Foundation review. Introduction. Learning objectives


 Annis Higgins
 1 years ago
 Views:
Transcription
1 Foundation review: Introduction Foundation review Introduction Throughout FN1, you will be expected to apply techniques and concepts that you learned in prerequisite courses. The purpose of this foundation review is to give you an opportunity to review some of these techniques and concepts before you apply them in FN1. The first topic in this foundation review looks at the various legal forms of organizations. The second topic reviews some basic concepts of the time value of money, and illustrates how to solve for the various parameters using a preprogrammed financial calculator. Learning objectives Explain fundamental differences in taxation, legal liability, longevity, and sourcing funds based on the legal form of the business. Interpret and solve basic time value of money questions. Foundation Review 1: Legal forms of organization Foundation Review 2: Time value of money Print the Foundation Review Foundation review: Introduction
2 FR.1 Legal forms of organization FR.1 Legal forms of organization Accountants provide services to all types of business entities. It is important, therefore, that you are familiar with the characteristics of the different forms of business ownership. The three most common legal forms of business ownership are summarized as follows: A single or sole proprietorship is a business that is owned by one individual, but is not established as a separate legal entity. A partnership differs from a single proprietorship only in that it has more than one owner. The owner or owners of proprietorships and partnerships are personally liable for the debts of the business. A corporation is established under the law as a separate legal entity; hence, its owners (shareholders) are not liable for the debt obligations of the corporation. These concepts were covered in both FA2 and LW1. As it may have been a while since you covered this material, the following material and review questions are provided to allow you to assess your understanding of the essentials of the various organizational forms. For taxation purposes, owners of sole proprietorship and partnership firms include business income and expenses on their personal tax returns, since there is no distinction between the business and the owner. In addition, if the sole proprietorship or partnership business incurs debt, all the assets of the owners, whether related to the business or not, are usually accessible by the lenders to recover any defaulted debt obligations. On the other hand, owners of the corporation are separate from the business; that is, the corporation is a separate legal entity. The corporate business entity files its own tax return, totally independent from those of its owners. And, if the corporation incurs debt, only the assets of the corporation are exposed to recoupment by the lenders. The corporate form is used for most large business enterprises; there are many sole proprietorships and partnerships, but corporations are responsible for the greatest dollar volume of business. One reason for this dominance of the corporation is that sole proprietorships and partnerships directly link the enterprise to the owner. For example, when the owner of a sole proprietorship dies, so does the business. Likewise, income from a proprietorship is included with the owner's other sources of income for tax purposes; that is, the proprietorship is not viewed as a separate entity by Canada Revenue Agency. For the purpose of this course, the major ways in which the corporation differs from the partnership or sole proprietorship are as follows: The corporation treats the taxation of the business separately from that of the owner. The corporation provides its owners with limited liability. The longevity of the corporation is independent of the lifespan of its owners. The corporation is generally better suited for raising large amounts of funds for investment in capital assets. Example FR.11: Comparing investment in a partnership with investment in a corporation Mrs. Peal won $5,000 in a lottery. She will use this money to either (1) buy equity shares of BCE Inc., a corporation, or (2) start a babysitting partnership with her friend, Mrs. Smith. Suppose Mrs. Peal enters the partnership and, a year later, she and Mrs. Smith realize that they cannot repay a bank debt of $8,000 now due out of the partnership's cash flow. Because partners in a partnership are not automatically protected by limited liability, the bank can attempt to take possession of both women's personal wealth. Suppose Mrs. Peal now discovers that Mrs. Smith is broke! The bank may take legal action against Mrs. Peal for the entire $8,000. Alternatively, Mrs. Peal could have bought the BCE shares. If BCE subsequently defaulted on its bank loans, the limited liability feature of the corporate form would apply: The banks that loaned funds to BCE cannot litigate for Mrs. Peal's personal wealth. At worst, Mrs. Peal's shares in BCE will become worthless. Limited liability in the corporate form means that Mrs. Peal FR.1 Legal forms of organization
3 FR.1 Legal forms of organization does not have to investigate the personal wealth of all BCE's shareholders, just in case BCE defaults. No matter what happens to BCE, Mrs. Peal's loss is limited to her original investment, and any loss (for example, through declining share prices) is shared equally among all shareholders. The facts of limited liability and liquidity of ownership shares (that is, ease of resale to other investors) enable the corporate form to accommodate many owners. This is a necessary requirement to raise the large amounts of capital required for an efficient organization of real assets. FR.1 Legal forms of organization
4 FR.2 Time value of money FR.2 Time value of money Note: The preprogrammed financial calculator is used extensively throughout FN1. You are expected to be able to use a preprogrammed financial calculator for solving "time value of money" questions in online quizzes, assignments, and the final examination. Microsoft Excel is used throughout the course to prepare simple financial models for which you can easily change parameters and assess the resulting impact. However, during the final examination, you will only be allowed to use a financial calculator. In FN1, you are required to manipulate the present values of a lump sum, an annuity, and an annuity due. Present values are a critical valuation method for longterm liabilities and bonds. Present values are also used in evaluating capital budgeting projects. Be sure that you can do the following: Calculate the present value of an annuity and a lump sum. Calculate a debt payment that includes both principal and interest (a blended payment). Determine an interest rate implicit in a repayment pattern. Divide blended payments into principal and interest components. In addition to this short review, you may wish to consult the CGA Publication and Reference Handbook entitled Mathematics 4 Business, by T.B. Killip, or another basic business mathematics text. Future value and present value of single payments The following two formulas calculate the present value (PV) and future value (FV) of a single payment: FV n = PV o (1 + i) n PV o = FV n (1 + i) n where i = stated interest rate per period n = number of periods The future value equation above is referred to as the basic compounding equation, and the last term [(1 + i) n ] is referred to as the future value interest factor (FVIF) or the compound value interest factor (CVIF). This compound value interest factor gives the future value of $1 at various interest rates and periods. For example, at an interest rate of 5%, for 6 periods, the CVIF is (1.05) 6 or Similarly, you can use the second equation above to calculate the present value of a future amount. This equation states that you can divide the future value by the CVIF to get the present value. This is the basic discounting equation, and the last term [1 (1 + i) n ] is referred to as the discount factor or present value interest factor (PVIF). For example, at an interest rate of 5%, for six periods, the PVIF is 1 (1.05) 6 or If the future amount is $500, the present value is $ = $ Financial calculators Most financial calculators provide special keys to calculate future values and present values. It is important that you become very familiar with the way to use your calculator for these problems. In FN1, the financial calculator results are those obtained with TI BA II Plus. In general, for many calculations, the calculator is set at the "end" mode. The calculator is set at the "begin" mode when the FR.2 Time value of money
5 FR.2 Time value of money present value of an annuity due is involved. For example, to find the future value of $500 invested for 6 years at 5%: FV n = PV 0 (1 + i) n PMT = 0; PV = 500; I/Y = 5; N = 6; CPT FV FV = $ To find the present value of $500 invested for 6 years at 5%: PV o = FV n (1 + i) n PMT = 0; FV = 500; I/Y = 5; N = 6; CPT PV PV = $ Spreadsheet formulas Excel provides builtin functions to calculate future value and present value. FV(interest rate, term,, present value) PV(interest rate, term,, future value) Notice that you need to specify the present value or future value in the Excel functions as negative values. For details on Excel, see Computer Tutorial 2. Examples FR.21 to FR.24 demonstrate how to calculate future values and present values. Example FR.21: Future value of a present amount $1,000 is deposited in a savings account on January 1, 20X1. Interest of 12% is compounded annually. What is the balance in the account at the end of the fifth year (December 31, 20X5)? Using a financial calculator: For this question, you are given: Number of years: 5 Annual interest rate: 12% Present value: $1,000 Enter the following on the calculator: PMT = 0; PV = 1,000; I/Y = 12; N = 5; CPT FV FV = $1, Using Excel: Open Excel file FN1FR2E from the data folder and click the FRE2.1 sheet tab. (Before you begin working on the data files in FN1, you must first download them and save them to your hard drive. Click the data files link in the Course Modules window, and follow the instructions for downloading and saving the files.) FR.2 Time value of money
6 FR.2 Time value of money Note that cell B3 contains the present value ($1,000), cell B4 contains the annual interest rate, and cell B5 contains the number of years. Enter the following in cell B6: =FV(B4,B5,, B3) The future value is $1, Example FR.22: Calculating savings account balances To calculate the account balance at the end of 10, 15, and 25 years, calculate the future value of the present amount of $15,000, with an annual interest rate of 8%. Using a financial calculator: Number of years Future value 10 $ 32, (a) 15 $ 47, (b) 25 $ 102, (c) (a) PMT = 0; PV = 15,000; I/Y = 8; N = 10; CPT FV (b) PMT = 0; PV = 15,000; I/Y = 8; N = 15; CPT FV (c) PMT = 0; PV = 15,000; I/Y = 8; N = 25; CPT FV Using Excel: Using the worksheet from Example FR21, enter the appropriate values for present value, annual interest rate, and number of years in cells B3 to B5. You should obtain the same results in cell B6. Example FR.23: Present value of a future amount What is the present value of a single payment of $10,000, which is to be received three years from now using a discount rate of 10%? Using a financial calculator: Number of years: 3 Annual interest rate: 10% Future value: $10,000 FR.2 Time value of money
7 FR.2 Time value of money PMT = 0; FV = 10,000; I/Y = 10; N = 3; CPT PV PV = $7, Using Excel: Using the same worksheet, calculate the present value. The data for this question is in cells B8 through B10. Enter the following in cell B11: =PV(B9,B10,, B8) The present value is $7, Example FR.24: Calculating present values of a bond Assume that you have a legal contract, such as a bond, that specifies that you will receive $200,000 cash in the future. Assuming a 9% annual interest rate, how much must you pay now if the amount of $200,000 is to be received in 10, 15, or 25 years? Future value: $200,000 Annual interest rate: 9% You want to calculate the present value of bonds that will be paid in 10, 15, or 25 years. Using a financial calculator: Use the financial functions of your calculator to compute the present values. You should obtain the following results: Number of years Present value 10 $ 84, (a) 15 $ 54, (b) 25 $ 23, (c) (a) PMT = 0; FV = 200,000; I/Y = 9; N = 10; CPT PV (b) PMT = 0; FV = 200,000; I/Y = 9; N = 15; CPT PV (c) PMT = 0; FV = 200,000; I/Y = 9; N = 25; CPT PV Using Excel: Using your worksheet from the previous examples, enter the appropriate values for future value, annual interest rate, and number of years in cells B8 to B10. You should obtain the same results in cell B11. Determining the interest rate You may encounter a situation where the present and future values and the number of periods are known, but you do not FR.2 Time value of money
8 FR.2 Time value of money know the interest rate. To analyze and compare the yield of one investment to another, you must be able to determine what interest rate each investment will earn. Example FR.25 demonstrates how to determine the interest rate. Example FR.25: Determining interest rate A $100,000 investment will yield $146,933 in five periods. What is the interest rate earned on the investment? You need to find the annual interest rate that will result in a future value of $146,933 in five years, with an initial investment (present value) of $100,000. Using a financial calculator: PMT = 0; FV = 146,933; PV = 100,000; N = 5; CPT I/Y I/Y = 8 percent Using Excel: Using the same worksheet, enter the following formula for the annual interest rate in cell B16: =RATE(B15,, B14,B13) Ordinary annuities and annuities due Many financial transactions require a series of identical payments, received or paid at equally spaced intervals. An annuity is a series of identical payments, at identical periods or intervals, over a specified term, at a constant interest rate. The most common example of an annuity is a series of mortgage payments. Automobile leases, which require regular fixed monthly payments, are also annuities. An annuity paid or received at the end of the interest compounding period is an ordinary annuity. An annuity paid or received at the beginning of the interest compounding period is an annuity due. Canadian mortgage payments, where monthly payments are due at the end of each month, are examples of an ordinary annuity. A rental agreement where the monthly rents are paid at the beginning of each month is an example of an annuity due. Another type of annuity is a deferred annuity, where payments do not start immediately; an example is the purchase of equipment for which payments do not start until three months after delivery. The future value of an annuity is the sum of the future values of each of the payments. Similarly, it is possible to calculate the present value of an ordinary annuity or an annuity due by calculating the present value of each of the payments, then adding up these present value amounts. Calculations for annuities involve the following four items: payment amount per period interest rate per period number of interest periods FR.2 Time value of money
9 FR.2 Time value of money future value or present value of the annuity You can calculate any one of the four items if you know the remaining three. For example, if you know the payment amount per period, the interest rate per period, and the number of interest periods, you can calculate the future or present value of the annuity. Remember the importance of stating interest rates and periods in the same units of time. People often make errors in computation, perhaps because of the word "annuity." While the word originally signified annual payments, usage changed and the payment periods and terms of annuities are now frequently stated in other time periods. Notice also the use of the word "payment." In annuity calculations, this word may mean either an amount paid or received, depending on the context of the case. Here is the formula to calculate the future value of an ordinary annuity: Here is the formula to calculate the PV of an ordinary annuity: This formula is usually referred to as the present value annuity formula (PVAF) to distinguish it from the PVIF used for valuing single sum problems. Spreadsheet functions Excel provides the FV, PV, PMT and NPER functions (the Excel functions are explained in detail in Computer Tutorial 2). These functions are summarized in Exhibit FR.21. Exhibit FR.21: Financial functions in Excel Function =FV(rate, nper, pmt, pv, type) =PV(rate, nper, pmt, fv, type) =PMT(rate, nper, pv, fv, type) =NPER(rate, pmt, pv, fv, type) Purpose Calculates the future value of an annuity or a present amount Calculates the present value of an annuity or a future amount Calculates the payment per period for an annuity Calculates the number of interest periods for an annuity Examples FR.26 and FR.27 show you how to calculate annuities. Example FR.26: Future value of an ordinary annuity FR.2 Time value of money
10 FR.2 Time value of money It is January 1, 20X1. You have agreed to invest $5,000 per year, over six years, into an investment account. The payments are to be made at the end of each year on December 31. The interest rate is 8%. What is the investment account balance on December 31, 20X6 after the last payment? Annual payment amount: $5,000 Annual interest rate: 8% Number of payments: 6 You need to find the future value of the ordinary annuity. Using a financial calculator: Make sure that your calculator is set to "end" mode. PMT = 5,000; N = 6; PV = 0; I/Y = 8; CPT FV FV = $36, Using Excel: Continue with the previous worksheet. Enter the formula for the future value in cell B21: =FV(B19,B20, B18) Example FR.27: Present value of an ordinary annuity Suppose the situation is similar to that in Example FR.26, but you wish to determine the present value of the investment. Suppose also that the payments are semiannual, the interest rate is 8% compounded semiannually, the payment amount is $2,500, and the payments occur over 6 years. In this case, the annuity is an ordinary annuity. You need to calculate the present value of the ordinary annuity with a periodic interest rate of 4% (8% 2) and a total number of 12 payments (6 years 2 semiannual payments per year). Using a financial calculator: PMT = 2,500; N = 12; FV = 0; I/Y = 4; CPT PV PV = $23, Using Excel: Continue with the Excel worksheet. Enter the formula for the present value in cell B26: =PV(B24,B25, B23) FR.2 Time value of money
11 FR.2 Time value of money Compare your result with that shown. If you obtained different results, click on the FRE2.1S tab. Find and compare the information in the cell that is different from what you expected in the solution sheet to your sheet to determine your error. Using time lines to calculate an annuity due The difference between an ordinary annuity and an annuity due is the timing of the payment. For an ordinary annuity, the payment comes at the end of each interest period, whereas for an annuity due, the payment comes at the beginning of each interest period. You can see this difference by comparing the time line of an ordinary annuity with three annual payments to the time line of an annuity due with three annual payments, as shown in Exhibit FR.22. Exhibit FR.22: Comparison of an ordinary annuity and an annuity due In the time lines, you can see that the cash flow for an ordinary annuity is made up of three payments starting one period from the initial loan or investment date. In the case of an annuity due, the payments start one period ahead of the ordinary annuity, beginning with the first payment at the initial loan or investment date. In fact, the future value of an annuity due is equal to the future value of an ordinary annuity, compounded for one more interest period. Similarly, the present value of an annuity due is equal to the present value of an ordinary annuity, discounted for one less interest period. Future value of annuity due Since the future value of an annuity due equals the future value of an ordinary annuity, compounded one additional period at (1 + i), you can calculate the future value of an annuity due as the FV of an ordinary annuity times (1 + i), or FR.2 Time value of money
12 FR.2 Time value of money Present value of annuity due Recall that a threeyear annuity due is equivalent to a threeyear ordinary annuity that receives one less period of discounting at 1 (1 + i). Therefore, the PV of an annuity due is simply the PV of an ordinary annuity times (1 + i), or Examples FR.28 through FR.210 illustrate three typical annuity problems. Work through each example, using your calculator and Excel. Example FR.28: Future value of an annuity due For the investment in Example FR.26, suppose that instead of making the annual payment on December 31 of each year, the investments are made at the beginning of each year, on January 1, with the first investment on January 1, 20X1. In this case, the annuity is an annuity due and you wish to calculate its future value at maturity. Using a financial calculator: Number of years: 6 Payment amount: 5,000 Interest rate: 8% Set your calculator at the "begin" mode: 2 nd BEG 2 nd SET PMT = 5,000; N = 6; PV = 0; I/Y = 8; CPT FV FV = $39, Using Excel: Continue with the worksheet. Enter the following formula in cell B31: =FV(B29,B30, B28,,1) Example FR.29: Present value of an annuity due Suppose that for the same investment in Example FR28, you wish to calculate the present value. Once again, observe that the investment is an annuity due. FR.2 Time value of money
13 FR.2 Time value of money Using a financial calculator: Number of years: 6 Payment amount: 5,000 Interest rate: 8% Set your calculator at the "begin" mode: 2 nd BEG 2 nd SET PMT = 5,000; N = 6; FV = 0; I/Y = 8; CPT PV PV = $24, Using Excel: Continue with the worksheet. Enter the following formula in cell B36: =PV(B34,B35, B33,,1) Example FR.210: Annuity payment per period On May 1, 20X2, Job Company obtains a $100,000 loan from the bank and promises to repay the loan in three equal annual payments. The payments are to be made each April 30, with the first payment due on April 30, 20X3. For this type of loan, the bank charges 12% interest per annum. Is this an ordinary annuity or an annuity due? Compute the annual payment amounts. Using a financial calculator: This is an ordinary annuity. Number of years: 3 Annual interest rate: 12% Present value: $100,000 Set your calculator to "end" mode: 2 nd BGN 2 nd SET PV = 100,000; I/Y = 12; N = 3; FV = 0; CPT PMT PMT = $41, Using Excel: Continue with the worksheet. Enter the following formula in cell B41: =PMT(B39,B40, B38) FR.2 Time value of money
14 FR.2 Time value of money FR.2 Time value of money
15 Foundation review Review questions Foundation review Review questions Topic FR.1 1. What is a sole proprietorship? 2. What are some of the consequences that flow from a sole proprietorship s lack of a separate legal identity from its owner? 3. Do partnerships have a separate legal identity? 4. Describe the implications of separate legal existence for a corporation and its shareholders. 5. Describe the advantages associated with the corporate method of carrying on business. Solutions Topic FR.2 1. Compute the following amounts. Each case is independent. a. On January 1, 20X1, Dardon Corporation signs a contract agreeing to pay $40,000 on December 31, 20X3. Assuming the following factors, what is the present value of the payment? 1. Annual compounding, 8% annual interest 2. Semiannual compounding, 8% annual interest 3. Quarterly compounding, 8% annual interest b. On January 1, 20X2, Dardon Corporation agrees to pay Servicon Corporation $4,000 per year for five years in exchange for the right to use a patented process. Assuming the following factors, what is the present value of the payment stream? 1. Payments in advance each January 1, 12% annual interest, annual compounding 2. Payments each January 1, 12% annual interest, semiannual compounding 3. Payments each December 31, 12% annual interest, annual compounding 4. Payments each December 31, 12% annual interest, semiannual compounding c. On January 1, 20X3, Dardon Corporation agrees to pay Canadian Finance Co. as follows: December 31, 20X3 $ 6,000 December 31, 20X4 $ 6,000 December 31, 20X5 $ 6,000 December 31, 20X6 $ 6,000 December 31, 20X7 $ 106,000 Canadian Finance Co. advances the present value of this payment stream to Dardon Corporation on January 1, 20X3; the present value of the payment stream is the principal amount of the loan, while the rest is interest. Complete the following table: Principal Interest 1. 6% annual interest, annual compounding $ $ 2. 8% annual interest, annual compounding $ $ 3. 4% annual interest, annual compounding $ $ Foundation review Review questions
16 Foundation review Review questions 4. 6% annual interest, semiannual compounding $ $ 5. 8% annual interest, semiannual compounding $ $ d. On January 1, 20X1, Dardon Corporation agrees to lease a machine, with the following terms required by the lease contract: December 31, 20X120X5, per year $ 40,000 December 31, 20X620Y0, per year $ 20,000 December 31, 20Y1 $ 10,000 December 31, 20Y2 $ 5,000 What is the present value of the payment stream, assuming 1. 6% annual interest, annual compounding 2. 16% annual interest, annual compounding 2. Compute the following amounts. Each case is independent. a. On January 1, 20X0, Marcon Corporation borrowed $120,000 from The Canadian Bank. Repayment is to be in six equal annual instalments, including both principal and interest. Compounding is annual. Calculate the annual payment for 1. December 31 payment, 10% annual interest 2. December 31 payment, 6% annual interest 3. January 1 payment, 10% annual interest 4. January 1 payment, 6% annual interest b. On January 1, 20X2, Marcon Corporation borrowed $40,000 from The Canadian Bank. Repayment is to be made in equal annual instalments, including both principal and interest. Compounding is annual. Calculate the implicit interest rate associated with 1. December 31 payment of $10,856 with 6 payments 2. January 1 payment of $5,323 with 10 payments Calculate the number of payments needed for 3. December 31 payment of $4,074 at 8% 4. January 1 payment of $4,936 at 10% 3. It is January 1, 20X7, and Terry Corporation is about to borrow $100,000 from The Canadian Bank. The loan will be repaid in five equal instalments, including both principal and compound interest at 10%; interest is compounded annually. a. Calculate the annual loan payment that would be made if (1) the first payment is made on December 31, 20X7, or (2) the first payment is made on January 1, 20X7. b. Prepare a debt amortization schedule for each alternative as follows: Date Beginning principal Instalment payment Interest Principal Ending principal Solutions Foundation review Review questions
17 Solution FR.1 Solution FR.1 1. A sole proprietorship is perhaps the most common and simplest form of business organization. The business has no separate legal identity from the owner of the business, since the business is not incorporated. A sole proprietorship is a person who is carrying on business for herself or himself, although this person may have employees. 2. First, the lack of separate legal identity of a sole proprietorship means that the liability of sole proprietors is unlimited. They are personally responsible for all the debts of the business. If the business does not have sufficient assets to meet the sums owed to creditors, the personal assets of the sole proprietor (such as savings accounts, automobile, house, boat and cottage) are available to satisfy the debts of the sole proprietorship. Second, the owner owns all the assets and is entitled to all the profits. Consequently, the sole proprietorship does not file a separate income tax return since the profits of the business (income less expenses) of the sole proprietorship are taxable in the hands of the proprietor. Third, a person engaged in business as a sole proprietorship may be able to claim certain tax advantages that would not be available to employees. However, the profits of the sole proprietorship are taxed in the hands of the owner at progressive personal tax rates as opposed to corporate tax rates. The sole proprietorship may end up paying more taxes than would a corporation with similar income. Fourth, an owner is free of outside interference. The owner does not have to report to shareholders or have audited statements prepared (unless required by a lender). The proprietorship still has to keep adequate books and records, and obtain licences as necessary. 3. Partnerships do not have a legal identity that is separate from the partners; the partners are the partnership, and are therefore personally responsible for the debts and the actions of the partnership. 4. The shareholders of a corporation enjoy the benefit of limited liability. They are only liable for the debts of the corporation to the extent of their capital contribution. The corporation is solely responsible and liable for the payment of its debts. Its debts are not the debts of its owners, the shareholders. The liability of a corporation for its debts is limited to its assets; a corporation's creditors have no claim on the personal assets of its shareholders for the payment of the corporation's debts. There is no need for the approval of other shareholders before purchasing a corporation's shares. Lacking any rules to the contrary, such as those found in a shareholder agreement, no restrictions exist on the sale and purchase or transfer of ownership of a corporation's shares. This absence of restrictions also makes it easier to raise capital to fund the corporation's operations, which is one of the reasons why people choose to incorporate. A corporation has a continuous existence. Shareholders do not have a duty of good faith towards the corporation, nor must they act in the corporation's best interests. The shareholders, the owners, are not necessarily the managers. The corporate vehicle allows for the separation of ownership and management. It is the officers of the corporation and not its shareholders who manage the corporation and who may bind the corporation by forming contracts in the name of the corporation. 5. Major advantages of carrying on business through a corporation are the limited liability of the members, the separation of ownership and management, the ability to raise capital by share issues, a separate existence for tax purposes, the ease of transfer of ownership, particularly in publicly traded companies, and the fact that a corporation has a continuous existence. Solution FR.1
18 Solution FR.2 Solution FR.2 Notes: PV = present value of a lump sum PVOA = present value of an ordinary annuity PVAD = present value of an annuity due N = number of compounding periods Question 1a This is an ordinary annuity with the formula: PV o = FV n (1 + i) n 1. FV = $40,000; I/Y = 8; N = 3; PMT = 0; CPT PV PV = $31, FV = $40,000; I/Y = 8 2 = 4; N = 3 2 = 6; PMT = 0; CPT PV PV = $31, FV = $40,000; I/Y = 8 4 = 2; N = 3 4 = 12; PMT = 0; CPT PV PV = $31, Question 1b 1. This is the future value of an annuity due with the formula: Set your calculator to "begin" mode. PMT = 4,000; N = 5; I/Y = 12; FV = 0; CPT PV PV = $16, This is an annuity due. However, the payments are made annually but the compounding is semiannual. You need to calculate the present value of each payment using the formula for the present value of a lump sum: PV o = FV n (1 + i) n 1st payment (i): 0 compounding periods 2nd payment (ii): 2 compounding periods 3rd payment (iii): 4 compounding periods 4th payment (iv): 6 compounding periods Solution FR.2
19 Solution FR.2 5th payment (v): 8 compounding periods (i) 4, (ii) PMT = 0; FV = 4,000; I/Y = 12/2 = 6; N = 2; CPT PV 3, (iii) PMT = 0; FV = 4,000; I/Y = 12/2 = 6; N = 4; CPT PV 3, (iv) PMT = 0; FV = 4,000; I/Y = 12/2 = 6; N = 6; CPT PV 2, (v) PMT = 0; FV = 4,000; I/Y = 12/2 = 6; N = 8; CPT PV 2, $16, Alternatively, you can find the annual compounding rate that is equivalent to 12% compounded semiannually: ( /2) 2 = (1 + i) 1 i = (1.06) 2 1 i = or 12.36% A rate of 12.36% compounded annually is equivalent to 12% compounded semiannually. Use this rate to solve the question using a financial calculator: Set your calculator to "begin" mode. PMT = 4,000; N = 5; I/Y = 12.36; FV = 0; CPT PV PV = $16, This is the future value of an ordinary annuity. The formula is: Set your calculator to "end" mode. PMT = 4,000; I/Y = 12; N = 5; FV = 0; CPT PV PV = $14, This is an ordinary annuity. However, the payments are made annually but the compounding is semiannual. You need to calculate the present value of each payment using the formula for the present value of a lump sum: PV o = FV n (1 + i) n 1st payment (i): 2 compounding periods 2nd payment (ii): 4 compounding periods 3rd payment (iii): 6 compounding periods 4th payment (iv): 8 compounding periods 5th payment (v): 10 compounding periods (i) PMT = 0; FV = 4,000; I/Y = 12/2 = 6; N = 2; CPT PV 3, (ii) PMT = 0; FV = 4,000; I/Y = 12/2 = 6; N = 4; CPT PV 3, (iii) PMT = 0; FV = 4,000; I/Y = 12/2 = 6; N = 6; CPT PV 2, (iv) PMT = 0; FV = 4,000; I/Y = 12/2 = 6; N = 8; CPT PV 2, (v) PMT = 0; FV = 4,000; I/Y = 12/2 = 6; N = 10; CPT PV 2, $14, Alternatively, you can find the annual compounding rate that is equivalent to 12% compounded semiannually. In Solution FR.2
20 Solution FR.2 other words, ( /2) 2 = (1 + i) 1 i = (1.06) 2 1 i = or 12.36% A rate of 12.36% compounded annually is equivalent to 12% compounded semiannually. Use this rate to solve the question using a financial calculator: Set your calculator to "end" mode. PMT = 4,000; N = 5; I/Y = 12.36; FV = 0; CPT PV PV = $14, Question 1c This is the present value of an ordinary annuity + the present value of a lump sum: (1) (2) (3) Principal Interest Total 1. $ 100,0001 $ 30,000 $ 130, , , , , , , , , , , , ,000 1 PMT = 6,000; N= 4; I/Y= 6; FV= 0; CPT PV 20, PMT = 0; FV = 106,000; N = 5; I/Y = 6; CPT PV 79, , PMT = 6,000; N= 4; I/Y= 8; FV= 0; CPT PV 19, PMT = 0; FV = 106,000; N = 5; I/Y = 8; CPT PV 72, , PMT = 6,000; N= 4; I/Y= 4; FV= 0; CPT PV 21, PMT = 0; FV = 106,000; N = 5; I/Y = 4; CPT PV 87, , , 6 There are annual payments but semiannual compounding. You need to calculate the present value of each payment using the formula for the present value of a lump sum: PV o = FV n (1 + i) n 1st payment (i): 2 compounding periods 2nd payment (ii): 4 compounding periods 3rd payment (iii): 6 compounding periods 4th payment (iv): 8 compounding periods Solution FR.2
21 Solution FR.2 5th payment (v): 10 compounding periods 4 PMT = 0; FV = 6,000; I/Y = 6/2 = 3; N = 2; CPT PV 5, PMT = 0; FV = 6,000; I/Y = 6/2 = 3; N = 4; CPT PV 5, PMT = 0; FV = 6,000; I/Y = 6/2 = 3; N = 6; CPT PV 5, PMT = 0; FV = 6,000; I/Y = 6/2 = 3; N = 8; CPT PV 4, PMT = 0; FV = 106,000; I/Y = 6/2 = 3; N = 10; CPT PV 78, , (6,000 4) + 106,000 = 130,000 6 PMT = 0; FV = 6,000; I/Y = 8/2 = 4; N = 2; CPT PV 5, PMT = 0; FV = 6,000; I/Y = 8/2 = 4; N = 4; CPT PV 5, PMT = 0; FV = 6,000; I/Y = 8/2 = 4; N = 6; CPT PV 4, PMT = 0; FV = 6,000; I/Y = 8/2 = 4; N = 8; CPT PV 4, PMT = 0; FV = 106,000; I/Y = 8/2 = 4; N = 10; CPT PV 71, , Question 1d N I/Y = 6 I/Y = 16 Payment $ 40,000 5 Amount $168,4951 Amount $130, ,000 10, ,9542 5, ,1796 1,9547 5, , $239,202 $164,947 1, 2, 5, 6 Present value of an ordinary annuity: 3, 4, 7, 8 Present value of a lump sum: PV o = FV n (1 + i) n 1 PMT = 40,000; N = 5; I/Y = 6; FV = 0; CPT PV 168, PMT = 20,000; N = 10; I/Y = 6; FV = 0; CPT PV 147, PMT = 20,000; N = 5; I/Y = 6; FV = 0; CPT PV 84, , PMT = 0; N = 11; I/Y = 6; FV = 10,000; CPT PV PMT = 0; N = 12; I/Y = 6; FV = 5,000; CPT PV 5, , , PMT = 40,000; N = 5; I/Y = 16; FV = 0; CPT PV 130, PMT = 20,000; N = 10; I/Y = 16; FV = 0; CPT PV PMT = 20,000; N = 5; I/Y = 16; FV = 0; CPT PV 96, , , PMT = 0; N = 11; I/Y = 16; FV = 10,000; CPT PV 1, PMT = 0; N = 12; I/Y = 16; FV = 5,000; CPT PV , Question 2a For 1 and 2, use the formula for the present value of an ordinary annuity and solve for PMT: Solution FR.2
22 Solution FR.2 1. PV= 120,000; N = 6; I/Y = 10; FV = 0; CPT PMT PMT = $27, PV= 120,000; N = 6; I/Y= 6; FV = 0; CPT PMT PMT = $24,404 For 3 and 4, use the formula for the present value of an annuity due and solve for PMT: Set your calculator to "begin" mode. 3. PV = 120,000; N = 6; I/Y = 10; FV = 0; CPT PMT PMT = $25, PV = 120,000; N = 6; I/Y = 6; FV = 0; CPT PMT PMT = $23,022 Question 2b For 1 and 3, use the formula for the present value of an ordinary annuity: 1. PMT = 10,856; N = 6; FV = 0; PV = 40,000; CPT I/Y I/Y = 16.00% 3. PMT = 4,074; FV = 0; PV = 40,000; I/Y = 8; CPT N Solution FR.2
23 Solution FR.2 N = 20 payments For 2 and 4, use the formula for the present value of an annuity due: Set your calculator to "begin" mode. 2. PMT = 5,323; N = 10; FV = 0; PV = 40,000; CPT I/Y I/Y = 7.00% 4. PMT = 4,936; FV = 0; PV = 40,000; I/Y = 10; CPT N N = 14 payments Question 3a 1. Use the formula for the present value of an ordinary annuity and solve for PMT: PV = 100,000; N = 5; FV = 0; I/Y = 10; CPT PMT PMT = $26, Use the formula for the present value of an annuity due and solve for PMT: Set your calculator to "begin" mode. PV = 100,000; N = 5; FV = 0; I/Y = 10; CPT PMT PMT = 23, Question 3b 1. Payment rounded to $26,380. Solution FR.2
24 Solution FR.2 Instalment payment Date Beginning principal (1) Interest (2) Principal (3) Ending principal (4) Dec. 31, 20X7 $100,000 $10,000 $16,380 $83,620 Dec. 31, 20X8 83,620 8,362 18,018 65,602 Dec. 31, 20X9 65,602 6,560 19,820 45,782 Dec. 31, 20Y0 45,782 4,578 21,802 23,980 Dec. 31, 20Y1 23,980 2,400* 23,980 Calculations: (2) Interest = (1) 10% (3) Principal = $26,380 (2) (4) Ending principal = (1) (3) * Adjusted $2 to compensate for rounding the payment. 2. Payment rounded to $23,981 Instalment payment Date Beginning principal (1) Interest (2) Principal (3) Ending principal (4) Jan. 1, 20X7 $100,000 $23,981 $76,019 Jan. 1, 20X8 76,019 $ 7,602 16,380 59,639 Jan. 1, 20X9 59,639 5,964 18,018 41,621 Jan. 1, 20Y0 41,621 4,162 19,820 21,801 Jan. 1, 20Y1 21,801 2,180 21,801 Calculations: (2) Interest = (1) 10% (3) Principal = $23,981 (2) (4) Ending principal = (1) (3) Solution FR.2
Corporate Finance Fundamentals [FN1]
Page 1 of 32 Foundation review Introduction Throughout FN1, you encounter important techniques and concepts that you learned in previous courses in the CGA program of professional studies. The purpose
More informationModule 5: Interest concepts of future and present value
Page 1 of 23 Module 5: Interest concepts of future and present value Overview In this module, you learn about the fundamental concepts of interest and present and future values, as well as ordinary annuities
More informationModule 5: Interest concepts of future and present value
file:///f /Courses/201011/CGA/FA2/06course/m05intro.htm Module 5: Interest concepts of future and present value Overview In this module, you learn about the fundamental concepts of interest and present
More informationFinance 331 Corporate Financial Management Week 1 Week 3 Note: For formulas, a Texas Instruments BAII Plus calculator was used.
Chapter 1 Finance 331 What is finance?  Finance has to do with decisions about money and/or cash flows. These decisions have to do with money being raised or used. General parts of finance include: 
More informationChapter 6. Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams
Chapter 6 Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams 1. Distinguish between an ordinary annuity and an annuity due, and calculate present
More informationDISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS
Chapter 5 DISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS The basic PV and FV techniques can be extended to handle any number of cash flows. PV with multiple cash flows: Suppose you need $500 one
More informationChapter 6 Contents. Principles Used in Chapter 6 Principle 1: Money Has a Time Value.
Chapter 6 The Time Value of Money: Annuities and Other Topics Chapter 6 Contents Learning Objectives 1. Distinguish between an ordinary annuity and an annuity due, and calculate present and future values
More informationKey Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Chapter Outline. Multiple Cash Flows Example 2 Continued
6 Calculators Discounted Cash Flow Valuation Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute
More informationPresent Value Concepts
Present Value Concepts Present value concepts are widely used by accountants in the preparation of financial statements. In fact, under International Financial Reporting Standards (IFRS), these concepts
More information1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%?
Chapter 2  Sample Problems 1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%? 2. What will $247,000 grow to be in
More informationCALCULATOR TUTORIAL. Because most students that use Understanding Healthcare Financial Management will be conducting time
CALCULATOR TUTORIAL INTRODUCTION Because most students that use Understanding Healthcare Financial Management will be conducting time value analyses on spreadsheets, most of the text discussion focuses
More informationDeterminants of Valuation
2 Determinants of Valuation Part Two 4 Time Value of Money 5 FixedIncome Securities: Characteristics and Valuation 6 Common Shares: Characteristics and Valuation 7 Analysis of Risk and Return The primary
More informationDiscounted Cash Flow Valuation
6 Formulas Discounted Cash Flow Valuation McGrawHill/Irwin Copyright 2008 by The McGrawHill Companies, Inc. All rights reserved. Chapter Outline Future and Present Values of Multiple Cash Flows Valuing
More informationTVM Applications Chapter
Chapter 6 Time of Money UPS, Walgreens, Costco, American Air, Dreamworks Intel (note 10 page 28) TVM Applications Accounting issue Chapter Notes receivable (longterm receivables) 7 Longterm assets 10
More informationChapter 4. The Time Value of Money
Chapter 4 The Time Value of Money 1 Learning Outcomes Chapter 4 Identify various types of cash flow patterns Compute the future value and the present value of different cash flow streams Compute the return
More informationChapter The Time Value of Money
Chapter The Time Value of Money PPT 92 Chapter 9  Outline Time Value of Money Future Value and Present Value Annuities TimeValueofMoney Formulas Adjusting for NonAnnual Compounding Compound Interest
More information3. If an individual investor buys or sells a currently owned stock through a broker, this is a primary market transaction.
Spring 2012 Finance 3130 Sample Exam 1A Questions for Review 1. The form of organization for a business is an important issue, as this decision has very significant effect on the income and wealth of the
More informationTime Value of Money. Reading 5. IFT Notes for the 2015 Level 1 CFA exam
Time Value of Money Reading 5 IFT Notes for the 2015 Level 1 CFA exam Contents 1. Introduction... 2 2. Interest Rates: Interpretation... 2 3. The Future Value of a Single Cash Flow... 4 4. The Future Value
More informationThe time value of money: Part II
The time value of money: Part II A reading prepared by Pamela Peterson Drake O U T L I E 1. Introduction 2. Annuities 3. Determining the unknown interest rate 4. Determining the number of compounding periods
More informationChapter 3. Understanding The Time Value of Money. PrenticeHall, Inc. 1
Chapter 3 Understanding The Time Value of Money PrenticeHall, Inc. 1 Time Value of Money A dollar received today is worth more than a dollar received in the future. The sooner your money can earn interest,
More informationChapter 4 Time Value of Money ANSWERS TO ENDOFCHAPTER QUESTIONS
Chapter 4 Time Value of Money ANSWERS TO ENDOFCHAPTER QUESTIONS 41 a. PV (present value) is the value today of a future payment, or stream of payments, discounted at the appropriate rate of interest.
More informationBasic financial arithmetic
2 Basic financial arithmetic Simple interest Compound interest Nominal and effective rates Continuous discounting Conversions and comparisons Exercise Summary File: MFME2_02.xls 13 This chapter deals
More informationAppendix C 1. Time Value of Money. Appendix C 2. Financial Accounting, Fifth Edition
C 1 Time Value of Money C 2 Financial Accounting, Fifth Edition Study Objectives 1. Distinguish between simple and compound interest. 2. Solve for future value of a single amount. 3. Solve for future
More informationReview for Exam 1. Instructions: Please read carefully
Review for Exam 1 Instructions: Please read carefully The exam will have 20 multiple choice questions and 4 work problems. Questions in the multiple choice section will be either concept or calculation
More informationThe Time Value of Money
The Time Value of Money Time Value Terminology 0 1 2 3 4 PV FV Future value (FV) is the amount an investment is worth after one or more periods. Present value (PV) is the current value of one or more future
More information6: Financial Calculations
: Financial Calculations The Time Value of Money Growth of Money I Growth of Money II The FV Function Amortisation of a Loan Annuity Calculation Comparing Investments Worked examples Other Financial Functions
More informationOrdinary Annuities Chapter 10
Ordinary Annuities Chapter 10 Learning Objectives After completing this chapter, you will be able to: > Define and distinguish between ordinary simple annuities and ordinary general annuities. > Calculate
More informationBond valuation. Present value of a bond = present value of interest payments + present value of maturity value
Bond valuation A reading prepared by Pamela Peterson Drake O U T L I N E 1. Valuation of longterm debt securities 2. Issues 3. Summary 1. Valuation of longterm debt securities Debt securities are obligations
More informationTime Value of Money. 2014 Level I Quantitative Methods. IFT Notes for the CFA exam
Time Value of Money 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction... 2 2. Interest Rates: Interpretation... 2 3. The Future Value of a Single Cash Flow... 4 4. The
More informationProblem Set: Annuities and Perpetuities (Solutions Below)
Problem Set: Annuities and Perpetuities (Solutions Below) 1. If you plan to save $300 annually for 10 years and the discount rate is 15%, what is the future value? 2. If you want to buy a boat in 6 years
More informationDiscounted Cash Flow Valuation
Discounted Cash Flow Valuation Chapter 5 Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute
More informationStatistical Models for Forecasting and Planning
Part 5 Statistical Models for Forecasting and Planning Chapter 16 Financial Calculations: Interest, Annuities and NPV chapter 16 Financial Calculations: Interest, Annuities and NPV Outcomes Financial information
More informationContinue this process until you have cleared the stored memory positions that you wish to clear individually and keep those that you do not.
Texas Instruments (TI) BA II PLUS Professional The TI BA II PLUS Professional functions similarly to the TI BA II PLUS model. Any exceptions are noted here. The TI BA II PLUS Professional can perform two
More informationCompounding Quarterly, Monthly, and Daily
126 Compounding Quarterly, Monthly, and Daily So far, you have been compounding interest annually, which means the interest is added once per year. However, you will want to add the interest quarterly,
More informationChapter 2 Applying Time Value Concepts
Chapter 2 Applying Time Value Concepts Chapter Overview Albert Einstein, the renowned physicist whose theories of relativity formed the theoretical base for the utilization of atomic energy, called the
More informationCompound Interest Formula
Mathematics of Finance Interest is the rental fee charged by a lender to a business or individual for the use of money. charged is determined by Principle, rate and time Interest Formula I = Prt $100 At
More informationPV Tutorial Using Excel
EYK 153 PV Tutorial Using Excel TABLE OF CONTENTS Introduction Exercise 1: Exercise 2: Exercise 3: Exercise 4: Exercise 5: Exercise 6: Exercise 7: Exercise 8: Exercise 9: Exercise 10: Exercise 11: Exercise
More informationFIN 3000. Chapter 6. Annuities. Liuren Wu
FIN 3000 Chapter 6 Annuities Liuren Wu Overview 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams Learning objectives 1. Distinguish between an ordinary annuity and an annuity due, and calculate
More informationTime Value of Money Concepts
BASIC ANNUITIES There are many accounting transactions that require the payment of a specific amount each period. A payment for a auto loan or a mortgage payment are examples of this type of transaction.
More informationPV Tutorial Using Calculator (Sharp EL738)
EYK 152 PV Tutorial Using Calculator (Sharp EL738) TABLE OF CONTENTS Calculator Configuration and Abbreviations Exercise 1: Exercise 2: Exercise 3: Exercise 4: Exercise 5: Exercise 6: Exercise 7: Exercise
More informationREVIEW MATERIALS FOR REAL ESTATE ANALYSIS
REVIEW MATERIALS FOR REAL ESTATE ANALYSIS 1997, Roy T. Black REAE 5311, Fall 2005 University of Texas at Arlington J. Andrew Hansz, Ph.D., CFA CONTENTS ITEM ANNUAL COMPOUND INTEREST TABLES AT 10% MATERIALS
More informationFinding the Payment $20,000 = C[1 1 / 1.0066667 48 ] /.0066667 C = $488.26
Quick Quiz: Part 2 You know the payment amount for a loan and you want to know how much was borrowed. Do you compute a present value or a future value? You want to receive $5,000 per month in retirement.
More informationCHAPTER 9 Time Value Analysis
Copyright 2008 by the Foundation of the American College of Healthcare Executives 6/11/07 Version 91 CHAPTER 9 Time Value Analysis Future and present values Lump sums Annuities Uneven cash flow streams
More informationMAT116 Project 2 Chapters 8 & 9
MAT116 Project 2 Chapters 8 & 9 1 81: The Project In Project 1 we made a loan workout decision based only on data from three banks that had merged into one. We did not consider issues like: What was the
More informationChapter 5 Time Value of Money 2: Analyzing Annuity Cash Flows
1. Future Value of Multiple Cash Flows 2. Future Value of an Annuity 3. Present Value of an Annuity 4. Perpetuities 5. Other Compounding Periods 6. Effective Annual Rates (EAR) 7. Amortized Loans Chapter
More informationModule 8: Current and longterm liabilities
Module 8: Current and longterm liabilities Module 8: Current and longterm liabilities Overview In previous modules, you learned how to account for assets. Assets are what a business uses or sells to
More informationTime Value of Money. If you deposit $100 in an account that pays 6% annual interest, what amount will you expect to have in
Time Value of Money Future value Present value Rates of return 1 If you deposit $100 in an account that pays 6% annual interest, what amount will you expect to have in the account at the end of the year.
More informationMain TVM functions of a BAII Plus Financial Calculator
Main TVM functions of a BAII Plus Financial Calculator The BAII Plus calculator can be used to perform calculations for problems involving compound interest and different types of annuities. (Note: there
More informationThis is Time Value of Money: Multiple Flows, chapter 7 from the book Finance for Managers (index.html) (v. 0.1).
This is Time Value of Money: Multiple Flows, chapter 7 from the book Finance for Managers (index.html) (v. 0.1). This book is licensed under a Creative Commons byncsa 3.0 (http://creativecommons.org/licenses/byncsa/
More informationThe Time Value of Money
The following is a review of the Quantitative Methods: Basic Concepts principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in: The Time
More informationChapter 6. Time Value of Money Concepts. Simple Interest 61. Interest amount = P i n. Assume you invest $1,000 at 6% simple interest for 3 years.
61 Chapter 6 Time Value of Money Concepts 62 Time Value of Money Interest is the rent paid for the use of money over time. That s right! A dollar today is more valuable than a dollar to be received in
More informationANNUITIES. Ordinary Simple Annuities
An annuity is a series of payments or withdrawals. ANNUITIES An Annuity can be either Simple or General Simple Annuities  Compounding periods and payment periods coincide. General Annuities  Compounding
More informationIntroduction to the HewlettPackard (HP) 10BII Calculator and Review of Mortgage Finance Calculations
Introduction to the HewlettPackard (HP) 10BII Calculator and Review of Mortgage Finance Calculations Real Estate Division Sauder School of Business University of British Columbia Introduction to the HewlettPackard
More information9. Time Value of Money 1: Present and Future Value
9. Time Value of Money 1: Present and Future Value Introduction The language of finance has unique terms and concepts that are based on mathematics. It is critical that you understand this language, because
More information2 The Mathematics. of Finance. Copyright Cengage Learning. All rights reserved.
2 The Mathematics of Finance Copyright Cengage Learning. All rights reserved. 2.3 Annuities, Loans, and Bonds Copyright Cengage Learning. All rights reserved. Annuities, Loans, and Bonds A typical definedcontribution
More informationCHAPTER 6. Accounting and the Time Value of Money. 2. Use of tables. 13, 14 8 1. a. Unknown future amount. 7, 19 1, 5, 13 2, 3, 4, 6
CHAPTER 6 Accounting and the Time Value of Money ASSIGNMENT CLASSIFICATION TABLE (BY TOPIC) Topics Questions Brief Exercises Exercises Problems 1. Present value concepts. 1, 2, 3, 4, 5, 9, 17, 19 2. Use
More informationExercise 1 for Time Value of Money
Exercise 1 for Time Value of Money MULTIPLE CHOICE 1. Which of the following statements is CORRECT? a. A time line is not meaningful unless all cash flows occur annually. b. Time lines are useful for visualizing
More informationFuture Value. Basic TVM Concepts. Chapter 2 Time Value of Money. $500 cash flow. On a time line for 3 years: $100. FV 15%, 10 yr.
Chapter Time Value of Money Future Value Present Value Annuities Effective Annual Rate Uneven Cash Flows Growing Annuities Loan Amortization Summary and Conclusions Basic TVM Concepts Interest rate: abbreviated
More informationChapter 4. The Time Value of Money
Chapter 4 The Time Value of Money 42 Topics Covered Future Values and Compound Interest Present Values Multiple Cash Flows Perpetuities and Annuities Inflation and Time Value Effective Annual Interest
More informationThe explanations below will make it easier for you to use the calculator. The ON/OFF key is used to turn the calculator on and off.
USER GUIDE Texas Instrument BA II Plus Calculator April 2007 GENERAL INFORMATION The Texas Instrument BA II Plus financial calculator was designed to support the many possible applications in the areas
More informationAppendix. Time Value of Money. Financial Accounting, IFRS Edition Weygandt Kimmel Kieso. Appendix C 1
C Time Value of Money C 1 Financial Accounting, IFRS Edition Weygandt Kimmel Kieso C 2 Study Objectives 1. Distinguish between simple and compound interest. 2. Solve for future value of a single amount.
More informationTime Value of Money. 15.511 Corporate Accounting Summer 2004. Professor S. P. Kothari Sloan School of Management Massachusetts Institute of Technology
Time Value of Money 15.511 Corporate Accounting Summer 2004 Professor S. P. Kothari Sloan School of Management Massachusetts Institute of Technology July 2, 2004 1 LIABILITIES: Current Liabilities Obligations
More informationPresent Value (PV) Tutorial
EYK 151 Present Value (PV) Tutorial The concepts of present value are described and applied in Chapter 15. This supplement provides added explanations, illustrations, calculations, present value tables,
More informationCHAPTER 6 Accounting and the Time Value of Money
CHAPTER 6 Accounting and the Time Value of Money 61 LECTURE OUTLINE This chapter can be covered in two to three class sessions. Most students have had previous exposure to single sum problems and ordinary
More informationHow To Use Excel To Compute Compound Interest
Excel has several built in functions for working with compound interest and annuities. To use these functions, we ll start with a standard Excel worksheet. This worksheet contains the variables used throughout
More informationTHE TIME VALUE OF MONEY
QUANTITATIVE METHODS THE TIME VALUE OF MONEY Reading 5 http://proschool.imsindia.com/ 1 Learning Objective Statements (LOS) a. Interest Rates as Required rate of return, Discount Rate and Opportunity Cost
More informationThe Time Value of Money C H A P T E R N I N E
The Time Value of Money C H A P T E R N I N E Figure 91 Relationship of present value and future value PPT 91 $1,000 present value $ 10% interest $1,464.10 future value 0 1 2 3 4 Number of periods Figure
More informationTexas Instruments BAII Plus Tutorial for Use with Fundamentals 11/e and Concise 5/e
Texas Instruments BAII Plus Tutorial for Use with Fundamentals 11/e and Concise 5/e This tutorial was developed for use with Brigham and Houston s Fundamentals of Financial Management, 11/e and Concise,
More informationMBA Financial Management and Markets Exam 1 Spring 2009
MBA Financial Management and Markets Exam 1 Spring 2009 The following questions are designed to test your knowledge of the fundamental concepts of financial management structure [chapter 1], financial
More informationClick Here to Buy the Tutorial
FIN 534 Week 4 Quiz 3 (Str) Click Here to Buy the Tutorial http://www.tutorialoutlet.com/fin534/fin534week4quiz3 str/ For more course tutorials visit www.tutorialoutlet.com Which of the following
More informationCHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY
CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY 1. The simple interest per year is: $5,000.08 = $400 So after 10 years you will have: $400 10 = $4,000 in interest. The total balance will be
More informationCHAPTER 4 DISCOUNTED CASH FLOW VALUATION
CHAPTER 4 DISCOUNTED CASH FLOW VALUATION Answers to Concepts Review and Critical Thinking Questions 1. Assuming positive cash flows and interest rates, the future value increases and the present value
More informationAPPENDIX. Interest Concepts of Future and Present Value. Concept of Interest TIME VALUE OF MONEY BASIC INTEREST CONCEPTS
CHAPTER 8 Current Monetary Balances 395 APPENDIX Interest Concepts of Future and Present Value TIME VALUE OF MONEY In general business terms, interest is defined as the cost of using money over time. Economists
More informationFinQuiz Notes 2 0 1 4
Reading 5 The Time Value of Money Money has a time value because a unit of money received today is worth more than a unit of money to be received tomorrow. Interest rates can be interpreted in three ways.
More informationModule 1: Corporate Finance and the Role of Venture Capital Financing TABLE OF CONTENTS
1.0 ALTERNATIVE SOURCES OF FINANCE Module 1: Corporate Finance and the Role of Venture Capital Financing Alternative Sources of Finance TABLE OF CONTENTS 1.1 ShortTerm Debt (ShortTerm Loans, Line of
More informationTIME VALUE OF MONEY (TVM)
TIME VALUE OF MONEY (TVM) INTEREST Rate of Return When we know the Present Value (amount today), Future Value (amount to which the investment will grow), and Number of Periods, we can calculate the rate
More informationFinance Unit 8. Success Criteria. 1 U n i t 8 11U Date: Name: Tentative TEST date
1 U n i t 8 11U Date: Name: Finance Unit 8 Tentative TEST date Big idea/learning Goals In this unit you will study the applications of linear and exponential relations within financing. You will understand
More informationChapter 6. Discounted Cash Flow Valuation. Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Answer 6.1
Chapter 6 Key Concepts and Skills Be able to compute: the future value of multiple cash flows the present value of multiple cash flows the future and present value of annuities Discounted Cash Flow Valuation
More informationExercise 6 8. Exercise 6 12 PVA = $5,000 x 4.35526* = $21,776
CHAPTER 6: EXERCISES Exercise 6 2 1. FV = $10,000 (2.65330 * ) = $26,533 * Future value of $1: n = 20, i = 5% (from Table 1) 2. FV = $10,000 (1.80611 * ) = $18,061 * Future value of $1: n = 20, i = 3%
More informationTime Value of Money. 2014 Level I Quantitative Methods. IFT Notes for the CFA exam
Time Value of Money 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction...2 2. Interest Rates: Interpretation...2 3. The Future Value of a Single Cash Flow...4 4. The
More information2. How would (a) a decrease in the interest rate or (b) an increase in the holding period of a deposit affect its future value? Why?
CHAPTER 3 CONCEPT REVIEW QUESTIONS 1. Will a deposit made into an account paying compound interest (assuming compounding occurs once per year) yield a higher future value after one period than an equalsized
More informationUsing Financial Calculators
Chapter 4 Discounted Cash Flow Valuation 4B1 Appendix 4B Using Financial Calculators This appendix is intended to help you use your HewlettPackard or Texas Instruments BA II Plus financial calculator
More informationIntegrated Case. 542 First National Bank Time Value of Money Analysis
Integrated Case 542 First National Bank Time Value of Money Analysis You have applied for a job with a local bank. As part of its evaluation process, you must take an examination on time value of money
More informationCalculating Loan Payments
IN THIS CHAPTER Calculating Loan Payments...............1 Calculating Principal Payments...........4 Working with Future Value...............7 Using the Present Value Function..........9 Calculating Interest
More informationImportant Financial Concepts
Part 2 Important Financial Concepts Chapter 4 Time Value of Money Chapter 5 Risk and Return Chapter 6 Interest Rates and Bond Valuation Chapter 7 Stock Valuation 130 LG1 LG2 LG3 LG4 LG5 LG6 Chapter 4 Time
More informationCHAPTER 2. Time Value of Money 21
CHAPTER 2 Time Value of Money 21 Time Value of Money (TVM) Time Lines Future value & Present value Rates of return Annuities & Perpetuities Uneven cash Flow Streams Amortization 22 Time lines 0 1 2 3
More informationChapter F: Finance. Section F.1F.4
Chapter F: Finance Section F.1F.4 F.1 Simple Interest Suppose a sum of money P, called the principal or present value, is invested for t years at an annual simple interest rate of r, where r is given
More informationCHAPTER 6 DISCOUNTED CASH FLOW VALUATION
CHAPTER 6 DISCOUNTED CASH FLOW VALUATION Answers to Concepts Review and Critical Thinking Questions 1. The four pieces are the present value (PV), the periodic cash flow (C), the discount rate (r), and
More informationThe Time Value of Money
CHAPTER 7 The Time Value of Money After studying this chapter, you should be able to: 1. Explain the concept of the time value of money. 2. Calculate the present value and future value of a stream of cash
More informationDick Schwanke Finite Math 111 Harford Community College Fall 2013
Annuities and Amortization Finite Mathematics 111 Dick Schwanke Session #3 1 In the Previous Two Sessions Calculating Simple Interest Finding the Amount Owed Computing Discounted Loans Quick Review of
More informationTime Value of Money Problems
Time Value of Money Problems 1. What will a deposit of $4,500 at 10% compounded semiannually be worth if left in the bank for six years? a. $8,020.22 b. $7,959.55 c. $8,081.55 d. $8,181.55 2. What will
More information5. Time value of money
1 Simple interest 2 5. Time value of money With simple interest, the amount earned each period is always the same: i = rp o We will review some tools for discounting cash flows. where i = interest earned
More informationThe Institute of Chartered Accountants of India
CHAPTER 4 SIMPLE AND COMPOUND INTEREST INCLUDING ANNUITY APPLICATIONS SIMPLE AND COMPOUND INTEREST INCLUDING ANNUITY APPLICATIONS LEARNING OBJECTIVES After studying this chapter students will be able
More informationCHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY
CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY Answers to Concepts Review and Critical Thinking Questions 1. The four parts are the present value (PV), the future value (FV), the discount
More informationChapter 4. Time Value of Money. Copyright 2009 Pearson Prentice Hall. All rights reserved.
Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value
More informationChapter 4. Time Value of Money. Learning Goals. Learning Goals (cont.)
Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value
More information300 Chapter 5 Finance
300 Chapter 5 Finance 17. House Mortgage A couple wish to purchase a house for $200,000 with a down payment of $40,000. They can amortize the balance either at 8% for 20 years or at 9% for 25 years. Which
More informationFinance CHAPTER OUTLINE. 5.1 Interest 5.2 Compound Interest 5.3 Annuities; Sinking Funds 5.4 Present Value of an Annuity; Amortization
CHAPTER 5 Finance OUTLINE Even though you re in college now, at some time, probably not too far in the future, you will be thinking of buying a house. And, unless you ve won the lottery, you will need
More informationIn Section 5.3, we ll modify the worksheet shown above. This will allow us to use Excel to calculate the different amounts in the annuity formula,
Excel has several built in functions for working with compound interest and annuities. To use these functions, we ll start with a standard Excel worksheet. This worksheet contains the variables used throughout
More informationDiscounted Cash Flow Valuation
BUAD 100x Foundations of Finance Discounted Cash Flow Valuation September 28, 2009 Review Introduction to corporate finance What is corporate finance? What is a corporation? What decision do managers make?
More information