ࡱ> 5@ bjbj22 "XXqi@JJJ8KdfKDhLO"OOOOOOhhhhhhh$jRlF8h9uPOOuPuP8hOOqh1V1V1VuPOOh1VuPh1V1VKVr^Tb_OL ExJRF_Vdh0hT_nTnb_b_nvcOP1VP "PSOOO8h8h#($"V"(Financial environment includes bond markets,  HYPERLINK "http://www.blurtit.com/q5841143.html" forex markets, stock markets, commodity markets, OTC markets, Real estate markets and  HYPERLINK "http://www.blurtit.com/q285462.html" \t "undefined" cash or spot markets. All these markets play an important role in raising finances for the  HYPERLINK "http://www.blurtit.com/q285462.html" \t "undefined" companies and at the same time give profits to the  HYPERLINK "http://www.blurtit.com/q285462.html" \t "undefined" investors  INCLUDEPICTURE "http://kona.kontera.com/javascript/lib/imgs/grey_loader.gif" \* MERGEFORMATINET  . Basically a financial environment comprises of  HYPERLINK "http://www.blurtit.com/q3868602.html" the public sector enterprises, legal authorities, fiscal authorities which are directly or indirectly impact the financial system, monetary institutions, financial institutions, and official organizations. All these organizations have a direct impact on the financial system of the companies including private and public. Therefore, in order to give the money to the people who need it and to give the  HYPERLINK "http://www.blurtit.com/q102904.html" profit to the people who want to invest it, financial markets play an important role. Money today is not the same as money tomorrow or even yesterday for that matter. The old adage time is money is an important concept in financial markets. Learn how the principle of the time value of money affects investors' decisions in financial markets. Read more:  HYPERLINK "http://www.brighthub.com/office/finance/articles/16349.aspx" \l "ixzz0sErDbgVY" http://www.brighthub.com Time Value of Money Anyone who  HYPERLINK "http://www.brighthub.com/money/personal-finance/articles/27729.aspx" \t "_self" uses a credit card knows that paying off debts over a long period of time costs more than if the debt is paid off more quickly. This is because there is a cost with taking more time to pay off a loan than if the loan had a shorter maturity. This increase in total payments is a function of the  HYPERLINK "http://www.brighthub.com/money/personal-finance/articles/18497.aspx" \t "_self" interest rate and the time taken to repay. When money is not invested, such as if it is kept in a mattress or in a non-interest bearing savings account, the owner  HYPERLINK "http://www.brighthub.com/office/finance/articles/15799.aspx" \t "_self" forgoes the opportunity to earn more money by investing. Essentially, the interest rate the owner could realize were the money invested represents the opportunity cost of not investing. Suppose an investor buys a Certificate of Deposit (CD) today for $100. The CD is paying 4% annually. In one year, the value of the investment has grown to $104. The original $100 is known as the  HYPERLINK "http://www.brighthub.com/office/finance/articles/15799.aspx" \t "_self" Present Value (PV), the $104 is called the  HYPERLINK "http://www.brighthub.com/money/personal-finance/articles/18345.aspx" \t "_self" Future Value (FV), and the rate of interest is simply r. This relationship can be generally shown with the following formula: FV = PV * (1 + r) However, this formula assumes one year of interest only. Suppose the investor rolls the CD over into another year. In other words the $104 is used to purchase a CD in year 2 at the same rate. We need a more general formula to account for the compounding of the interest over multiple years because interest rates are rarely expressed in any other form besides annually. The following formula is a more general representation of calculating FVs. FV = PV * (1 + r)n The n in the formula above is the number of years the money is invested at the current interest rate, r. Suppose the investor rolls the CD over for 10 year. What is the expected FV of the investment? $148.02 = $100 * (1 + 0.04)10 By keeping the original investment in the CD for 10 years, the expected FV of the investment is $148.02 at the current rate of 4%. Sometimes an investor knows how much money is needed in the future and wants to know how much to invest at a constant rate to realize the FV needed. A little algebra helps. By solving for PV in the formula above we get: PV = FV / (1 + r)n Suppose an investor needs $20,000 in 18 years to pay for his daughters college education. How much money (PV) does he need to invest at 5% to realize a $20,000 return in 25 years? $8,310.41 = $20,000 / (1 + 0.05)18 In, other words, the PV of the investment must be equal to $8,310.41 to grow to $20,000 at 5% in 18 years. Of course, the formulas above do not account for ongoing payments. Usually, investors will continue to add to an investment such as a CD. This type of investment is known as an annuity. The time value of money principle is an important lesson for investing in financial markets. Money today is not the same as money tomorrow. This is true for both sides of a transaction during the sale and purchase of an investment. By applying some basic mathematics, you can calculate the Present Value and Future Value of any investment. Opportunity Cost The Principle of Self-Interest comes to light when it is understood that people often choose among more than one alternative or opportunity. A person can not attend a party and study for an exam at the same time. A person can not often choose to work full time for two different companies simultaneously. Decision-making is a weighing of the pros and cons of not only choosing one alternative but of not choosing another. Choosing to work for one company may afford an attractive retirement plan but another may offer an excellent health plan. The fact that not everyones situation is the same describes why some people will work for one company and other people choose another company. The  HYPERLINK "http://www.brighthub.com/office/finance/articles/16349.aspx" \t "_self" difference between two or more options is known as the opportunity cost. Agency Theory Another aspect of The Principle of Self-Interest is what is known as agency theory. Agency theory is concerned with the conflicts of interest that can arise in a principal-agent relationship. S A Principal-agent relationship occurs whenever one person (agent) acts in the interest of another person (principal) such as when managers of a firm work to maximize shareholder equity. A manager working in his/her own self interest has an incentive to do what is right for him/her regardless of how it affects the firms owners. As such, the Principle of Self-Interest describes why a corporations owners make rules as to what power a manager is given or why they institute a profit-sharing program so that the self-interest of the manager is more in line with the self-interest of the owners. The Principle of Self-Interest does not suggest that people are cold and wish to attain money as the focal point of their lives. Instead, it indicates that given the opportunity, people will act in their own financial self-interest to avoid losses and realize gains by making good decisions. In conjunction with the other  HYPERLINK "http://www.brighthub.com/office/finance/articles/15805.aspx" \t "_self" Principles of Competitive Financial Markets, it helps create an accurate picture of the financial transaction landscape. The future value of an annuity formula is not adequate when the future cash flows of an asset are not regular. In this case, each cash flow must be calculated separately and added to the total future value of the asset. Learn how to use a formula to calculate the future value of uneven cash flows. The future value calculation of an asset with multiple uneven cash flows is  HYPERLINK "http://www.brighthub.com/money/personal-finance/articles/17948.aspx" \t "_self" more difficult than a standard annuity. Each cash flow must be evaluated separately to find its incremental contribution to the total future value. In fact, even an annuity can be calculated this way; the formula for the future value of an annuity is simply a short cut to calculating each time period of the annuitys life. Suppose that an  HYPERLINK "http://www.brighthub.com/office/finance/articles/19318.aspx" \t "_self" investor is interested in finding the future value of an asset. The investor estimates the future cash flows and has determined that an 8% required return is necessary given the risk of realizing the cash flows associated with the asset. The estimated cash flows are s follows: time 0: $5,000 time 1: $2,000 time 2: $500 time 3: $10,000 Notice that since the cash flows are uneven, the future value of the asset can not be calculated as an annuity because an annuity assumes equal payments at regular intervals. Instead, the future value of each cash flow must first be calculated. All of these future values are then summed to find the future value of all the cash flows over the life of the asset. Using the cash flows above: FV = 5000 * (1 + 0.08)4 + 2000 * (1 + 0.08)3 + 500 * (1 + 0.08)2 + 10000 * (1 + 0.08)1 = 6802.44 + 2519.42 + 583.20 + 10800 = $20,705.06 So, the future value of the asset is approximately $20,705 at an 8% discount rate. This is, of course, assuming that the future cash flows are realized. The legitimacy of the future value formula is dependent on accurate estimates of the future cash flows. Lower or higher realized cash flows as well as a lower or higher required return changes the future value of the underlying asset. The formula used above is a general method of calculating the future value of multiple uneven expected cash flows. With it, any number of applications is possible for any number of periods and cash flows, even negative cash flows. For example, suppose an investor must payout money (a negative cash flow) for two year before a positive cash flow is possible. The formula is still useful in this case as long as the investor takes care to calculate the individual time periods with a negative number where appropriate. There are also more  HYPERLINK "http://www.brighthub.com/money/personal-finance/articles/18346.aspx" \t "_self" complicated examples of uneven cash flow. Suppose that an investor is interested in valuing an assets cash flows. The asset will cost the investor $2,000 at time zero and $1,500 in the first period. These costs represent negative cash flows (complication one). The asset will then pay $5,000, $7,000, and $12,000 in periods two, three, and four respectively (complication 2). Finally, the investor wants to know the value of the asset in period three (complication 3). The investor assumes a discount rate of 6%. The cash flows are summarized below: time 0: -$2,000 time 1: -$1,500 time 2: $5,000 time 3: $7,000 time 4: $12,000 To solve this problem, both present and future value components are needed. Essentially, cash flows in periods zero, one, and two need to be brought forward with a future value component and time period fours cash flow needs to be brought back to time three with a present value component. The cash flow at time three is unaffected by the discount rate because time three is the period in which the valuation is needed. The equation to solve this problem is given as: FV3 = -2000 * (1 + 0.06)3 + -1500 * (1 + 0.06)2 + 5000 * (1 + 0.06)1 + 7000 + 12000 / (1 + 0.06)1 = -2382.03 + -1685.40 + 5300 +7000 + 11320.75 = $19,553.32 So, the value of these cash flows at time three assuming a 6% discount rate is approximately $19,553. The example illustrated in this article shows just how complicated present and future value calculations can be when valuing an asset. However complicated, the example does point out how powerful the method is for valuing alternative investment decisions. With a few changes, the value of an asset can be calculated for any time period and for any discount rate. Of course, when different rates need to be evaluated, a spreadsheet or multifunction financial calculator makes setting up the formulas and changing of discount rates and time periods much simpler. You can also learn to  HYPERLINK "http://www.brighthub.com/money/personal-finance/articles/18345.aspx" \t "_self" calculate the future value of uneven cash flow. Problem 1: Determining Present Value Lets suppose your rich uncle promises to give you $500,000 in forty years. Assuming a 6 percent  HYPERLINK "http://personalfinance.byu.edu/?q=glossary/term/79" interest rate, what is the  HYPERLINK "http://personalfinance.byu.edu/?q=glossary/term/98" present value of the amount your uncle is promising to give you in forty years? To solve this problem, use the equation given above, which would appear as follows: PV = 500,000/ (1 +.06)40, or $48,611. You can also use a financial calculator. Set your calculator to end mode, meaning payments are at the end of each period, and clear the memory registers to make sure you have no old data in the calculator memories. Set $500,000 as your  HYPERLINK "http://personalfinance.byu.edu/?q=glossary/term/69" future value (FV), 40 as your number of years (N), and 6 as your  HYPERLINK "http://personalfinance.byu.edu/?q=glossary/term/79" interest rate (I); then solve for the present value (PV). You should get the same result as you did when you used the PV equation. Problem 2: Determining Future Value Lets look at two similar problems: A. Calculate the  HYPERLINK "http://personalfinance.byu.edu/?q=glossary/term/69" future value (in fifteen years) of $5,000 that is earning 10 percent; assume an annual  HYPERLINK "http://personalfinance.byu.edu/?q=glossary/term/130" compounding period. B. Calculate the  HYPERLINK "http://personalfinance.byu.edu/?q=glossary/term/69" future value of $5,000 that is earning 10 percent; assume simple  HYPERLINK "http://personalfinance.byu.edu/?q=glossary/term/79" interest (the  HYPERLINK "http://personalfinance.byu.edu/?q=glossary/term/78" interest earned does not earn interest). C. How much did interest on interest (bunga merah/ bunga berbunga) earn in the first problem? A. To solve this problem, we must consider  HYPERLINK "http://personalfinance.byu.edu/?q=glossary/term/130" compound interest. On your calculator, clear your registers and your memory. Set -$5,000 as the  HYPERLINK "http://personalfinance.byu.edu/?q=glossary/term/98" present value (PV), 10 percent as the  HYPERLINK "http://personalfinance.byu.edu/?q=glossary/term/79" interest rate (I), and 15 as the number of years in the future (N); then solve for the future value (FV), which is $20,886. With a standard calculator, the result is 5,000 * (1 +.10)15, or the same sum of $20,886. B. To solve for simple interest, which does not accrue interest on interest, it is easiest to use a standard calculator. First, calculate your annual interest, which is $5,000 times 10 percent (5,000 *.10), or $500. Multiply $500 by 15 years; the result should be $7,500. Then add the amount of the original  HYPERLINK "http://personalfinance.byu.edu/?q=glossary/term/80" investment of $5,000 to get $12,500. C. The difference between $20,886 and $12,500 is $8,386, which is the amount of interest that your interest has earned. This concept is the key to financial successearn interest on your interest. Elder L. Tom Perry repeated what someone told him about interest when he said, Thems that understands it, earns it; and thems that dont, pays it ( Becoming Self-Reliant, Ensign, Nov. 1991, 64). Lets earn interest rather than pay interest! Case Study #1 Data: Brian has a  HYPERLINK "http://personalfinance.byu.edu/?q=glossary/term/70" goal to have $500,000 saved by the time he turns sixty-five, which is forty years from now. Calculation: Assuming he can make 6 percent on his money, what is the value of that money now (this indicates  HYPERLINK "http://personalfinance.byu.edu/?q=glossary/term/98" present value)? The math formula is as follows: PV = FV/ (1 + i)n Case Study #2 Data: Ron has $2,500 saved. Calculation: If his  HYPERLINK "http://personalfinance.byu.edu/?q=glossary/term/80" investment earns 8 percent per year for twenty years, how much will his investment be worth in twenty years (the investments  HYPERLINK "http://personalfinance.byu.edu/?q=glossary/term/69" future value)? The math formula is as follows: FV = PV (1 + i)n ANNUAL DEPOSITS: Present Value/Future Value exercises Relevant Formula for these exercises:  INCLUDEPICTURE "http://businessed101.com/wp-content/uploads/2009/05/annuity1.jpg" \* MERGEFORMATINET   Question One: A man decides to make 12 annual deposits of $250 starting from next year. The interest rate is 9%. What is the Present value of this stream of cash flows? Answers: Question 1:  INCLUDEPICTURE "http://businessed101.com/wp-content/uploads/2009/05/annuity2.jpg" \* MERGEFORMATINET  Question Two:A man decides to make annual deposits (C) from his 21st Birthday. At 50 he will make his final deposit and start withdrawing equal annual amounts of $20,000 a year. The interest rate is expected to be a constant 8% p.a throughout the time period. How much must he deposit each year to achieve exactly 10 annual withdrawals between the age 50 and 60. Present/Future Answers Answers: Question 2: Step 1: We know that the Future value (at 50 years old) of the first set of annuities must equal the PV of the second set of annuities (at 50 years old). FV of Annuity 1 = PV of annuity 2 Step 2: For annuity number two we know, r=8%, FV=0, n=10  INCLUDEPICTURE "http://businessed101.com/wp-content/uploads/2009/05/annuity4.jpg" \* MERGEFORMATINET  Step 3: The PV of this second annuity must equal the future value of the set of deposits the man makes:  INCLUDEPICTURE "http://businessed101.com/wp-content/uploads/2009/05/annuity5.jpg" \* MERGEFORMATINET  Present Value Present Value Of A Single Amount Present Value is an amount today that is equivalent to a future payment, or series of payments, that has been discounted by an appropriate interest rate. Since money has time value, the present value of a promised future amount is worth less the longer you have to wait to receive it. The difference between the two depends on the number of compounding periods involved and the interest (discount) rate. The relationship between the present value and  HYPERLINK "http://www.getobjects.com/Components/Finance/TVM/fv.html" future value can be expressed as: PV = FV [ 1 / (1 + i)n ]Where: PV = Present Value FV = Future Value i = Interest Rate Per Period n = Number of Compounding Periods Example:You want to buy a house 5 years from now for $150,000. Assuming a 6% interest rate compounded annually, how much should you invest today to yield $150,000 in 5 years? FV = 150,000 i =.06 n = 5 PV = 150,000 [ 1 / (1 + .06)5 ] = 150,000 (1 / 1.3382255776) = 112,088.73 End of Year12345Principal112,088.73118,814.05125,942.89133,499.46141,509.43Interest6,725.327,128.847556.578,009.978,490.57Total118,814.05125,942.89133,499.46141,509.43150,000.00Example 2: You find another financial institution that offers an interest rate of 6% compounded semiannually. How much less can you deposit today to yield $150,000 in five years? Interest is compounded twice per year so you must divide the annual interest rate by two to obtain a rate per period of 3%. Since there are two compounding periods per year, you must multiply the number of years by two to obtain the total number of periods. FV = 150,000 i = .06 / 2 = .03 n = 5 * 2 = 10 PV = 150,000 [ 1 / (1 + .03)10] = 150,000 (1 / 1.343916379) = 111,614.09 Present Value of Annuities An annuity is a series of equal payments or receipts that occur at evenly spaced intervals. Leases and rental payments are examples. The payments or receipts occur at the end of each period for an ordinary annuity while they occur at the beginning of each period.for an annuity due. Present Value of an Ordinary Annuity The Present Value of an Ordinary Annuity (PVoa) isthe value of a stream of expected or promised future payments that have been discounted to a single equivalent value today. It is extremely useful for comparing two separate cash flows that differ in some way. PV-oa can also be thought of as the amount you must invest today at a specific interest rate so that when you withdraw an equal amount each period, the original principal and all accumulated interest will be completely exhausted at the end of the annuity. The Present Value of an Ordinary Annuity could be solved by calculating the present value of each payment in the series using the  HYPERLINK "http://www.getobjects.com/Components/Finance/TVM/pv.html" present value formula and then summing the results. A more direct formula is: PVoa = PMT [(1 - (1 / (1 + i)n)) / i]Where: PVoa = Present Value of an Ordinary Annuity PMT = Amount of each payment i = Discount Rate Per Period n = Number of Periods Example 1:What amount must you invest today at 6% compounded annually so that you can withdraw $5,000 at the end of each year for the next 5 years? PMT = 5,000 i = .06 n = 5 PVoa = 5,000 [(1 - (1/(1 + .06)5)) / .06] = 5,000 (4.212364) = 21,061.82 Year12345Begin21,061.8217,325.5313,365.069,166.964,716.98Interest1,263.711,039.53801.90550.02283.02Withdraw-5,000-5,000-5,000-5,000-5,000End17,325.5313,365.069,166.964,716.98.00Example 2: In practical problems, you may need to calculate both the present value of an annuity (a stream of future periodic payments) and the  HYPERLINK "http://www.getobjects.com/Components/Finance/TVM/pv.html" present value of a single future amount: For example, a computer dealer offers to lease a system to you for $50 per month for two years. At the end of two years, you have the option to buy the system for $500. You will pay at the end of each month. He will sell the same system to you for $1,200 cash. If the going interest rate is 12%, which is the better offer? You can treat this as the sum of two separate calculations: the present value of an ordinary annuity of 24 payments at $50 per monthly period Plus the present value of $500 paid as a single amount in two years. PMT = 50 per period i = .12 /12 = .01 Interest per period (12% annual rate / 12 payments per year) n = 24 number of periods PVoa = 50 [ (1 - ( 1/(1.01)24)) / .01] = 50 [(1- ( 1 / 1.26973)) /.01] = 1,062.17 + FV = 500 Future value (the lease buy out) i = .01 Interest per period n = 24 Number of periods  HYPERLINK "http://www.getobjects.com/Components/Finance/TVM/pv.html" PV = FV [ 1 / (1 + i)n ] = 500 ( 1 / 1.26973 ) = 393.78 The present value (cost) of the lease is $1,455.95 (1,062.17 + 393.78). So if taxes are not considered, you would be $255.95 better off paying cash right now if you have it. Present Value of an Annuity Due (PVad) The Present Value of an Annuity Due isidentical to an ordinary annuity except that each payment occurs at the beginning of a period rather than at the end. Since each payment occurs one period earlier, we can calculate the present value of an ordinary annuity and then multiply the result by (1 + i). PVad = PVoa (1+i)Where: PV-ad = Present Value of an Annuity Due PV-oa = Present Value of an Ordinary Annuity i = Discount Rate Per Period Example:What amount must you invest today a 6% interest rate compounded annually so that you can withdraw $5,000 at the beginning of each year for the next 5 years? PMT = 5,000 i = .06 n = 5 PVoa = 21,061.82 (1.06) = 22,325.53 Year12345Begin22,325.5318,365.0614,166.969,716.985,000.00Interest1,039.53801.90550.02283.02Withdraw-5,000.00-5,000.00-5,000.00-5,000.00-5,000.00End18,365.0614,166.969,716.985,000.00.00 EXERCISES 1. You can afford to put $10,000 in a savings account today that pays 6% interest compounded annually. How much will you have 5 years from now if you make no withdrawals? CLUES: PV = 10,000 i = .06 n = 5 2. Another financial institution offers to pay 6% compounded semiannually. How much will your $10,000 grow to in five years at this rate? CLUES: PV = 10,000 i = .06 / 2 = .03 n = 5 * 2 = 10 3. If you put $100 in a savings account that pays 5% interest annually, but is compounded daily, how much will be in the account after 10 years? CLUES: i = .05/365 n = 10x365 Formula: FV = P(1+i % c)n*c FV = Future Value of Savings Account P = Principal i = interest rate per year n = number of years c = number of compounding periods in a year4. Should I pay $11,000 today for a copier or $3,000 a year for 5 years? (with a 12 percent cost of capital) 5. If I invest $2,000 a year for 40 years toward my retirement and earn 8 percent a year on my investments, how much will I have when I retire? 6. I am borrowing $10,000 on a 10 month loan with an annual interest rate of 8 percent. What will my monthly payments be? How much principal and interest am I paying each month? CLUES: PV=10,000, i = 8/12 n=10 Further Exercises You have just won the lottery. At the end of each of the next 20 years, you'll receive a payment of $50,000. If the cost of capital is 10 percent per year, what's the present value of your lottery winnings? If I rent my house and at the beginning of each year receive $14,000, what is the value of this perpetuity? Assume an annual cost of capital of 10 percent. I now have $250,000 in the bank. At the end of each of the next 20 years, I withdraw $15,000 to live on. If I earn 8 percent per year on my investments, how much money will I have in 20 years? I deposit $1,000 per month (at the end of each month) over the next 10 years. My investments earn 0.8 percent per month. I would like to have $1,000,000 in 10 years. How much money should I deposit now? An NBA player is receiving $15 million at the end of each of the next 7 years. He can earn 6 percent per year on his investments. What is the present value of his future revenues? We are borrowing $200,000 on a 30-year mortgage with an annual interest rate of 10 percent. Assuming end of month payments, determine the monthly payment, interest payment each month, and amount paid toward principal each month. You have a liability of $1,000,000 due in 10 years. The cost of capital is 10 percent per year. What amount of money would you need to set aside at the end of each of the next 10 years to meet this liability? You are going to buy a new car. The cost of the car is $50,000. You have been offered two payment plans: A 10 percent discount on the cost of the car, followed by 60 monthly payments financed at 9 percent per year. No discount on the cost of the car, but the 60 monthly payments are financed at only 2 percent per year. If you believe your annual cost of capital is 9 percent, which payment plan is a better deal? Assume all payments occur at the end of the month. 9 I currently have $10,000 in the bank. 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