rate of return on this investment? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Real rate of return %

Ch 12 # 3 a. The total dollar return is the increase in price plus the coupon payment, so: Total dollar return = $940 - 900 + 74 Total dollar return = $114 b. The total percentage return of the bond is: R = ($940 - 900 + 74) / $900 R = .1267, or 12.67% Notice here that we could have simply used the total dollar return of $114 in the numerator of this equation. c. Using the Fisher equation, the real return was: (1 + R) = (1 + r)(1 + h) r = (1.1267 / 1.020) - 1 r = .1046, or 10.46%

Returns Year X Y 1 17 % 22 % 2 31 32 3 12 16 4 - 24 - 29 5 10 23 Using the returns shown above, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y. (Do not round intermediate calculations. Enter your average return and standard deviation as a percent rounded to 2 decimal places, e.g., 32.16, and round the variance to 5 decimal places, e.g., 32.16161.) X Y Average return % % Variance Standard deviation % %

Ch 12 # 4 The average return is the sum of the returns, divided by the number of returns. The average return for each stock was: formula4.mml formula5.mml Remembering back to "sadistics," we calculate the variance of each stock as: formula10.mml formula11.mml formula12.mml The standard deviation is the square root of the variance, so the standard deviation of each stock is: σX = (.04117)1/2 σX = .2029, or 20.29% σY = (.05787)1/2 σY = .2406, or 24.06%

You've observed the following returns on Crash-n-Burn Computer's stock over the past five years: 13 percent, -8 percent, 16 percent, 16 percent, and 10 percent. a. What was the arithmetic average return on Crash-n-Burn's stock over this five-year period? (Do not round intermediate calculations. Enter your answer as a percent rounded to 1 decimal place, e.g., 32.1.) Average return % b-1 What was the variance of Crash-n-Burn's returns over this period? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., 32.16161.) Variance b-2 What was the standard deviation of Crash-n-Burn's returns over this period? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Standard deviation %

Ch 12 # 5 a. To find the average return, we sum all the returns and divide by the number of returns, so: Average return = (.13 - .08 + .16 + .16 + .10) / 5 Average return = .094, or 9.4% b. Using the equation to calculate variance, we find: Variance = 1/4[(.13 - .094)2 + (-.08 - .094)2 + (.16 - .094)2 + (.16 - .094)2 + (.10 - .094)2] Variance = .01008 So, the standard deviation is: Standard deviation = (.01008)1/2 Standard deviation = .1004, or 10.04%

You've observed the following returns on Crash-n-Burn Computer's stock over the past five years: 12 percent, -12 percent, 19 percent, 24 percent, and 10 percent. Suppose the average inflation rate over this period was 2.5 percent and the average T-bill rate over the period was 3.2 percent. a. What was the average real return on Crash-n-Burn's stock? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Average real return % b. What was the average nominal risk premium on Crash-n-Burn's stock? (Do not round intermediate calculations. Enter your answer as a percent rounded to 1 decimal place, e.g., 32.1.) Average nominal risk premium %

Ch 12 # 6 a. To find the average return, we sum all the returns and divide by the number of returns, so: Average return = (.12 - .12 + .19 + .24 + .10) / 5 Average return = .106, or 10.6% To calculate the average real return, we can use the average return of the asset, and the average inflation in the Fisher equation. Doing so, we find: (1 + R) = (1 + r)(1 + h) formula19.mml = (1.106 / 1.025) - 1 formula19.mml = .0790, or 7.90% b. The average risk premium is simply the average return of the asset, minus the average risk-free rate, so, the average risk premium for this asset would be: Average risk premium = Average return − Average risk-free rate Average risk premium = .106 − .032 Average risk premium = .074, or 7.4%

A stock has had the following year-end prices and dividends: Year Price Dividend 1 $ 43.51 - 2 48.49 $ .81 3 57.41 .84 4 45.49 .95 5 52.41 1.00 6 61.49 1.08 What are the arithmetic and geometric returns for the stock? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Arithmetic return % Geometric return %

Ch 12 # 7 To calculate the arithmetic and geometric average returns, we must first calculate the return for each year. The return for each year is: R1 = ($48.49 - 43.51 + .81) / $43.51 = .1331, or 13.31% R2 = ($57.41 - 48.49 + .84) / $48.49 = .2013, or 20.13% R3 = ($45.49 - 57.41 + .95) / $57.41 = -.1911, or -19.11% R4 = ($52.41 - 45.49 + 1.00) / $45.49 = .1741, or 17.41% R5 = ($61.49 - 52.41 + 1.08) / $52.41 = .1939, or 19.39% The arithmetic average return was: RA = (.1331 + .2013 - .1911 + .1741 + .1939) / 5 RA = .1022, or 10.22% And the geometric average return was: RG = [(1 + .1331)(1 + .2013)(1 - .1911)(1 + .1741)(1 + .1939)]1/5 - 1 RG = .0907, or 9.07%

What are the portfolio weights for a portfolio that has 134 shares of Stock A that sell for $44 per share and 114 shares of Stock B that sell for $34 per share? (Do not round intermediate calculations and round your answers to 4 decimal places, e.g., 32.1616.) Portfolio weights Stock A Stock B

Ch 13 # 1 The portfolio weight of an asset is the total investment in that asset divided by the total portfolio value. First, we will find the portfolio value, which is: Total value = 134($44) + 114($34) Total value = $9,772 The portfolio weight for each stock is: WeightA = 134($44) / $9,772 WeightA = .6034 WeightB = 114($34) / $9,772 WeightB = .3966

You own a portfolio that has $3,400 invested in Stock A and $4,400 invested in Stock B. If the expected returns on these stocks are 12 percent and 15 percent, respectively, what is the expected return on the portfolio? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Portfolio expected return %

Ch 13 # 2 The expected return of a portfolio is the sum of the weight of each asset times the expected return of each asset. The total value of the portfolio is: Total portfolio value = $3,400 + 4,400 Total portfolio value = $7,800 So, the expected return of this portfolio is: E(RP) = ($3,400 / $7,800)(.12) + ($4,400 / $7,800)(.15) E(RP) = .1369, or 13.69%

Consider the following information: State of Economy Probability of State of Economy Portfolio Return If State Occurs Recession .18 − .14 Normal .54 .15 Boom .28 .23 Calculate the expected return. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Expected return %

Ch 13 # 3 The expected return of an asset is the sum of each return times the probability of that return occurring. So, the expected return of the asset is: E(R) = .18(−.14) + .54(.15) + .28(.23) E(R) = .1202, or 12.02%

You own a stock portfolio invested 35 percent in Stock Q, 25 percent in Stock R, 25 percent in Stock S, and 15 percent in Stock T. The betas for these four stocks are .88, 1.21, 1.05, and 1.23, respectively. What is the portfolio beta? (Do not round intermediate calculations. Round your answer to 2 decimal places, e.g., 32.16.) Portfolio beta

Ch 13 # 5 The beta of a portfolio is the sum of the weight of each asset times the beta of each asset. So, the beta of the portfolio is: βP = .35(.88) + .25(1.21) + .25(1.05) + .15(1.23) βP = 1.06

A stock has a beta of 1.36, the expected return on the market is 10 percent, and the risk-free rate is 2.5 percent. What must the expected return on this stock be? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Expected return %

Ch 13 # 6 CAPM states the relationship between the risk of an asset and its expected return. CAPM is: E(Ri) = Rf + [E(RM) − Rf] × βi Substituting the values we are given, we find: E(Ri) = .025 + (.10 − .025)(1.36) E(Ri) = .1270, or 12.70%

A stock has an expected return of 12 percent, the risk-free rate is 3.5 percent, and the market risk premium is 5 percent. What must the beta of this stock be? (Do not round intermediate calculations. Round your answer to 2 decimal places, e.g., 32.16.) Beta of stock

Ch 13 # 7 We are given the values for the CAPM except for the β of the stock. We need to substitute these values into the CAPM, and solve for the β of the stock. One important thing we need to realize is that we are given the market risk premium. The market risk premium is the expected return of the market minus the risk-free rate. We must be careful not to use this value as the expected return of the market. Using the CAPM, we find: E(Ri) = .120 = .035 + .050βi βi = 1.70

A stock has an expected return of 16.5 percent, its beta is 1.30, and the risk-free rate is 6.5 percent. What must the expected return on the market be? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Market expected return %

Ch 13 # 8 Here we need to find the expected return of the market using the CAPM. Substituting the values given, and solving for the expected return of the market, we find: E(Ri) = .165 = .065 + [E(RM) − .065](1.30) E(RM) = .1419, or 14.19%

Investment X offers to pay you $4,700 per year for 9 years, whereas Investment Y offers to pay you $6,800 per year for 5 years. If the discount rate is 5 percent, what is the present value of these cash flows? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) Present value Investment X $ Investment Y $ If the discount rate is 15 percent, what is the present value of these cash flows? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) Present value Investment X $ Investment Y $

Ch 6 #2 PVA = C({1 - [1 / (1 + r)t]} / r ) At an interest rate of 5 percent: X@5%: PVA = $4,700{[1 - (1 / 1.05)9 ] / .05 } = $33,406.76 Y@5%: PVA = $6,800{[1 - (1 / 1.05)5 ] / .05 } = $29,440.44 And at an interest rate of 15 percent: X@15%: PVA = $4,700{[1 - (1 / 1.15)9 ] / .15 } = $22,426.44 Y@15%: PVA = $6,800{[1 - (1 / 1.15)5 ] / .15 } = $22,794.65

Suppose a stock had an initial price of $70 per share, paid a dividend of $2.30 per share during the year, and had an ending share price of $82. Compute the percentage total return. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Total return %

ch 12 # 1 The return of any asset is the increase in price, plus any dividends or cash flows, all divided by the initial price. The return of this stock is: R = ($82 - 70 + 2.30) / $70 R = .2043, or 20.43%

Consider the following information: Rate of Return If State Occurs State of Probability of Economy State of Economy Stock A Stock B Recession .19 .08 − .19 Normal .56 .11 .10 Boom .25 .16 .27 Calculate the expected return for each stock. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Expected return Stock A % Stock B % Calculate the standard deviation for each stock. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Standard deviation Stock A % Stock B %

ch 13 #4 The expected return of an asset is the sum of each return times the probability of that return occurring. So, the expected return of each stock asset is: E(RA) = .19(.08) + .56(.11) + .25(.16) E(RA) = .1168, or 11.68% E(RB) = .19(−.19) + .56(.10) + .25(.27) E(RB) = .0874, or 8.74% To calculate the standard deviation, we first need to calculate the variance. To find the variance, we find the squared deviations from the expected return. We then multiply each possible squared deviation by its probability, then add all of these up. The result is the variance. So, the variance and standard deviation of each stock is: σA2 =.19(.08 − .1168)2 + .56(.11 − .1168)2 + .25(.16 − .1168)2 σA2 = .00075 σA = (.00075)1/2 σA = .0274, or 2.74% σB2 =.19(−.19 − .0874)2 + .56(.10 − .0874)2 + .25(.27 − .0874)2 σB2 = .02305 σB = (.02305)1/2 σB = .1518, or 15.18%

For each of the following, compute the future value: (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) Present Value Years Interest Rate Future Value $ 1,900 12 12 % $ 8,052 6 10 69,355 13 11 176,796 7 7

ch 5 #1 FV = PV(1 + r)t FV = $1,900(1.12)12 = $7,402.35 FV = $8,052(1.10)6 = $14,264.61 FV = $69,355(1.11)13 = $269,324.90 FV = $176,796(1.07)7 = $283,895.74

Your coin collection contains 42 1952 silver dollars. If your grandparents purchased them for their face value when they were new, how much will your collection be worth when you retire in 2052, assuming they appreciate at an annual rate of 5.9 percent? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.) Future value $

ch 5 #10 To find the FV of a lump sum, we use: FV = PV(1 + r)t FV = $42(1.059)100 FV = $12,967.17

In 1895, the first Putting Green Championship was held. The winner's prize money was $170. In 2014, the winner's check was $1,390,000. What was the percentage increase per year in the winner's check over this period? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Increase per year % If the winner's prize increases at the same rate, what will it be in 2046? (Do not round intermediate calculations. Round your answer to 2 decimal places, e.g., 32.16.) Winner's prize in 2046 $

ch 5 #11 To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r)t Solving for r, we get: r = (FV / PV)1/t - 1 r = ($1,390,000 / $170)1/119 - 1 r = .0786, or 7.86% To find the FV of the first prize in 2046, we use: FV = PV(1 + r)t FV = $1,390,000(1.0786)32 FV = $15,672,322.36

A coin that was featured in a famous novel sold at auction in 2014 for $3,685,500. The coin had a face value of $15 when it was issued in 1790 and had previously been sold for $390,000 in 1974. At what annual rate did the coin appreciate from its first minting to the 1974 sale? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Rate of return % What annual rate did the 1974 buyer earn on his purchase? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Rate of return % At what annual rate did the coin appreciate from its first minting to the 2014 sale? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Rate of return %

ch 5 #12 The time line from minting to the first sale is: To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r)t Solving for r, we get: r = (FV / PV)1/t - 1 r = ($390,000 / $15)1/184 - 1 r = .0568, or 5.68% The time line from the first sale to the second sale is: To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r)t Solving for r, we get: r = (FV / PV)1/t - 1 r = ($3,685,500 / $390,000)1/40 - 1 r = .0578, or 5.78% The time line from minting to the second sale is: To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r)t Solving for r, we get: r = (FV / PV)1/t - 1 r = ($3,685,500 / $15)1/224 - 1 r = .0570, or 5.70%

In March 2012, Daniela Motor Financing (DMF), offered some securities for sale to the public. Under the terms of the deal, DMF promised to repay the owner of one of these securities $800 in March 2047, but investors would receive nothing until then. Investors paid DMF $400 for each of these securities; so they gave up $400 in March 2012, for the promise of a $800 payment 35 years later. a. Assuming that you purchased the bond for $400, what rate of return would you earn if you held the bond for 35 years until it matured with a value $800? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Rate of return n/r incorrect % b. Suppose under the terms of the bond you could redeem the bond in 2022. DMF agreed to pay an annual interest rate of 1.2 percent until that date. How much would the bond be worth at that time? (Do not round intermediate calculations. Round your answer to 2 decimal places, e.g., 32.16.) Bond value $n/r incorrect c. In 2022, instead of cashing in the bond for its then current value, you decide to hold the bond until it matures in 2047. What annual rate of return will you earn over the last 25 years? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Rate of return n/r incorrect %

ch 5 #13 To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r)t Solving for r, we get: r = (FV / PV)1/t - 1 r = (FV / PV)1/t - 1 r = ($800 / $400)1/35 - 1 r = .0200, or 2.00% Using the FV formula, we get: FV = PV(1 +r)t FV = $400(1 + .012)10 FV = $450.68 Using the FV formula and solving for the interest rate, we get: r = (FV / PV)1/t - 1 r = ($800 / $450.68)1/25 - 1 r = .0232, or 2.32%

For each of the following, compute the present value (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.): Present Value Years Interest Rate Future value $ 12 6 % $ 14,451 3 12 41,557 28 13 876,073 30 10 540,164

ch 5 #2 To find the PV of a lump sum, we use: PV = FV / (1 + r)t PV = $14,451 / (1.06)12 = $7,181.70 PV = $41,557 / (1.12)3 = $29,579.45 PV = $876,073 / (1.13)28 = $28,598.54 PV = $540,164 / (1.10)30 = $30,956.02

Solve for the unknown interest rate in each of the following (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.): Present Value Years Interest Rate Future Value $ 300 4 % $ 380 420 18 1,394 45,000 19 237,520 44,261 25 703,627

ch 5 #3 We can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r)t Solving for r, we get: r = (FV / PV)1 / t - 1 FV = $380 = $300(1 + r)4 r = ($380 / $300)1/4 - 1 r = .0609, or 6.09% FV = $1,394 = $420(1 + r)18 r = ($1,394 / $420)1/18 - 1 r = .0689, or 6.89% FV = $237,520 = $45,000(1 + r)19 r = ($237,520 / $45,000)1/19 - 1 r = .0915, or 9.15% FV = $703,627 = $44,261(1 + r)25 r = ($703,627 / $44,261)1/25 - 1 r = .1170, or 11.70%

Solve for the unknown number of years in each of the following (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.): Present Value Years Interest Rate Future Value $ 500 8 % $ 1,075 750 12 1,836 17,800 18 294,671 20,900 14 320,610

ch 5 #4 We can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r)t Solving for t, we get: t = ln(FV / PV) / ln(1 + r) FV = $1,075 = $500(1.08)t t = ln($1,075 / $500) / ln(1.08) t = 9.95 years FV = $1,836 = $750(1.12)t t = ln($1,836 / $750) / ln(1.12) t = 7.90 years FV = $294,671 = $17,800(1.18)t t = ln($294,671 / $17,800) / ln(1.18) t = 16.96 years FV = $320,610 = $20,900(1.14)t t = ln($320,610 / $20,900) / ln(1.14) t = 20.84 years

You want to buy a new sports coupe for $81,500, and the finance office at the dealership has quoted you an APR of 6.3 percent for a 60 month loan to buy the car. What will your monthly payments be? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Monthly payment $ What is the effective annual rate on this loan? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Effective annual rate %

ch 6 # 10 We first need to find the annuity payment. We have the PVA, the length of the annuity, and the interest rate. Using the PVA equation: PVA = C({1 − [1 / (1 + r)t]} / r) $81,500 = $C[1 − {1 / [1 + (.063 / 12)]60} / (.063 / 12)] Solving for the payment, we get: C = $81,500 / 51.35420 C = $1,587.02 To find the EAR, we use the EAR equation: EAR = [1 + (APR / m)]m − 1 EAR = [1 + (.063 / 12)]12 − 1 EAR = .0649, or 6.49%

At 5.5 percent interest, how long does it take to double your money? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Length of time years At 5.5 percent interest, how long does it take to quadruple it? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Length of time years

ch 5 #6 To find the length of time for money to double, triple, etc., the present value and future value are irrelevant as long as the future value is twice the present value for doubling, three times as large for tripling, etc. We can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r)t Solving for t, we get: t = ln(FV / PV) / ln(1 + r) The length of time to double your money is: FV = $2 = $1(1.055)t t = ln(2) / ln(1.055) t = 12.95 years The length of time to quadruple your money is: FV = $4 = $1(1.055)t t = ln(4) / ln(1.055) t = 25.89 years

Assume that in January 2013, the average house price in a particular area was $287,400. In January 2001, the average price was $204,300. What was the annual increase in selling price? (Do not round intermediate calculations. Enter your answer as a percent rounded answer to 2 decimal places, e.g., 32.16.) Annual increase in selling price %

ch 5 #7 To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r)t Solving for r, we get: r = (FV / PV)1/t - 1 r = ($287,400 / $204,300)1/12 - 1 r = .0288, or 2.88%

You're trying to save to buy a new $195,000 Ferrari. You have $45,000 today that can be invested at your bank. The bank pays 5.3 percent annual interest on its accounts. How long will it be before you have enough to buy the car? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.) Number of years

ch 5 #8 To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r)t Solving for t, we get: t = ln(FV / PV) / ln(1 + r) t = ln($195,000 / $45,000) / ln(1.053) t = 28.39 years

You have just received notification that you have won the $2 million first prize in the Centennial Lottery. However, the prize will be awarded on your 100th birthday (assuming you're around to collect), 76 years from now. What is the present value of your windfall if the appropriate discount rate is 8 percent? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.) Present value $

ch 5 #9 To find the PV of a lump sum, we use: PV = FV / (1 + r)t PV = $2,000,000 / (1.08)76 PV = $5,765.34

You are planning to make monthly deposits of $470 into a retirement account that pays 9 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your retirement account be in 35 years? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.) Future value $

ch 6 # 11 The equation to find the FVA is: FVA = C{[(1 + r)t − 1] / r} FVA = $470[{[1 + (.09 / 12)]420 - 1} / (.09 / 12)] FVA = $1,382,638.70

Huggins Co. has identified an investment project with the following cash flows. Year Cash Flow 1 $ 750 2 990 3 1,250 4 1,350 If the discount rate is 7 percent, what is the present value of these cash flows? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Present value $ n/r incorrect What is the present value at 18 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Present value $ n/r incorrect What is the present value at 24 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

ch 6 #1 PV = FV / (1 + r)t PV@7% = $750 / 1.07 + $990 / 1.072 + $1,250 / 1.073 + $1,350 / 1.074 = $3,615.92 PV@18% = $750 / 1.18 + $990 / 1.182 + $1,250 / 1.183 + $1,350 / 1.184 = $2,803.70 PV@24% = $750 / 1.24 + $990 / 1.242 + $1,250 / 1.243 + $1,350 / 1.244 = $2,475.32

You want to be a millionaire when you retire in 40 years. How much do you have to save each month if you can earn an annual return of 11.9 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Savings per month $ How much do you have to save each month if you wait 15 years before you begin your deposits? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Savings per month $ How much do you have to save each month if you wait 25 years before you begin your deposits? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Savings per month $

ch 6 #12 Starting today: FVA = C[{[1 + (.119 / 12)]480 - 1} / (.119 / 12)] C = $1,000,000 / 11,399.037 C = $87.73 Starting in 15 years: FVA = C[{[1 + (.119 / 12)]300 - 1} / (.119 / 12)] C = $1,000,000 / 1,845.847 C = $541.76 Starting in 25 years: FVA = C[{[1 + (.119 / 12)]180 - 1} / (.119 / 12)] C = $1,000,000 / 494.865 C = $2,020.75

You're prepared to make monthly payments of $210, beginning at the end of this month, into an account that pays 6.2 percent interest compounded monthly. How many payments will you have made when your account balance reaches $12,000? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Number of payments

ch 6 #13 FVA = $12,000 = $210[{[1 + (.062 / 12)]t - 1} / (.062 / 12)] Solving for t, we get: 1.00517t = 1 + [($12,000) / ($210)](.062 / 12) t = ln 1.29524 / ln 1.00517 t = 50.20 payments

Assume the total cost of a college education will be $300,000 when your child enters college in 18 years. You presently have $60,000 to invest. What annual rate of interest must you earn on your investment to cover the cost of your child's college education? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Annual rate of interest %

ch5 #5 To answer this question we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r)t Solving for r, we get: r = (FV / PV)1/t - 1 r = ($300,000 / $60,000)1/18 - 1 r = .0935, or 9.35%

Cannonier, Inc., has identified an investment project with the following cash flows. Year Cash Flow 1 $ 930 2 1,160 3 1,380 4 2,120 If the discount rate is 7 percent, what is the future value of these cash flows in Year 4? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Future value $ What is the future value at a discount rate of 13 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Future value $ What is the future value at a discount rate of 22 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Future value $

ch 6 #3 FV = PV(1 + r)t FV@7% = $930(1.07)3 + $1,160(1.07)2 + $1,380(1.07) + $2,120 = $6,063.97 FV@13% = $930(1.13)3 + $1,160(1.13)2 + $1,380(1.13) + $2,120 = $6,502.50 FV@22% = $930(1.22)3 + $1,160(1.22)2 + $1,380(1.22) + $2,120 = $7,218.88

If you put up $47,000 today in exchange for a 6.75 percent, 14-year annuity, what will the annual cash flow be? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.) Annual cash flow $

ch 6 #5 PVA = C({1 − [1 / (1 + r)t]} / r) PVA = $47,000 = $C{[1 − (1 / 1.067514)] / .0675} We can now solve this equation for the annuity payment. Doing so, we get: C = $47,000 / 8.878105 C = $5,293.92

The Maybe Pay Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs $24,000 per year forever. If the required return on this investment is 6.3 percent, how much will you pay for the policy? (Do not round intermediate calculations. Round your answer to 2 decimal places, e.g., 32.16.) Present value $

ch 6 #7 This cash flow is a perpetuity. To find the PV of a perpetuity, we use the equation: PV = C / r PV = $24,000 / .0630 PV = $380,952.38

Find the EAR in each of the following cases (Use 365 days a year. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.): Stated Rate (APR) Number of Times Compounded Effective Rate (EAR) 9.4 % Quarterly % 18.4 Monthly 14.4 Daily 11.4 Infinite

ch 6 #8 For discrete compounding, to find the EAR, we use the equation: EAR = [1 + (APR / m)]m − 1 EAR = [1 + (.094 / 4)]4 − 1 = .0974, or 9.74% EAR = [1 + (.184 / 12)]12 − 1 = .2003, or 20.03% EAR = [1 + (.144 / 365)]365 − 1 = .1549, or 15.49% To find the EAR with continuous compounding, we use the equation: EAR = eq − 1 EAR = e.114 − 1 = .1208, or 12.08%

First National Bank charges 13.6 percent compounded monthly on its business loans. First United Bank charges 13.9 percent compounded semiannually. Calculate the EAR for First National Bank and First United Bank. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) EAR First National % First United % As a potential borrower, which bank would you go to for a new loan? First United Bank

ch 6 #9 For discrete compounding, to find the EAR, we use the equation: EAR = [1 + (APR / m)]m − 1 So, for each bank, the EAR is: First National: EAR = [1 + (.136 / 12)]12 − 1 = .1448, or 14.48% First United: EAR = [1 + (.139 / 2)]2 − 1 = .1438, or 14.38% Notice that the higher APR does not necessarily mean the higher EAR. The number of compounding periods within a year will also affect the EAR.

An investment offers $6,200 per year for 20 years, with the first payment occurring one year from now. If the required return is 7 percent, what is the value of the investment? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.) Present value $ n/r incorrect What would the value be if the payments occurred for 45 years? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.) Present value $ n/r incorrect What would the value be if the payments occurred for 70 years? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.) Present value $ n/r incorrect What would the value be if the payments occurred forever? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.) Present value $ n/r incorrect

ch6 #4 PVA = C({1 − [1 / (1 + r)t]} / r) PVA@20 yrs: PVA = $6,200{[1 − (1 / 1.0720)] / .07} = $65,682.89 PVA@45 yrs: PVA = $6,200{[1 − (1 / 1.0745)] / .07} = $84,354.23 PVA@70 yrs: PVA = $6,200{[1 − (1 / 1.0770)] / .07} = $87,794.41 To find the PV of a perpetuity, we use the equation: PV = C / r PV = $6,200 / .07 = $88,571.43

If you deposit $5,300 at the end of each of the next 20 years into an account paying 10.8 percent interest, how much money will you have in the account in 20 years? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.) Future value $ How much will you have if you make deposits for 40 years? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.) Future value $

ch6 #6 Here we need to find the FVA. The equation to find the FVA is: FVA = C{[(1 + r)t − 1] / r} FVA for 20 years = $5,300[(1.108020 − 1) / .1080] FVA for 20 years = $332,560.16 FVA for 40 years = $5,300[(1.108040 − 1) / .1080] FVA for 40 years = $2,918,779.91