Present Value Concepts


 Adam Barker
 4 years ago
 Views:
Transcription
1 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 are more widely applied than under traditional Canadian GAAP. This appendix will explain the basics that you must be aware of to understand related topics in this text. INTEREST RATES Interest is payment for the use of money. It is the difference between the amount borrowed or invested (the principal) and the amount repaid or collected. The amount of interest to be paid or collected is usually stated as a rate over a specific period of time. The rate of interest is generally stated as an annual rate. The amount of interest involved in any financing transaction is based on three elements: 1. Principal (p): The original amount borrowed or invested 2. Interest rate (i): An annual percentage of the principal 3. Number of periods (n): The time period that the principal is borrowed or invested Simple Interest Simple interest is calculated on the principal amount only. It is the return on the principal for one period. Simple interest is usually expressed as shown in Illustration PV1. Interest Principal Interest Rate Number of Periods (p) (i) (n) Illustration PV1 Simple interest formula For example, if you borrowed $1,000 for 3 years at a simple interest rate of 9% annually, you would pay $270 in total interest, calculated as follows: Interest p i n Year 1 Year 2 Year 3 $1,000 9% 3 $90 $90 $90 $270 $270
2 2 Present Value Concepts Compound Interest Compound interest is the return on (or growth of) the principal for two or more time periods. Compounding calculates interest not only on the principal but also on the interest earned to date on that principal, assuming the interest is left on deposit (i.e., added to the original principal amount). To illustrate the difference between simple and compound interest, assume that you deposit $1,000 in the Last Canadian Bank, where it will earn simple interest of 9% per year, and you deposit another $1,000 in the First Canadian Bank, where it will earn interest of 9% per year compounded annually. Also assume that in both cases you will not withdraw any interest until three years from the date of deposit. The calculation of interest to be received and the accumulated yearend balances are given in Illustration PV2. Last Canadian Bank Accumulated Simple Interest Simple YearEnd Calculation Interest Balance Year 1 $1, % $ $1, Year 2 $1, % $1, First Canadian Bank Accumulated Compound Interest Compound YearEnd Calculation Interest Balance Year 1 $1, % $ $1, Year 2 $1, % $1, Year 3 $1, % $1, Year 3 $1, % $1, $ $25.03 $ Difference Illustration PV2 Simple versus compound interest Note in Illustration PV2 that simple interest uses the initial principal of $1,000 to calculate the interest in all three years. Compound interest uses the accumulated balance (principal plus interest to date) at each year end to calculate interest in the following year. This explains why your compound interest account is larger: you are earning interest on interest. For practical purposes, compounding assumes that unpaid interest earned becomes a part of the principal. The accumulated balance at the end of each year becomes the new principal on which interest is earned during the next year. Assuming all else is equal (especially risk), if you had a choice between investing your money at simple interest or at compound interest, you would choose compound interest. In the example, compounding provides $25.03 of additional interest income. Compound interest is used in most business situations. Simple interest is generally applicable only to shortterm situations of one year or less. Present value concepts use compound interest. CALCULATING PRESENT VALUES In the previous section on compound and simple interest, the initial principal was given. It was used to calculate the interest earned and the value of the investment at the end of three years. The initial principal, invested at the beginning of year one, is the present value of the investment. The value of the investment at the end of three years is the future value of the investment. You are probably more accustomed to being given the present value and then calculating the future value. But in business, there are many situations in which the future value is given, and it is necessary to calculate the present value. For example, we determine the market price of a bond by calculating the present value of the principal and interest payments. Calculating the amount to be reported for fixed and intangible assets, notes payable, pensions, and finance lease liabilities can also involve present value calculations. Present value calculations are always based on three variables:
3 Calculating Present Values 3 1. The dollar amount to be received (the future amount or future value) 2. The length of time until the amount is received (the number of periods) 3. The interest rate (the discount rate) per period The process of determining the present value is often referred to as discounting the future cash flows. The word discount has many meanings in accounting, each of which varies with the context in which it is being used. Be careful not to confuse the use of this term. Present Value of a Single Future Amount In the following section, we will show three methods of calculating the present value of a single future amount: present value formula, present value tables, and financial calculators. Present Value Formula To illustrate present value concepts, assume that you want to invest a sum of money at 5% in order to have $1,000 at the end of one year. The amount that you would need to invest today is called the present value of $1,000 discounted for one year at 5%. The variables in this example are shown in the time diagram in Illustration PV3. Present Value = $ Future Amount = $1,000 i 5% n 1 year Now 1 Year Illustration PV3 Time diagram for the present value of $1,000 discounted for one period at 5% The formula used to determine the present value for any interest (discount) rate (i), number of periods (n), and future amount (FV) is shown in Illustration PV4. Future value (FV) Present value (PV) (l i) n FV (1 i) n Illustration PV4 Present value of a single future amount formula In applying this formula to calculate the present value (PV) for the above example, the future value (FV) of $1,000, the interest (discount) rate (i) of 5%, and the number of periods (n) of one are used as follows: PV $1,000 (1 5%) 1 $1, $ If the single future cash flow of $1,000 is to be received in two years and discounted at 5%, its present value is calculated as follows: PV $1,000 (1 5%) 2 $1, or [($1, ) 1.05] $ The time diagram in Illustration PV5 shows the variables used to calculate the present value when cash is received in two years.
4 4 Present Value Concepts Illustration PV5 Time diagram for present value of $1,000 discounted for two periods at 5% Present Value = $ Future Amount = $1,000 Now i 5% n 2 years 1 2 Years Present Value Tables The present value may also be determined through tables that show the present value of 1 for n periods for different periodic interest rates or discount rates. In Table PV1, the rows represent the number of discounting periods and the columns the periodic interest or discount rates. The fivedigit decimal numbers in the respective rows and columns are the factors for the present value of 1. When present value tables are used, the present value is calculated by multiplying the future cash amount by the present value factor specified at the intersection of the number of periods and the discount rate. For example, if the discount rate is 5% and the number of periods is 1, Table PV1 shows that the present value factor is Then the present value of $1,000 discounted at 5% for one period is calculated as follows: PV $1, $ For two periods at a discount rate of 5%, the present value factor is The present value of $1,000 discounted at 5% for two periods is calculated as follows: PV $1, $ Note that the present values in these two examples are identical to the amounts determined previously when using the present value formula. This is because the factors in a present value table have been calculated using the present value formula. The benefit of using a present value table is that it can be quicker than using the formula. If you are using a simple calculator (not a financial calculator) or doing the calculations by hand, there are more calculations involved as the number of periods increase, making it more tedious than using the present value tables. Table PV1 can also be used if you know the present value and wish to determine the future cash flow. The present value amount is divided by the present value factor specified at the intersection of the number of periods and the discount rate in Table PV1. For example, it can easily be determined that an initial investment of $ will grow to yield a future amount of $1,000 in two periods, at an annual discount rate of 5% ($1,000 $ ).
5 Calculating Present Values 5 Table PV1 PRESENT VALUE OF 1 PV 1 (1 i) n (n) Periods 2% 2 1 /2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 15% Financial Calculators Present values can also be calculated using financial calculators. A financial calculator will perform the same calculation as a simple calculator, but it requires fewer steps and less input. Basically, with a financial calculator, you input the future value, the discount rate, and the number of periods, and then tell it to calculate the present value. We will not illustrate how to use a financial calculator because the details vary with different financial calculators. But you should know that the present value amounts calculated with a financial calculator can be slightly different than those calculated with present value tables. That is because the numbers in a present value table are rounded. For example, in Table PV1 the factors are rounded to five digits. In a financial calculator, only the final answer is rounded to the number of digits you have specified. A major benefit of using a financial calculator is that you are not restricted to the interest rates or numbers of periods on a present value table. In Table PV1, present value factors have been calculated for 13 interest rates (there are 13 columns in that table) and the maximum number of periods is 20. With a financial calculator you could, for example, calculate the present value of a future amount to be received in 25 periods using 5.75% as the discount rate. Later in this appendix, we will illustrate how to partly overcome this limitation of present value tables through a method called interpolation. Regardless of the method used in calculating present values, a higher discount rate produces a smaller present value. For example, using an 8% discount rate, the present value of $1,000 due one year from now is $ versus $ at 5%. It should also be recognized that the further away from the present the future cash flow is, the smaller the present value. For example, using the same discount rate of 5%, the present value of $1,000 due in five years is $ The present value of $1,000 due in one year is $
6 6 Present Value Concepts BEFORE YOU GO ON Review It 1. Distinguish between simple and compound interest. 2. Distinguish between present value and future value. 3. What are the three variables used in calculating present value? 4. When calculating present value, what are the benefits of using present value tables and of using financial calculators? Do It Suppose you have a winning lottery ticket and the lottery commission gives you the option of taking $10,000 three years from now, or taking the present value of $10,000 now. If an 8% discount rate is used, what is the present value of your winnings if you take the option of receiving $10,000 three years from now? Show the calculation using either (a) the present value formula or (b) Table PV1. Action Plan Note that $10,000 is the future value, the number of periods is 3, and the discount rate is 8%. Recall that the present value of $10,000 to be received in 3 years is less than $10,000 because interest can be earned on an amount invested today (i.e., the present value) over the next three years. Understand that the discount rate used to calculate the present value is the compound interest rate that would be used to earn $10,000 in 3 years if the present value is invested today. Draw a time diagram showing when the future value will be received, the discount rate, and the number of periods. PV (?) $10,000 i 8% n 3 Now Years Solution (a) Using the present value formula: PV $10,000 (1 8%) 3 $10, or {[($10, ) 1.08] 1.08} $7, (b) Using the present value factor from Table PV1: The present value factor for three periods at 8% is PV $10, $7, Do It Again Determine the amount you must deposit now in your savings account, paying 3% interest, in order to accumulate $5,000 for a down payment on a hybrid electric car four years from now, when you graduate. Show the calculation using either (a) present value formula, or (b) Table PV1. Action Plan Note that $5,000 is the future value, n 4, and i 3%. Draw a time diagram showing when the future value will be received, the discount rate, and the number of periods. PV (?) $5,000 i 3% n 4 2 Now Years
7 Present Value of a Series of Future Cash Flows (Annuities) 7 Solution The amount you must deposit now in your savings account is the present value calculated as follows: (a) Using the present value formula: PV $5,000 (1 3%) 4 $5, or ({[($5, ) 1.03] 1.03} 1.03) $4, (b) Using the present value factor from Table PV1: The present value factor for four periods at 3% is PV $5, PV $4, Note: The difference in the two answers is due to rounding the factors in Table PV1. Related exercise material: BEPV1, BEPV2, BEPV3, BEPV4, and BEPV5. PRESENT VALUE OF A SERIES OF FUTURE CASH FLOWS (ANNUITIES) The preceding discussion was for the discounting of only a single future amount. Businesses and individuals frequently engage in transactions in which a series of equal dollar amounts are to be received or paid periodically. Examples of a series of periodic receipts or payments are loan agreements, instalment sales, mortgage notes, lease (rental) contracts, and pension obligations. These series of periodic receipts or payments are called annuities. In calculating the present value of an annuity, it is necessary to know (1) the discount rate (i), (2) the number of discount periods (n), and (3) the amount of the periodic receipts or payments (FV). To illustrate the calculation of the present value of an annuity, assume that you will receive $1,000 cash annually for three years, and that the discount rate is 4%. This situation is shown in the time diagram in Illustration B6. PV (?) $1,000 $1,000 $1,000 i 4% n 3 Now Years Illustration PV6 Time diagram for a threeyear annuity One method of calculating the present value of this annuity is to use the present value formula to determine the present value of each of the three $1,000 payments and then add those amounts as follows: PV [$1,000 (1 4%) 1 ] [$1,000 (1 4%) 2 ] [$1,000 (1 4%) 3 ] $ $ $ $2, The same result is achieved by using present value factors from Table PV1, as shown in Illustration PV7. Present Value of 1 Future Value Factor at 4% Present Value $1,000 (one year away) $ ,000 (two years away) ,000 (three years away) $2, Illustration PV7 Present value of a series of future cash flows
8 8 Present Value Concepts Determining the present value of each single future cash flow, and then adding the present values, is required when the periodic cash flows are not the same in each period. But when the future receipts are the same in each period, there are three other ways to calculate present value. The first is to use the present value of an ordinary annuity formula, as shown in Illustration PV8. Illustration PV8 Present value of an ordinary annuity of 1 formula Present value (PV ) Future value (FV ) 1 1 (1 i) n $1,000 [(1 (1 (1 + 4%) 3 )) 4%] $1,000 [(1 (1 (1.04) 3 )) 0.04] $1,000 [(1 ( )) 0.04] $1,000 [( ) 0.04] $1, $2, i Table PV2 PRESENT VALUE OF AN ANNUITY OF 1 PV 1 1 (1 i) n (n) Periods 2% 2 1 /2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 15% i The second is to use a present value of an annuity table. As illustrated in Table PV2, these tables show the present value of 1 to be received periodically for a given number of periods. From Table PV2, it can be seen that the present value factor of an annuity of 1 for three periods at 4% is This present value factor is the total of the three individual present value factors, as shown in Illustration PV7.1 Applying this present value factor to the annual cash flow of $1,000 produces a present value of $2, ($1, ).
9 Present Value of a Series of Future Cash Flows (Annuities) 9 The third method is to use a financial calculator and input the number of periods, the interest rate, and the amount of the annual payment. When using a financial calculator to calculate the present value of an annuity, it is also necessary to specify if the annual cash flow is an ordinary annuity or an annuity in arrears. In an ordinary annuity, the first payment is at the end of the first period, as in our example. In an annuity in arrears, the first payment starts immediately, at the beginning of the first period. In this appendix and textbook, all of the annuity examples are ordinary annuities. Interest Rates and Time Periods In the preceding calculations, the discounting has been done on an annual basis using an annual interest rate. There are situations where adjustments may be required to the interest rate, the time period, or both. Using Time Periods of Less Than One Year Discounting may be done over shorter periods of time than one year, such as monthly, quarterly, or semiannually. When the time frame is less than one year, it is necessary to convert the annual interest rate to the applicable time frame. Assume, for example, that the investor in Illustration PV6 received $500 semiannually for three years instead of $1,000 annually. In this case, the number of periods (n) becomes six (three annual periods 2), and the discount rate (i) is 2% (4% 6 /12 months). If present value tables are used to determine the present value, the appropriate present value factor from Table PV2 is The present value of the future cash flows is $2, ( $500). This amount is slightly higher than the $2, calculated in Illustration PV8 because interest is calculated twice during the same year. Thus, interest is compounded on the first halfyear s interest. Interpolation As previously discussed, one of the limitations of the present value tables is that the tables contain a limited number of interest rates. But in certain situations where the factor for a certain interest rate is not available, it can be deduced or interpolated from the tables. For example, if you wished to find the factor to determine the present value of 1 for a 3 1 /2% interest rate and five periods, it would be difficult to use Table PV1 to do so. Table PV1 (or Table PV2 for that matter) does not have a 3 1 /2% interest rate column. We can, however, average the factors for the 3% and 4% interest rates to approximate the factor for a 3 1 /2% interest rate. Factor, n 5, i 3% Factor, n 5, i 4% Sum of two factors Average two factors 2 Factor, n 5, i 31 2% Illustration PV9 Interpolation of 3 1 /2% interest rate factor 1 The difference of between and is due to rounding. As previously mentioned, interpolation is only necessary when using present value tables. If a financial calculator is used, any interest rate can be used in the calculations.
10 10 Present Value Concepts BEFORE YOU GO ON Review It 1. What is an annuity? 2. How is Table PV2 used to calculate the present value of an annuity? 3. If an annuity is paid every three months for five years and 8% is the annual discount rate, what are the number of periods (n) and the interest rate (i) used in the present value calculation? 4. When is it necessary to interpolate an interest rate? Do It Corkum Company has just signed a capital lease contract for equipment that requires rental payments of $6,000 each, to be paid at the end of each of the next five years. The appropriate discount rate is 6%. What is the present value of the rental payments; that is, the amount used to capitalize the leased equipment? Show the calculation using either (a) the present value of an annuity formula or (b) Table PV2. Action Plan Draw a time diagram showing when the future value will be received, the discount rate, and the number of periods. PV (?) $6,000 $6,000 $6,000 $6,000 $6,000 i 6% n 5 Now Years Note that each of the future payments is the same amount paid at even intervals; therefore, use present value of an annuity calculations to determine the present value (i 6% and n 5). Solution The present value of lease rental payments of $6,000 paid at the end of each year for five years, discounted at 6%, is calculated as follows: (a) Using the present value of an annuity formula: PV $6,000 [(1 (1 (1 6%) 5 ) 6%] $6,000 [(1 (1 (1.06) 5 ) 0.06] $6,000 [(1 ( ) 0.06] $6,000 [( ) 0.06] $6, $25, (b) Using the present value factor from Table PV2: The present value factor from Table PV2 is (five periods at 6%). PV $6, PV $25, Related exercise material: BEPV6, BEPV7, and BEPV8. APPLYING PRESENT VALUE CONCEPTS Calculating the Market Price or Present Value of a Bond The present value (or market price) of a bond is a function of three variables: (1) the payment amounts, (2) the length of time until the amounts are paid, and (3) the market interest rate, also known as the discount rate. The first variable (dollars to be paid) is made up of two elements: (1) the principal amount (a single sum), and (2) a series of interest payments (an annuity). To calculate the present value of the bond, both the principal amount and the interest payments must be discounted, which requires two different calculations. The present value of a bond can be calculated using present value formulas, factors from the two present value tables, or a financial calculator. We will illustrate only present value tables.
11 It is important to note that the interest rate used to determine the annual or semiannual interest payments is fixed over the life of a bond. This is the bond s contractual interest rate. The company issuing the bond chooses the specific interest rate before issuing the bonds. But investors may use a different interest rate when determining how much they are willing to pay (the present value) for the bonds. Investors are influenced by both general economic conditions and their assessment of the company issuing the bonds. Investors use the market interest rate to determine the present value of the bonds. In the following sections, we will illustrate how to calculate the present value of the bonds using a market interest rate that is equal to, greater than, or less than the contractual interest rate. Market Interest Rate Equals the Contractual Interest Rate Applying Present Value Concepts 11 When the investor s market interest rate is equal to the bond s contractual interest rate, the bonds present value will equal their face value. To illustrate, assume there is a bond issue of fiveyear, 6% bonds with a face value of $100,000. Interest is payable semiannually on January 1 and July 1. In this case, the investor will receive (1) $100,000 at maturity, and (2) a series of 10 $3,000 interest payments [($100,000 6%) 6 /12 months] over the term of the bonds. The length of time (n) is the total number of interest periods (10 periods 5 years 2 payments per year), and the discount rate (i) is the rate per semiannual interest period (3% 6% 6 /12 months). The time diagram in Illustration PV10 shows the variables involved in this discounting situation. DIAGRAM FOR PRINCIPAL Principal Present Amount Value (?) $100,000 i 3% n 10 Now Periods Illustration PV10 Time diagram for the present value of a fiveyear, 6% bond paying interest semiannually DIAGRAM FOR INTEREST Interest Present Payments Value (?) $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 i 3% n 10 Now Periods The calculation of the present value of these bonds using factors from the appropriate present value tables is shown in Illustration PV11. 6% Contractual Rate and 6% Market Rate Present value of principal to be received at maturity $100,000 PV of 1 due in 10 periods (n) at 3% (i) $100, (Table PV1) $ 74,409 Present value of interest to be received periodically over the term of the bonds $3,000 PV of 1 due periodically for 10 periods (n) at 3% (i) $3, (Table PV2) 25,591* Present value of bonds $100,000 Illustration PV11 Present value of principal and interest (face value) *Rounded
12 12 Present Value Concepts Thus, when the market rate is the same as the contractual rate, the bonds will sell at face value. Market Interest Rate Is Greater Than the Contractual Interest Rate Now assume that the investor s market rate of return is 8%, not 6%. The future cash flows are again $100,000 and $3,000, respectively. These cash flows are based on the bond contract and do not vary with the investor s rate of return. But the investor s rate of return can vary, depending on available rates in the marketplace. If the market interest rate is 8%, then the present value is calculated using this rate. In this case, 4% (8% 6 /12 months) will be used because the bonds pay interest semiannually. The present value of the bonds is $91,889, as calculated in Illustration PV12. Illustration PV12 Present value of principal and interest (discount) 6% Contractual Rate and 8% Market Rate Present value of principal to be received at maturity $100,000 PV of 1 due in 10 periods (n) at 4% (i) $100, (Table PV1) $67,556 Present value of interest to be received periodically over the term of the bonds $3,000 PV of 1 due periodically for 10 periods (n) at 4% (i) $3, (Table PV2) 24,333* Present value of bonds $91,889 *Rounded In this situation, the bonds will sell for $91,889, at a discount of $8,111. If the market interest rate is greater than the contract interest rate, the bonds will always sell at a discount. If investors determine that the bond s contract interest rate is too low, they will compensate by paying less for the bonds. Note that they will still collect the full $100,000 at the maturity date. Market Interest Rate Is Less Than the Contractual Interest Rate On the other hand, the market rate might be lower than the contract interest rate. In this case, the interest paid on the bonds is higher than what investors expected to earn. As a result, they will compensate by paying more for the bonds. If the market interest rate is 5%, the present value will be calculated using 2.5% (5% 6 /12 months) as the discount rate. The cash payments and number of periods remain the same. In this case, the present value of the bonds is $104,376, calculated as in Illustration PV13. Illustration PV13 Present value of principal and interest (premium) 6% Contractual Rate and 5% Market Rate Present value of principal to be received at maturity $100,000 PV of 1 due in 10 periods (n) at 2.5% (i) $100, (Table PV1) $ 78,120 Present value of interest to be received periodically over the term of the bonds $3,000 PV of 1 due periodically for 10 periods (n) at 2.5% (i) $3, (Table PV2) 26,256* Present value of bonds $104,376 *Rounded
13 Applying Present Value Concepts 13 These bonds will sell at a $4,376 premium for $104,376. If the market interest rate is less than the contract interest rate, the bonds will always sell at a premium. The above discussion relied on present value tables to solve present value problems. As previously discussed, financial calculators may also be used to calculate present values without the use of these tables. In addition, most computer spreadsheets and programs also have builtin formulas to perform the discounting functions. BEFORE YOU GO ON Review It 1. Explain how the present value of a bond is determined. 2. Distinguish between the market rate of interest and the contractual rate of interest. How is each of these used in determining the present value of a bond? 3. If the bonds have interest payable semiannually, how is the discount rate (i) determined? How is the number of periods (n) determined? 4. If the market rate is greater than the contract rate, will the bonds sell at a premium or a discount? Explain. Do It Forest Lake Enterprises issued $1 million of sixyear, 4.5% bonds that pay interest semiannually. The market rate of interest for the bonds at the issue date is 4%. What cash proceeds did Forest Lake Enterprises receive from the issue of the bonds? Action Plan Note that Forest Lake will be able to sell these bonds at a premium because the bonds pay higher interest (4.5%) than the current market interest rate (4%). Recall that the contractual interest rate is used to determine the interest payment; the market rate is used to determine the present value. Adjust the interest rates and number of periods for the effect of the semiannual periods. Use Table PV1 to determine the present value of the principal. Use Table PV2 to determine the present value of the interest payments. Solution 1. Amount to be received at maturity is the face value of the bonds, $1,000, Semiannual interest payment $22,500 ($1,000, % 6 /12 months) 3. Number of periods n 12 (6 years 2 payments a year) 4. Discount rate i 2% (4% 2 payments a year) The cash proceeds that Forest Lake will receive from issuing the bonds is the present value of principal to be received at maturity plus the present value of the interest received periodically, calculated as follows: Present value of principal to be received at maturity: $1,000, (PV of $1 due in 12 periods at 2% from Table PV1) $788,490 Present value of interest to be received periodically over the term of the bonds: $22, (PV of $1 due each period for 12 periods at 2% from Table PV2) 237,945 Present value of bonds $1,026,435 Related exercise material: BEPV9 and BEPV10. Calculating the Present Value of Notes Payable Longterm notes payable are normally repayable in a series of periodic payments. These payments may be fixed principal payments plus interest, or blended principal and interest payments. The accounting treatment of notes is similar to that for bonds. The present value of a note is a function of the same three variables: (1) the payment amounts, (2) the length of time until the amounts are paid (time to maturity date), and (3) the market interest rate. Examples of longterm notes payable include unsecured notes, mortgages (which are secured notes on real property, such as a house), and loans (e.g., student or car).
14 14 Present Value Concepts Note Payable: Fixed Principal Payments Plus Interest Let s assume Heathcote Company obtains a fiveyear note payable, with an 8% interest rate, to purchase a piece of equipment costing $25,000. If we first assume that repayment is to be in fixed principal payments plus interest, paid annually, then the payment amount would be $5,000 ($25,000 5 years) plus 8% interest on the outstanding balance. Illustration PV14 details the total cost of this loan over the fiveyear period. Illustration PV14 Cost of equipment loan fixed principal payments plus interest Year 1 Year 2 Year 3 Year 4 Year 5 Total Principal $5,000 $5,000 $5,000 $5,000 $5,000 $25,000 Interest 1 2,000 1,600 1, ,000 Total 7,000 6,600 6,200 5,800 5,400 $31,000 Present value factor Present value $6,482 $5,658 $4,922 $4,263 $3,675 $25,000 1 Interest is calculated on the outstanding principal balance at the beginning of the year. In Year 1, it is $25,000 8% $2,000. In Year 2, it is $20,000 ($25,000 $5,000) 8% $1,600, and so on. 2 These factors are taken from Table PV1, for i 8% and the appropriate n, or number of periods. Note Payable: Blended Principal Plus Interest Payments In the case of blended principal and interest payments, present value concepts are used to calculate the amount of the annual payment. If we divide the total loan amount of $25,000 by the present value factor for an annuity from Table PV2 for i 8% and n 5, then we can determine that the annual payment is $6,261 ($25, ). Illustration PV15 details the total cost of this loan over the fiveyear period. Illustration PV15 Cost of equipment loan blended principal and interest payments Year 1 Year 2 Year 3 Year 4 Year 5 Total Payment $6,261 $6,261 $6,261 $6,261 $6,261 $31,305 Present value factor Present value 2 $5,797 $5,368 $4,970 $4,602 $4,261 $25,000 1 These factors are taken from Table PV1, for i 8% and the appropriate n, or number of periods. 2 The sum of the annual present values is not exactly equal to $25,000 because of rounding. If full digits were used, the total would be $25,000. Comparison of Notes Payable with Fixed Principal versus Blended Payments Both options result in a present value cost of $25,000, but the blended principal and interest payment option results in a higher total cash outflow, $31,305, compared with $31,000 for the fixed principal payments plus interest option. Note the difference also in the annual cash flows required under each option. For example, the fixed principal and interest payment option results in a higher cash outflow in the first two years and lower cash outflow in the last three years. These examples illustrate the effect of the timing and amount of cash flows on the present value. Basically, payments made further away from the present are worth less in present value terms, and payments made closer to the present are worth more.
15 Notes Payable: Stated Interest Rate below Market Interest Rate In the previous two examples, the stated (contract) interest rate and the market (discount) interest rate were both 8%. As a result of these rates being equal, the present value and the principal amount of the loan were both $25,000. We found the same result in the previous section on bonds payable. Businesses sometimes offer financing with stated interest rates below market interest rates to stimulate sales. Examples of notes with stated interest rates below market are seen in advertisements offering no payment for two years. These zerointerestbearing notes do not specify an interest rate to be applied, but the face value is greater than the present value. The present value of these notes is determined by discounting the repayment stream at the market interest rate. As an example, assume that a furniture retailer is offering No payment for two years, or $150 off on items with a sticker price of $2,000. The implicit interest cost over the two years is $150, and the present value of the asset is then $1,850 ($2,000 $150). From Table PV1, the effective interest rate can be determined: PV FV discount factor $1,850 $2, Applying Present Value Concepts 15 Looking at the n 2 row, this would represent an interest rate of approximately 4%. Most notes have an interest cost, whether explicitly stated or not. If a financial calculator is used, the exact interest rate can be determined by inputting $1,850 as the present value, $2,000 as the future value, 2 as the number of periods, and then instructing the calculator to compute the interest rate. The result is an interest rate of 3.975%, which is very close to the 4% estimated by using the present value tables. Also note that the purchaser should record the furniture at a cost of $1,850 even if the purchaser chose the option of no payment for two years. In this case, the purchaser will recognize interest expense of $74 ($1,850 4%) in the first year and $76 [($1,850 $74) 4%] in the second year (numbers have been rounded so total interest expense over two years is equal to $150). Canada Student Loans The Canadian federal government, in an effort to encourage postsecondary education, offers loans to eligible students with no interest accruing while they maintain their student status. When schooling is complete, the entire loan must be repaid within 10 years. Repayment of the loan can be at a fixed rate of prime 5%, or a floating rate of prime 2.5%. Let s assume that you attend school for four years and borrow $2,500 at the end of each year. Upon graduation, you have a total debt of $10,000. If you had not been eligible for the student loan, and had borrowed the money as needed through a conventional lender who agreed to let the interest accrue at 9% over the four years, with no payments required, how much would you owe upon graduation? Compound interest would accrue as shown in Illustration PV16. Year 1 Year 2 Year 3 Year 4 Balance, beginning of period $ 0 $2,500 $5,225 $ Interest 9%) ,725 5,695 8,933 Increase in borrowings 2,500 2,500 2,500 2,500 Balance, end of period $2,500 $5,225 $8,195 $11,433 Illustration PV16 Cost of student loan with a conventional lender
16 16 Present Value Concepts The loan would total $11,433 at the end of Year 4. Note that this is the future value of the loan at an interest rate of 9%. This amount can also be determined using present value concepts as shown in Illustration PV17. Illustration PV17 Cost of student loan with a conventional lender using PV calculations Year 1 Year 2 Year 3 Year 4 Balance, beginning of period (PV) $ 0 $2,500 $5,225 $ From Table PV1; FV PV/ ,725 5,695 8,933 Increase in borrowings 2,500 2,500 2,500 2,500 Balance, end of period $2,500 $5,225 $8,195 $11,433 1 n 1, i 9%; calculation done for each year separately, based on the balance at the beginning of each period. A third way of calculating this future value is to first calculate the PV of an annuity of $2,500 over four years at 9%, and to then calculate the FV of this figure, as follows: From Table PV2, the present value of an annuity of $2,500 per year for 4 years at 9% is: $2, $8, From Table PV1, the future value (4 years at 9%) of $8, is: $8, $11, The benefit of having a Canada Student Loan, as opposed a loan with a conventional lender, is shown in Illustration PV18 by comparing the cost of repaying these two types of loans. Illustration PV18 Calculation of annuity required to repay two loans Canada Student Loan Conventional Loan Value of loan at the end of 4 years $10,000 $11,433 PV factor from Table PV2: n 10; i 9% Annual annuity required to pay the loan $1, $1, Under the Canada Student Loan, there is a nominal savings of $2, [10 ($1, $1,558.20)] over the life of the loan. This example uses present value calculations to illustrate the effect of not incurring interest while you are in school. BEFORE YOU GO ON Review It 1. Explain how calculating the present value of a note is similar to, or different from, calculating the present value of a bond. 2. Differentiate between the two kinds of payment options on a note payable. 3. What are the benefits of having a Canada Student Loan instead of a conventional bank loan? Do It You are about to purchase your first car. You decide to finance the car at an annual interest rate of 7% over a period of 48 months. If your monthly payment is $574.71, how much is the car worth today? Action Plan The present value factor of an annuity for n 48 and i 0.58% (7% 12 months) is Solution The day the car is purchased, it is worth the present value of the future cash payments. The present value of $ to be paid monthly for four years, discounted at 7%, is $24,000 ($ ). Related exercise material: BEPV11, BEPV12, BEPV13, BEPV14, BEPV15, BEPV16, and BEPV17.
17 Assets Estimating Value in Use Using Future Cash Flows As we have learned in a previous section, a bond can be valued based on future cash flows. So too can an asset. In Chapter 9, you learned that companies are required to regularly determine whether the value of property, plant, and equipment has been impaired. Recall that an asset is impaired if the carrying amount reported on the balance sheet is greater than its recoverable amount. The recoverable amount is either the asset s fair value or its value in use. Determining the value in use requires the application of present value concepts. The computation of value in use is a twostep process: (1) future cash flows are estimated, and (2) the present value of these cash flows is calculated. For example, assume JB Company owns a specialized piece of equipment used in its manufacturing process. JB needs to determine the asset s value in use to test for impairment. As the first step in determining value in use, JB s management estimates that the equipment will last for another five years and that it will generate the following future cash flows at the end of each year: Year 1 Year 2 Year 3 Year 4 Year 5 $9,000 $10,000 $13,000 $10,000 $7,000 Applying Present Value Concepts 17 In the second step of determining value in use, JB calculates the present value of each of these future cash flows. Using a discount rate of 8%, the present value of each future cash flow is shown in Illustration PV19. Year 1 Year 2 Year 3 Year 4 Year 5 Future cash flows $9,000 $10,000 $13,000 $10,000 $7,000 Present value factor Present value amount $8,333 $ 8,573 $10,320 $ 7,350 $4,764 Illustration PV19 Present value of estimated future cash flows of specialized equipment 1 The appropriate interest rate to be used is based on current market rates; however, adjustments for uncertainties related to the specific asset may be made. Further discussion on this topic is covered in more advanced texts. The value in use of JB s specialized equipment is the sum of the present value of each year s cash flow, $39,340 ($8,333 $8,573 $10,320 $7,350 $4,764). If this amount is less than the asset s carrying amount, JB will be required to record an impairment as shown in Chapter 9. The present value method of estimating the value in use of an asset can also be used for intangible assets. For example, assume JB purchases a licence from Redo Industries for the right to manufacture and sell products using Redo s processes and technologies. JB estimates it will earn $6,000 per year from this licence over the next 10 years. What is the value in use to JB of this licence? Since JB expects to earn the same amount each year, Table PV2 is used to find the present value factor of the annuity after determining the appropriate discount rate. As pointed out in the previous example, JB should choose a rate based on current market rates; however, adjustments for uncertainties related to the specific asset may be required. Assuming JB uses 8% as the discount rate, the present value factor from Table PV2 for 10 periods is The value in use of the licence is $40,260 ($6, ).
18 18 Present Value Concepts BEFORE YOU GO ON Review It 1. When is it necessary to calculate the value in use of an asset? 2. Explain the two steps in calculating the value in use of an asset. Do It You are attempting to estimate the value in use of your company s production equipment, which you estimate will be used in operations for another eight years. You estimate that the equipment will generate annual cash flows of $16,000, at the end of each year, for the remainder of its productive life, and that 9% is the appropriate discount rate. What is the value in use of this equipment? Action Plan Identify future cash flows. Use Table PV2 to determine the present value of an annuity factor for n 8 and i 9% and calculate the present value. Solution The value in use is equal to the present value of the estimated annual future cash flows for the remaining life of the asset discounted at an appropriate discount rate. Future annual cash flows: $16,000 Number of periods: 8 Discount rate: 9% Present value annuity factor (n 8, i 9%): Present value: $88,557 $16, Related exercise material: BEPV18, BEPV19, and BEPV20. Brief Exercises Calculate simple and compound interest. Calculate present value of a singlesum investment. Calculate future value of a singlesum investment and demonstrate the effect of compounding. Calculate number of periods of a single investment sum. Calculate interest rate on single sum. Calculate present value of an annuity investment. Determine number of periods and discount rate. BEPV 1 Determine the amount of interest that will be earned on each of the following investments: (i) (n) Investment Interest Rate Number of Periods Type of Interest (a) $100 5% 1 Simple (b) $500 6% 2 Simple (c) $500 6% 2 Compound BEPV 2 Smolinski Company is considering an investment that will return a lump sum of $500,000 five years from now. What amount should Smolinski Company pay for this investment in order to earn a 4% return? BEPV 3 Mehmet s parents invest $8,000 in a 10year guaranteed investment certificate (GIC) in his name. The investment pays 4% annually. How much will the GIC yield when it matures? Compare the interest earned in the first and second fiveyear periods, and provide an explanation for the difference. BEPV 4 Janet Bryden has been offered the opportunity to invest $44,401 now. The investment will earn 7% per year, and at the end of that time will return Janet $100,000. How many years must Janet wait to receive $100,000? BEPV 5 If Kerry Dahl invests $3,152 now, she will receive $10,000 at the end of 15 years. What annual rate of interest will Kerry earn on her investment? Round your answer to the nearest whole number. BEPV 6 Kilarny Company is considering investing in an annuity contract that will return $25,000 at the end of each year for 15 years. What amount should Kilarny Company pay for this investment if it earns a 6% return? BEPV 7 For each of the following cases, indicate in the chart below the appropriate discount rate (i) and the appropriate number of periods (n) to be used in present value calculations. Show calculations. The first one has been completed as an example.
19 Brief Exercises 19 Annual Number Frequency (n) Number (i) Discount Interest Rate of Years of Payments of periods Rate 1. 8% 3 Quarterly % 4 2% 2. 5% 4 Semiannually 3. 7% 5 Annually 4. 4% 3 Quarterly 5. 6% 6 Semiannually 6. 6% 15 Monthly BEPV 8 Insert the appropriate discount factor into the table below for each of the situations given. These factors have to be interpolated from Tables PV1 and PV2. Interpolate discount factors. (a) n 4, i 4½% (b) n 6, i 6½% PV of 1 PV of an Annuity of 1 (Table PV1) (Table PV2) BEPV 9 Cross Country Railroad Co. is about to issue $100,000 of 10year bonds that pay a 5.5% annual interest rate, with interest payable semiannually. The market interest rate is 5%. How much can Cross Country expect to receive for the sale of these bonds? BEPV 10 Assume the same information as BEPV9, except that the market interest rate is 6% instead of 5%. In this case, how much can Cross Country expect to receive from the sale of these bonds? BEPV 11 Caledonian Company receives a sixyear, $50,000 note that bears interest at 8% (paid annually) from a customer at a time when the market interest rate is 7%. What is the present value of the note received by Caledonian? BEPV 12 HungChao Yu Company issues a sixyear, 8% mortgage note on January 1, 2011, to obtain financing for new equipment. The terms provide for semiannual instalment payments of $112,825. What were the cash proceeds received from the issue of the note? BEPV 13 You are told that a note has repayment terms of $4,000 per year for five years, with a stated interest rate of 4%. How much of the total payment is for principal, and how much is for interest? BEPV 14 You would like to purchase a car with a list price of $30,000, and the dealer offers financing over a fiveyear period at 8%. If repayments are to be made annually, what would your annual payments be? BEPV 15 Assume the same information as in BEPV14, except that you can only afford to make annual payments of $6,000. If you decide to trade in your present car to help reduce the amount of financing required, what tradein value would you need to negotiate to ensure your annual payment is $6,000? BEPV 16 As CFO of a small manufacturing firm, you have been asked to determine the best financing for the purchase of a new piece of equipment. If the vendor is offering repayment options of $10,000 per year for five years, or no payment for two years followed by one payment of $46,000, which option would you recommend? The current market rate of interest is 8%. Calculate present value of bonds. Calculate present value of bonds. Calculate present value of note. Calculate present value of note. Determine interest and principal payments. Calculate annual payments. Calculate tradein value of car. Compare financing options. BEPV 17 If the market rate of interest in BEPV16 is 10%, would you choose the same option? Compare financing options. BEPV 18 Barney Googal owns a garage and is contemplating purchasing a tire retreading machine for $16,100. After estimating costs and revenues, Barney projects a net cash flow from the retreading machine of $2,690 annually for eight years. Barney hopes to earn a return of 11% on such investments. What is the present value of the retreading operation? Should Barney Googal purchase the retreading machine? BEPV 19 Chang Company must perform an impairment test on its equipment. The equipment will produce the following cash flows: Year 1, $35,000; Year 2, $45,000; Year 3, $55,000. Chang requires a minimum rate of return of 10%. What is the value in use for this equipment? Calculate value of machine for purchase decision. Calculate value in use for a machine.
20 20 Present Value Concepts Calculate value in use of a patent. BEPV 20 ABC Company signs a contract to sell the use of its patented manufacturing technology to DEF Corp for 15 years. The contract for this transaction stipulates that DEF Corp pays ABC $18,000 at the end of each year for the use of this technology. Using a discount rate of 9%, what is the value in use of the patented manufacturing technology? Solutions
Time Value of Money. Nature of Interest. appendix. study objectives
2918T_appC_C01C20.qxd 8/28/08 9:57 PM Page C1 appendix C Time Value of Money study objectives After studying this appendix, you should be able to: 1 Distinguish between simple and compound interest.
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 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. appendix B NATURE OF INTEREST
appendix B Time value of money LEARNING OBJECTIVES After studying this appendix, you should be able to: Distinguish between simple and compound interest. Solve for future value of a single amount. Solve
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 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 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 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, 7
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 2. Use of
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 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 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 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 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 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 informationCalculations for Time Value of Money
KEATMX01_p001008.qxd 11/4/05 4:47 PM Page 1 Calculations for Time Value of Money In this appendix, a brief explanation of the computation of the time value of money is given for readers not familiar with
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 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 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 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 informationAccounting Building Business Skills. Interest. Interest. Paul D. Kimmel. Appendix B: Time Value of Money
Accounting Building Business Skills Paul D. Kimmel Appendix B: Time Value of Money PowerPoint presentation by Kate WynnWilliams University of Otago, Dunedin 2003 John Wiley & Sons Australia, Ltd 1 Interest
More informationPREVIEW OF CHAPTER 62
61 PREVIEW OF CHAPTER 6 62 Intermediate Accounting IFRS 2nd Edition Kieso, Weygandt, and Warfield 6 Accounting and the Time Value of Money LEARNING OBJECTIVES After studying this chapter, you should
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 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 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 informationCorporate 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 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 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 informationPractice Problems. Use the following information extracted from present and future value tables to answer question 1 to 4.
PROBLEM 1 MULTIPLE CHOICE Practice Problems Use the following information extracted from present and future value tables to answer question 1 to 4. Type of Table Number of Periods Interest Rate Factor
More informationChapter 16. Debentures: An Introduction. Noncurrent Liabilities. Horngren, Best, Fraser, Willett: Accounting 6e 2010 Pearson Australia.
PowerPoint to accompany Noncurrent Liabilities Chapter 16 Learning Objectives 1. Account for debentures payable transactions 2. Measure interest expense by the straight line interest method 3. Account
More informationAccounting for Longterm Assets,
1 Accounting for Longterm Assets, Longterm Debt and Leases TABLE OF CONTENTS Introduction 2 Longterm Assets 2 Acquiring or creating 2 Tangible assets 2 Intangible assets 3 Depreciating, amortizing and
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 informationCHAPTER 5. Interest Rates. Chapter Synopsis
CHAPTER 5 Interest Rates Chapter Synopsis 5.1 Interest Rate Quotes and Adjustments Interest rates can compound more than once per year, such as monthly or semiannually. An annual percentage rate (APR)
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 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 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 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 1. Compound Interest
CHAPTER 1 Compound Interest 1. Compound Interest The simplest example of interest is a loan agreement two children might make: I will lend you a dollar, but every day you keep it, you owe me one more penny.
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 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 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 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 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 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 informationFoundation review. Introduction. Learning objectives
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
More informationUSING FINANCIAL CALCULATORS
lwww.wiley.com/col APPEDIX C USIG FIACIAL CALCULATORS OBJECTIVE 1 Use a financial calculator to solve time value of money problems. Illustration C1 Financial Calculator Keys Business professionals, once
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 informationSolutions to Supplementary Questions for HP Chapter 5 and Sections 1 and 2 of the Supplementary Material. i = 0.75 1 for six months.
Solutions to Supplementary Questions for HP Chapter 5 and Sections 1 and 2 of the Supplementary Material 1. a) Let P be the recommended retail price of the toy. Then the retailer may purchase the toy at
More informationPowerPoint. to accompany. Chapter 5. Interest Rates
PowerPoint to accompany Chapter 5 Interest Rates 5.1 Interest Rate Quotes and Adjustments To understand interest rates, it s important to think of interest rates as a price the price of using money. When
More informationTime Value of Money. Work book Section I True, False type questions. State whether the following statements are true (T) or False (F)
Time Value of Money Work book Section I True, False type questions State whether the following statements are true (T) or False (F) 1.1 Money has time value because you forgo something certain today for
More informationThe Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820)
The Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820) Using the Sharp EL738 Calculator Reference is made to the Appendix Tables A1 to A4 in the course textbook Investments:
More informationSample Examination Questions CHAPTER 6 ACCOUNTING AND THE TIME VALUE OF MONEY MULTIPLE CHOICE Conceptual Answer No. Description d 1. Definition of present value. c 2. Understanding compound interest tables.
More informationIntroduction to Real Estate Investment Appraisal
Introduction to Real Estate Investment Appraisal Maths of Finance Present and Future Values Pat McAllister INVESTMENT APPRAISAL: INTEREST Interest is a reward or rent paid to a lender or investor who has
More informationMathematics. Rosella Castellano. Rome, University of Tor Vergata
and Loans Mathematics Rome, University of Tor Vergata and Loans Future Value for Simple Interest Present Value for Simple Interest You deposit E. 1,000, called the principal or present value, into a savings
More informationCheck off these skills when you feel that you have mastered them.
Chapter Objectives Check off these skills when you feel that you have mastered them. Know the basic loan terms principal and interest. Be able to solve the simple interest formula to find the amount of
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 information5.1 Simple and Compound Interest
5.1 Simple and Compound Interest Question 1: What is simple interest? Question 2: What is compound interest? Question 3: What is an effective interest rate? Question 4: What is continuous compound interest?
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 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 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 4 DISCOUNTED CASH FLOW VALUATION
CHAPTER 4 DISCOUNTED CASH FLOW VALUATION Solutions to Questions and Problems NOTE: Allendof chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability
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 informationThe Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820)
The Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820) Using the Sharp EL733A Calculator Reference is made to the Appendix Tables A1 to A4 in the course textbook Investments:
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 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, 4, 6, 7, 11
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 2. Use of
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 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 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 informationFin 3312 Sample Exam 1 Questions
Fin 3312 Sample Exam 1 Questions Here are some representative type questions. This review is intended to give you an idea of the types of questions that may appear on the exam, and how the questions might
More informationTime Value of Money. Background
Time Value of Money (Text reference: Chapter 4) Topics Background One period case  single cash flow Multiperiod case  single cash flow Multiperiod case  compounding periods Multiperiod case  multiple
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 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 informationApplications of Geometric Se to Financ Content Course 4.3 & 4.4
pplications of Geometric Se to Financ Content Course 4.3 & 4.4 Name: School: pplications of Geometric Series to Finance Question 1 ER before DIRT Using one of the brochures for NTM State Savings products,
More informationCHAPTER 4. The Time Value of Money. Chapter Synopsis
CHAPTER 4 The Time Value of Money Chapter Synopsis Many financial problems require the valuation of cash flows occurring at different times. However, money received in the future is worth less than money
More informationApplying Time Value Concepts
Applying Time Value Concepts C H A P T E R 3 based on the value of two packs of cigarettes per day and a modest rate of return? Let s assume that Lou will save an amount equivalent to the cost of two packs
More informationthe Time Value of Money
8658d_c06.qxd 11/8/02 11:00 AM Page 251 mac62 mac62:1st Shift: 6 CHAPTER Accounting and the Time Value of Money he Magic of Interest T Sidney Homer, author of A History of Interest Rates, wrote, $1,000
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 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 informationICASL  Business School Programme
ICASL  Business School Programme Quantitative Techniques for Business (Module 3) Financial Mathematics TUTORIAL 2A This chapter deals with problems related to investing money or capital in a business
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 informationThe following is an article from a Marlboro, Massachusetts newspaper.
319 CHAPTER 4 Personal Finance The following is an article from a Marlboro, Massachusetts newspaper. NEWSPAPER ARTICLE 4.1: LET S TEACH FINANCIAL LITERACY STEPHEN LEDUC WED JAN 16, 2008 Boston  Last week
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 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 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 7 SOLUTIONS TO ENDOFCHAPTER PROBLEMS
Chapter 7 SOLUTIONS TO ENDOFCHAPTER PROBLEMS 71 0 1 2 3 4 5 10% PV 10,000 FV 5? FV 5 $10,000(1.10) 5 $10,000(FVIF 10%, 5 ) $10,000(1.6105) $16,105. Alternatively, with a financial calculator enter the
More informationSection 8.1. I. Percent per hundred
1 Section 8.1 I. Percent per hundred a. Fractions to Percents: 1. Write the fraction as an improper fraction 2. Divide the numerator by the denominator 3. Multiply by 100 (Move the decimal two times Right)
More informationMortgage Basics Glossary of Terms
Mortgage Basics Glossary of Terms Buying a home is an important financial decision. It is important to familiarize yourself with the features of the different types of mortgages, so that you understand
More informationTime Value of Money CAP P2 P3. Appendix. Learning Objectives. Conceptual. Procedural
Appendix B Time Value of Learning Objectives CAP Conceptual C1 Describe the earning of interest and the concepts of present and future values. (p. B1) Procedural P1 P2 P3 P4 Apply present value concepts
More informationLongTerm Debt. Objectives: simple present value calculations. Understand the terminology of longterm debt Par value Discount vs.
Objectives: LongTerm Debt! Extend our understanding of valuation methods beyond simple present value calculations. Understand the terminology of longterm debt Par value Discount vs. Premium Mortgages!
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 informationFinancial Math on Spreadsheet and Calculator Version 4.0
Financial Math on Spreadsheet and Calculator Version 4.0 2002 Kent L. Womack and Andrew Brownell Tuck School of Business Dartmouth College Table of Contents INTRODUCTION...1 PERFORMING TVM CALCULATIONS
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 informationIng. Tomáš Rábek, PhD Department of finance
Ing. Tomáš Rábek, PhD Department of finance For financial managers to have a clear understanding of the time value of money and its impact on stock prices. These concepts are discussed in this lesson,
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 informationSOCIETY OF ACTUARIES FINANCIAL MATHEMATICS. EXAM FM SAMPLE QUESTIONS Interest Theory
SOCIETY OF ACTUARIES EXAM FM FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS Interest Theory This page indicates changes made to Study Note FM0905. January 14, 2014: Questions and solutions 58 60 were
More informationChapter 21 The Statement of Cash Flows Revisited
Chapter 21 The Statement of Cash Flows Revisited AACSB assurance of learning standards in accounting and business education require documentation of outcomes assessment. Although schools, departments,
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 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 information