Chapter 4 (2)

# Chapter 4 (2) - 1 award 1 out of 1 point Assume the total...

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Unformatted text preview: 1. award: 1 out of 1 point Assume the total cost of a college education will be \$385,000 when your child enters college in 15 years. You presently have \$63,000 to invest. Required: What annual rate of interest must you earn on your investment to cover the cost of your child’s college education? (Do not include the percent sign (%). Round your answer to 2 decimal places (e.g., 32.16).) Annual rate eBook Link 12.83 % Assume the total cost of a college education will be \$385,000 when your child enters college in 15 years. You presently have \$63,000 to invest. Required: What annual rate of interest must you earn on your investment to cover the cost of your child’s college education? (Do not include the percent sign (%). Round your answer to 2 decimal places (e.g., 32.16).) Annual rate % Explanation: 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 = (\$385,000 / \$63,000)1/15 – 1 r = 0.1283 or 12.83% Calculator Solution: Enter 15 ±\$63,000 \$385,000 N I/Y PV PMT FV Solve for 12.83% 2. award: 1 out of 1 point Assume that in 2009, an 1886 Morgan silver dollar sold for \$7,850. Required: What was the rate of return on this investment? (Do not include the percent sign (%). Round your answer to 2 decimal places (e.g., 32.16).) Rate of return 7.56 % eBook Link Assume that in 2009, an 1886 Morgan silver dollar sold for \$7,850. Required: What was the rate of return on this investment? (Do not include the percent sign (%). Round your answer to 2 decimal places (e.g., 32.16).) Rate of return % Explanation: 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 = (\$7,850 / \$1)1/123 – 1 r = 0.0756 or 7.56% Calculator Solution: Enter 123 ±\$1 \$7,850 N I/Y PV PMT FV Solve for 7.56% 3. award: 1 out of 1 point You’re trying to save to buy a new \$220,000 Ferrari. You have \$37,000 today that can be invested at your bank. The bank pays 4.4 percent annual interest on its accounts. Required: How long will it be before you have enough to buy the car? (Round your answer to 2 decimal places (e.g., 32.16).) Length of time 41.00 years eBook Link You’re trying to save to buy a new \$220,000 Ferrari. You have \$37,000 today that can be invested at your bank. The bank pays 4.4 percent annual interest on its accounts. Required: How long will it be before you have enough to buy the car? (Round your answer to 2 decimal places (e.g., 32.16).) Length of time years Explanation: 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) FV = \$220,000 = \$37,000(1.044)t t = ln(\$220,000 / \$37,000) / ln 1.044 t = 41.40 years Calculator Solution: Enter 4.4% ±\$37,000 \$220,000 N I/Y PV PMT FV Solve for 41.40 4. award: 1 out of 1 point Imprudential, Inc., has an unfunded pension liability of \$758 million that must be paid in 15 years. To assess the value of the firm’s stock, financial analysts want to discount this liability back to the present. Required: If the relevant discount rate is 7 percent, what is the present value of this liability? (Do not include the dollar sign (\$). Enter your answer in dollars, not millions of dollars (e.g., 1,234,567). Round your answer to 2 decimal places (e.g., 32.16).) Present value \$ 274,734,082.88 eBook Link Imprudential, Inc., has an unfunded pension liability of \$758 million that must be paid in 15 years. To assess the value of the firm’s stock, financial analysts want to discount this liability back to the present. Required: If the relevant discount rate is 7 percent, what is the present value of this liability? (Do not include the dollar sign (\$). Enter your answer in dollars, not millions of dollars (e.g., 1,234,567). Round your answer to 2 decimal places (e.g., 32.16).) Present value \$ Explanation: To find the PV of a lump sum, we use: PV = FV / (1 + r)t PV = \$758,000,000 / (1.07)15 PV = \$274,734,082.89 Calculator Solution: Enter 15 7% \$758,000,000 N I/Y PV PMT FV Solve for –\$274,734,082.89 5. award: 0.50 out of 1 point In 1902, the first Putting Green Championship was held. The winner’s prize money was \$320. In 2009, the winner’s check was \$1,620,000. Requirement 1: What was the annual percentage increase in the winner’s check over this period? (Do not include the percent sign (%). Round your answer to 2 decimal places (e.g., 32.16).) Annual percentage 8.30 % Requirement 2: If the winner’s prize increases at the same rate, what will it be in 2051? (Do not include the dollar sign (\$). Enter your answer in dollars, not millions of dollars (e.g., 1,234,567). Round your answer to 2 decimal places (e.g., 32.16).) Price money \$ 46,215,751.10 eBook Links (2) In 1902, the first Putting Green Championship was held. The winner’s prize money was \$320. In 2009, the winner’s check was \$1,620,000. Requirement 1: What was the annual percentage increase in the winner’s check over this period? (Do not include the percent sign (%). Round your answer to 2 decimal places (e.g., 32.16).) Annual percentage % Requirement 2: If the winner’s prize increases at the same rate, what will it be in 2051? (Do not include the dollar sign (\$). Enter your answer in dollars, not millions of dollars (e.g., 1,234,567). Round your answer to 2 decimal places (e.g., 32.16).) Price money \$ Explanation: 1: 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 = (\$1,620,000 / \$320)1/107 – 1 r = 0.0830 or 8.30% 2: To find what the winner’s check will be in 2051, we use the FV of a lump sum, so: FV = PV(1 + r)t FV = \$1,620,000(1.0830)42 FV = \$46,085,557.11 Calculator Solution: Enter 107 ±\$320 \$1,620,000 N I/Y PV PMT FV Solve for 8.30% Enter 42 8.30% ±\$1,620,000 N I/Y PV PMT FV Solve for \$46,085,557.11 6. award: 1 out of 1 point Assume that in 2009, a \$10 silver certificate from 1893 was sold for \$11,400. Required: For this to have been true, what was the annual increase in the value of the certificate? (Do not include the percent sign (%). Round your answer to 2 decimal places (e.g., 32.16).) Annual increase 6.26 % eBook Link Assume that in 2009, a \$10 silver certificate from 1893 was sold for \$11,400. Required: For this to have been true, what was the annual increase in the value of the certificate? (Do not include the percent sign (%). Round your answer to 2 decimal places (e.g., 32.16).) Annual increase % Explanation: 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 = (\$11,400 / \$10)1/116 – 1 r = 0.0626 or 6.26% Calculator Solution: Enter 116 ±\$10 \$11,400 N I/Y PV PMT FV Solve for 6.26% 7. award: 1 out of 1 point On March 28, 2008, 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 \$100,000 on March 28, 2048, but investors would receive nothing until then. Investors paid DMF \$24,999 for each of these securities; so they gave up \$24,999 on March 28, 2008, for the promise of a \$100,000 payment 40 years later. Required: (a) Based on the \$24,999 price, what rate was DMF paying to borrow money? (Do not include the percent sign (%). Round your answer to 2 decimal places (e.g., 32.16).) Rate 3.53 % (b) Suppose that, on March 8, 2025, this security’s price is \$40,483. If an investor had purchased it for \$24,999 at the offering and sold it on this day, what annual rate of return would she have earned? (Do not include the percent sign (%). Round your answer to 2 decimal places (e.g., 32.16).) Rate of return 2.88 % (c) If an investor had purchased the security at market on March 8, 2025, and held it until it matured, what annual rate of return would she have earned? (Do not include the percent sign (%). Round your answer to 2 decimal places (e.g., 32.16).) Rate of return 4.01 % eBook Link Worksheet Difficulty: Intermediate Learning Objective: 04-03 Calculate the return on an investment. On March 28, 2008, 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 \$100,000 on March 28, 2048, but investors would receive nothing until then. Investors paid DMF \$24,999 for each of these securities; so they gave up \$24,999 on March 28, 2008, for the promise of a \$100,000 payment 40 years later. Required: (a) Based on the \$24,999 price, what rate was DMF paying to borrow money? (Do not include the percent sign (%). Round your answer to 2 decimal places (e.g., 32.16).) Rate % (b) Suppose that, on March 8, 2025, this security’s price is \$40,483. If an investor had purchased it for \$24,999 at the offering and sold it on this day, what annual rate of return would she have earned? (Do not include the percent sign (%). Round your answer to 2 decimal places (e.g., 32.16).) Rate of return % (c) If an investor had purchased the security at market on March 8, 2025, and held it until it matured, what annual rate of return would she have earned? (Do not include the percent sign (%). Round your answer to 2 decimal places (e.g., 32.16).) Rate of return % Explanation: (a) 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 = (\$100,000 / \$24,999)1 /40 – 1 r = 0.0353 or 3.53% (b) Using the FV formula and solving for the interest rate, we get: r = (FV / PV)1 / t – 1 r = (\$40,483 / \$24,999)1 /17 – 1 r = 0.0288 or 2.88% (c) Using the FV formula and solving for the interest rate, we get: r = (FV / PV)1 / t – 1 r = (\$100,000 / \$40,483)1 /23 – 1 r = 0.0401 or 4.01% Calculator Solution: (a) Enter 40 ±\$24,999 \$100,000 N I/Y PV PMT FV Solve for 3.53% (b) Enter 17 ±\$24,999 \$40,483 N I/Y PV PMT FV Solve for 2.88% (c) Enter 23 ±\$40,483 \$100,000 N I/Y PV PMT FV Solve for 4.01% 8. award: 1 out of 1 point Suppose you are committed to owning a \$180,000 Ferrari. Required: If you believe your mutual fund can achieve a 10.45 percent annual rate of return, and you want to buy the car in 12 years on the day you turn 30, how much must you invest today? (Do not include the dollar sign (\$). Round your answer to 2 decimal places (e.g., 32.16).) Amount to be invested \$ 54,611.47 eBook Link Suppose you are committed to owning a \$180,000 Ferrari. Required: If you believe your mutual fund can achieve a 10.45 percent annual rate of return, and you want to buy the car in 12 years on the day you turn 30, how much must you invest today? (Do not include the dollar sign (\$). Round your answer to 2 decimal places (e.g., 32.16).) Amount to be invested \$ Explanation: To find the PV of a lump sum, we use: PV = FV / (1 + r)t PV = \$180,000 / (1.1045)12 PV = \$54,611.47 Calculator Solution: Enter 12 10.45% \$180,000 N I/Y PV PMT FV Solve for –\$54,611.47 9. award: 1 out of 1 point You have just made your first \$5,000 contribution to your individual retirement account. Assume you earn a 11.10 percent rate of return and make no additional contributions. Requirement 1: What will your account be worth when you retire in 43 years? (Do not include the dollar sign (\$). Round your answer to 2 decimal places (e.g., 32.16).) Amount \$ 462,034.64 Requirement 2: What will your account be worth if you wait 10 years before contributing? (Do not include the dollar sign (\$). Round your answer to 2 decimal places (e.g., 32.16).) Amount \$ 161,262.71 Requirement 3: Which investment strategy is better? Start early eBook Link You have just made your first \$5,000 contribution to your individual retirement account. Assume you earn a 11.10 percent rate of return and make no additional contributions. Requirement 1: What will your account be worth when you retire in 43 years? (Do not include the dollar sign (\$). Round your answer to 2 decimal places (e.g., 32.16).) Amount \$ Requirement 2: What will your account be worth if you wait 10 years before contributing? (Do not include the dollar sign (\$). Round your answer to 2 decimal places (e.g., 32.16).) Amount \$ Requirement 3: Which investment strategy is better? Start early Explanation: 1: To find the FV of a lump sum, we use: FV = PV(1 + r)t FV = \$5,000(1.1110)43 FV = \$462,034.64 2: If you wait 10 years, the value of your deposit at your retirement will be: FV = \$5,000(1.1110)33 FV = \$161,262.71 3: Better start early! Calculator Solution: Enter 43 11.10% ±\$5,000 N I/Y PV PMT FV Solve for \$462,034.64 Enter 33 11.10% ±\$5,000 N I/Y PV PMT FV Solve for \$161,262.71 10. award: 1 out of 1 point You have decided that you want to be a millionaire when you retire in 45 years. Requirement 1: If you can earn an 11.36 percent annual return, how much do you have to invest today? (Do not include the dollar sign (\$). Round your answer to 2 decimal places (e.g., 32.16).) Investment \$ 7,891.97 Requirement 2: What if you can earn 5.68 percent? (Do not include the dollar sign (\$). Round your answer to 2 decimal places (e.g., 32.16).) Investment \$ 83,238.00 eBook Link Worksheet Difficulty: Intermediate Learning Objective: 04-02 Determine the present value of cash to be received at a future date. You have decided that you want to be a millionaire when you retire in 45 years. Requirement 1: If you can earn an 11.36 percent annual return, how much do you have to invest today? (Do not include the dollar sign (\$). Round your answer to 2 decimal places (e.g., 32.16).) Investment \$ Requirement 2: What if you can earn 5.68 percent? (Do not include the dollar sign (\$). Round your answer to 2 decimal places (e.g., 32.16).) Investment \$ Explanation: To find the PV of a lump sum, we use: PV = FV / (1 + r)t 1: So, if you can earn 11.36 percent, you will need to invest: PV = \$1,000,000 / (1.1136)45 PV = \$7,891.96 2: And if you can earn 5.68 percent, you will need to invest: PV = \$1,000,000 / (1.0568)45 PV = \$83,238.41 Calculator Solution: Enter 45 11.36% \$1,000,000 N I/Y PV PMT FV Solve for –\$7,891.96 Enter 45 5.68% \$1,000,000 N I/Y PV PMT FV Solve for –\$83,238.41 ...
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## This note was uploaded on 02/24/2011 for the course ACCT 416 taught by Professor Staff during the Winter '08 term at USC.

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