Financial Corporate homework (NON Plagiarised!!)
chapagIntro to Corporate Finance
700 words
Assume that you would like to purchase a home in the next 5 years. Also assume that you have already saved $50,000 so far and the approximate cost of the house is $250,000. Calculate how much you need to save for the next five years to purchase this home and put down 20% as a downpayment. Using the following website: http://www.proteam-corvette.com/1967.html
Base the interest rate on the five year interest rate from the Treasury department: http://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data=yield
· Calculate the required yearly savings on $50,000.
· How much money could be made using the same interest rate with the amount of yearly cash flows which would have been saved for the investment if these amounts had been invested instead?
· Which is the best option? Why?
· Phase Resources: don’t forget to site your references when using
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"Discounted Cash Flows Calculator" This calculator finds the fair value of a stock investment the theoretically correct way, as the present value of future earnings. |
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Annuities The purpose of this tutorial is to help you better identify, understand, and calculate future and present values of both ordinary annuities and annuities due. The tutorial assumes that you have a basic understanding of the time value of money, but might still need a little extra help with annuities. |
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Annuity Information Basics on understanding how annuities work. |
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Investopedia Present Value Calculator Provides a tool for calculating present value of future cash flows. |
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The Present and Future Value of an Annuity Definitions and step-by-step calculations for Present and Future Value. |
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Time Value of Money This site describes the concept of the Time Value of Money (TVM) with a concrete example |
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Time Value of Money This article explains formulas and concepts of various investment planning topics including compound interest, present value, bond yields, annuity, and stock valuation. |
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Time Value of Money Study This overview covers an introduction to simple interest and compound interest, illustrates the use of time value of money tables, shows a matrix approach to solving time value of money problems and introduces the concepts of intrayear compounding, annuities due, and perpetuities. A simple introduction to working time value of money problems on a financial calculator is included as well as additional resources to help understand time value of money, including an Excel worksheet. |
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Understanding the Time Value of Money This is an online tutorial for understanding the time value of money. |
Activity: Time Value of Money (TVM) |
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The concept of the time value of money refers to the idea that a dollar received today is worth more than a dollar received in the future. A dollar can be invested to earn interest. Even without inflation, the dollar is worth more today than it will be in the future because of the ability to use the money for investment purposes. Economists would call this an opportunity cost. We are deferring our consumption today so that we will have a greater amount in the future. The time value of money gives us the tools to compare dollars in different time periods. For example, we can compare the future value of the dollars to be received in terms of an equivalent amount of dollars today. Another way to view interest cost is simply the rent for the use of the money. Suppose you wanted to start investing your money and was asked by a borrower to consider investing with him or her without offering interest. If you do not recognize this offer as a bad investment, you will by the end of this activity. Most investments pay back the principle at the end of the time period plus interest. The interest amount is a percentage of the principal amount. What is Interest? To explain, let's use an example. Suppose you had a 10% interest on a $100 investment, which is equal to 10% of 100. To determine your investment return at the end of the period, follow these steps: Step 1: Calculate Total Interest Total Interest = Original Investment x Interest Total Interest = $100 x 0.10 = $10 Note: 10% = 0.10 Step 2: Find Return at End of Period Return at End of Period = Original Investment + Total Interest (from Step 1) = $100 + $10 = $110 SHORTCUT ALERT! You can determine the investment return at the end of the period in only 1 step instead of 2 steps, as shown above, using the following equation: Return at End of Period = Original Investment Amount (1 + Interest) = $100 (1 + 0.10) Compounding is one of the fundamental techniques of TVM. Compound interest includes interest on the initial investment and on the accumulated interest from previous periods. That is, compound interest includes interest on interest. This is the process of going from today's values, or present values (PVs), to future values (FVs). This process may include a series of equal payments spread periodically throughout a given time period. Payments such as these are known as annuity. The return-at-the-end-of-the-period component of the interest example was the future value, or FV. The FV is the amount by which a certain dollar amount will increase given a certain interest rate and a certain time period. Valuing a Single Lump Sum Cash Flow Future value (FV) of $1 The future value of a single amount or lump sum amount is the amount of money that a dollar will grow to in the future. Present value (PV) of $1 The present value of a single amount or lump sum amount is the amount of money that is equivalent to a dollar today for a given future amount. Instead of asking, "What is the future value of a present value or current amount today?" we are asking, “What amount we must invest today to accumulate a given or known future amount?" Valuing Equal Cash Flow Payments Future value of an ordinary annuity (FVA) of $1 An ordinary annuity is a series of equal payments (payments or deposits, that is, inflows or outflows) made at the end of each period. For an annuity due, which is covered below, cash flow payments are made at the beginning of the period. An annuity is simply a series of equal periodic payments. Some examples can be house and loan payments as well as equal deposits made to savings and investment accounts. These are outflow payments. In addition, annuities can include receipts of equal payments from investments accounts and other sources. The future value of an annuity amount is the amount of money that equals the amount that the payments of dollars will grow to in the future. It can be viewed as the sum of the individual future value calculations for each year. Present value of an ordinary annuity (PVA) of $1 The present value of equal cash flow payments amount is the amount of money that is equivalent to a dollar today for a given series of equal future payment amounts. Instead of asking, "What is the future value of an equal series of payment amounts?" we are asking, "What amount we must invest today to receive or pay these equal payments?" In general, use this shortcut to calculate the future value of some present value invested today at a rate of return i % (interest rate) for n periods (years) is given by the following: FVn = PV (1 + i%)n For example, the FV of $10,000 for 5 years at 10% annual interest is as follows: FV5 = $10,000 (1 + 0.10%)5 = $10,000 (1.61051) = $16,105.10 Interest Factor Tables Practice Tables like FVIFA also exist for future values (FVIF), present values (PVIF), and present values of annuity (PVIFA). The present value of a future amount is based on a certain interest rate and certain time period. PV of a cash flow due n years in the future is the amount which, if it were on hand today, would grow to equal the future amount. This concept is the opposite of compounding, known as discounting. The key difference is that compounding adds i% each year and finds the FV amount, while discounting finds the PV on a certain time period (length of time). In the previous example, you found the interest factor for the FV of $10,000 for 5 years at 10% annual interest by calculating (1 + 0.10%)5 = (1.61051) You can also find this interest factor using the FVIF table as follows:
Compound Interest: Future Value Suppose you deposit $1,500 in a bank that pays 10% interest each year. How much will the investment accumulate at the end of 3 years?
It is clear to see that the profit generated from a $1,500 investment with 10% interest over a 3-year period is equal to FV – PV = $1,996.50 – 1,500 = $496.50 This is called the compound interest. It is an interest on interest. Click here to download Interest Factor Tables. Problem 1 Present Value Using our first example with FV, we can go backward, in a sense, to find the PV. Because $1,500 would grow into $2,415.77 in 5 years at a 10% interest rate, $1,500 is the PV of $2,415.77 due in 5 years, when the opportunity cost is 10%. Confirm this using the PVIF table. Click here to download Interest Factor Tables. Answer: FV = 2,415.77, i% = 10%, n = 5 years The correct calculation is as follows: PV = FV (PVIF)i %, n = $2,415.77 (0.6209) = $1,499.95 or approximately $1,500. Problem 2 Amortized Loan Suppose you borrowed $83,000 from a bank. The loan is to be paid back in 4 years. The bank proposed the following payment plan: Year 1: $26,753 Year 2: $26,753 Year 3: $26,753 Year 4: $26,753 What is the interest rate on the loan? Click here to download Interest Factor Tables. Answer: The correct calculation is as follows: PV = FVn (PVIF)i %, n $83,000 = 26,753 (PVIFA) i %, 4 $83,000 / 26,753 = (PVIFA) i %, 4 3.1024 = (PVIFA) i %, 4 i % = 11% Problem 3 Cash Flow Stream & Discount Rate Suppose you are to receive the following cash flow stream, and the one period discount rate (opportunity rate) is 15%. What is the present value of this cash flow stream? Year 2: $3,000 Year 3: $4,500 Year 4: $5,000 i = 15% Hint: Use the equation PV = FVn (PVIF)i %, n Click here to download Interest Factor Tables. Answer: The correct calculation is as follows: PV = $3,000 (PVIF)15 %, 2 + $4,500 (PVIF)15 %, 3 + $5,500 (PVIF)15 %, 4 = $3,000 (0.756) + $4,500 (0.658) + $5,500 (0.572) = $2,268 + $2,961 + $3,146 = $8,375 Problem 4 Missing Cash Flows Suppose you have an investment opportunity that pays $150 at t = 1, $150 at t = 2, $150 at t = 3, and some fixed cash flow at the end of each of the remaining 12 years. The PV = $3,800, and an alternative investment of equal risk has a required rate of return of 11%. What is the annual cash flow received at the end of each of the final 12 years? Hint: Use the formula: PV = FVn (PVIFA) i %, n + x (PVIFA) i %, n (PVIF) i %, n Click here to download Interest Factor Tables. Answer: The correct calculation is as follows: PV = FVn (PVIFA) i %, n + x (PVIFA) i %, n (PVIF) i %, n $3,800 = $150(2.4437) + x (7.5488)(0.7312) $3,800 = $150(2.4437) + x (5.52) $3,800 = $366.56 + x (5.52) $3,433.44 = x (5.52) x = $622 End of Activity. |
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FAQ: Time Value of Money |
Question 1: What determines share prices? Answer 1: The economic model of value states that share prices are determined by an efficient market comprised of smart investors who ultimately care about just two things: the cash to be generated over the life of a business (or any investment) and the risk that is inherent in those cash flows. The timing of cash flows is also of critical importance in determining value. Question 2: How is shareholder value calculated? Answer 2: The calculation of shareholder value is straightforward. It is simply the cash to be generated by a venture divided by that venture's cost of capital less its growth rate. The denominator of this calculation is an adjustment for the venture's risk and the time value of money, and it is also known as the capitalization rate. Question 3: What is meant by the phrase time value of money? Answer 3: The concept of time value of money is simply the fact that a dollar today is worth more than a dollar tomorrow. This is true for two reasons. The first reason is that the purchasing power of a dollar diminishes over time. Think about it: a dollar today buys you fewer goods than it did 10 years ago, or even last year. This is basically because of inflation. The second reason that a dollar today is worth more than a dollar tomorrow is because of default risk. There is a chance that the person or entity that is promising to pay you at some point in the future will not be able to make that payment, or will not be able to make that payment in full when default risk is an issue, which it usually is when there is a promise of future payment. If you invest money in a venture, you need to be compensated for both of these factors: for the loss of purchasing power over time and the risk of default. Question 4: What is discounting, and how can it be calculated? Answer 4: The time value of money explains that a dollar today is worth more than a dollar tomorrow. Discounting quantifies this and explains by how much (given various assumptions). It is the means by which the concept of time value of money is applied. You use discounting when you know tomorrow's amount (the future value) and want to calculate what that amount is today (the present value). Discounting is simply the opposite of compounding. To have $121 in 2 years, given a 10% annual return, you will need to make an initial investment of $100.
Question 5: How can future compound value be calculated? Answer 5: You use compounding when you know today's amount (the present value) and want to calculate what that amount will be at some point in the future (the future value). You start with a known present value and calculate the future value. You use discounting when you know the future value and want to calculate the present value. You start with the future value and discount it to calculate a present value. If you invest $100 today for 1 year, and earn 10% on this investment annually, you will have $110 a year from now. If your investment is over 2 years, and interest is compounded annually, you will have $121 in 2 years.
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FAQ: Interest Rates and Money Markets |
Question 1: What are money market instruments? Answer 1: Money market instruments are short-term instruments in which investors invest their cash to achieve a short-term goal. A good example of a money market instrument is a 180-day U.S. Treasury bill. Money market instruments are typically low-yielding, highly liquid, and low-risk investments, meaning they can be turned into cash relatively quickly and have a lower return and risk than other investments, such as stocks. A key role money market instruments play is the parking of cash for institutional investors. That is, institutional investors, such as insurance companies, banks, pension funds, and the like will invest in money market instruments when other investments are not as attractive in the short-term. As you will note, financial institutions play a central role in money market instruments. First, they provide intermediation services, such as in the case of a bank selling certificates of deposits to banking customers. Also, they play the role of investor, such as in instances where insurance companies buy money market instruments to park some short-term cash as they divest other holdings. Question 2: How do interest rates impact money market instruments? Answer 2: · As interest rates decline, yields on money market instruments decline. · As yields increase (in particular, real yields), money market instruments become more attractive, and investors typically invest in them more. With the attractive qualities of being low-risk and high-liquidity, all things being equal, investors will find money market instruments attractive as interest rates rise. · As yields decline, money market instruments become less attractive investments, and investors typically invest in them less. Very low returns on money market instruments, like those experienced in the early part of the 21st century, make other investments look relatively more attractive and more sought after. Question 3: How do interest rate changes impact banks? Answer 3: Because interest rates have an inverse relationship with money demand, changes in interest rates have a direct impact on money demand and, thus, the amount of loans banks make. As interest rates decline, money demand increases because the price of borrowing (interest rates) is lower. This leads to more loans for all types of goods (homes, automobiles, etc.). Banks typically do fairly well during this period in business for new loans. As interest rates increase, money demand decreases because the price of borrowing is becoming more expensive. This leads to fewer loans of all types. In terms of loan generation, all things being equal, banks generate less business when interest rates are higher. Banks profit off the interest rate difference among what they pay savers, how much they charge for loans, and how much they generate from investment income. Thus, in periods when the spread between what they charge borrowers and how much they pay savers narrows, profits will be squeezed. Please note that this profit squeeze can occur in low- or high-interest rate environments, and the important thing for banks is to effectively manage the spread, irrespective of the interest rate environment. Question 4: How do interest changes impact businesses? Answer 4: Interest rates impact businesses in a number of important ways. First and most importantly, interest rates are the single most important factor in the cost of capital for businesses; as interest rates change, so does the cost of capital. The cost of capital for most businesses typically contains a large segment of debt capital. This debt capital is made up of bonds that firms issue and/or bank loans. As the cost of this debt increases, the cost of capital increases. The other related impacts that interest rates have on businesses is upon firm decision making: · When interest rates are low, the cost of capital is low. When the cost of capital is low, businesses will take on more projects because the risk to take on those projects is less and more projects meet the "hurdle rate" (the required rate of return on a project before a company decides to pursue it). · In addition, interest rates affect how businesses decide to finance investments and how they utilize cash on their balance sheet. When interest rates are low, the cost of debt capital is low, and firms issue more debt capital as compared to equity capital. When interest rates are low, firms have an incentive to redeem higher-cost debt and issue lower-cost debt (similar to home refinancing). Question 5: Can foreign investors impact U.S. interest rates? Answer 5: Yes—and they do. This is done primarily via the bond market and impacts U.S. interest rates. · In search of good returns for the level of risk, foreign investors buy U.S. Treasury bonds to add to their portfolio. As the demand for U.S. Treasury bonds increases, the price for bonds increases (just like any other good, price increases with demand). · The yields or interest rates on U.S. Treasury bonds move in the opposite direction of the price; therefore, as demand drove up the price for the bonds, it drove down the yield. · U.S. Treasury bond yields are linked to many interest-bearing financial instruments in the United States, and these instruments typically move in the same direction as U.S. Treasury bonds. For example, the U.S. Treasury 10-year bond yield is directly linked to U.S. mortgage interest rates. As the 10-year yield changes, so does the 30-year mortgage rate. In this example, U.S. interest rates would decline following the decline in yields for U.S. Treasury bonds. Question 6: If interest rates are higher in foreign markets, why would foreign investors invest in the United States? Answer 6: The primary reasons why investors invest in the United States, even when interest rates are high in their home country, are due to currency adjusted, real interest rates and risk-adjusted returns. · Currency adjusted, real interest rates are interest rates that are adjusted for foreign exchange (currency) and inflation (real). Assume, as an example, an investor in a euro zone country is willing to make an investment in Eurobonds or U.S. Treasury bonds and sees the risk of each as the same. Furthermore, the interest rates on the U.S. bonds have a real return of 5 percent, while the interest rates on the Eurobonds have a real return of 7 percent. In this situation, it would appear the investor would get a better return by investing in the Eurobonds. However, if the U.S. dollar is expected to appreciate greater than 2 percent versus the euro over the life of the investment, the investor would get a better return by purchasing the U.S. Treasury bonds. Situations like these play out every day in financial markets. With its relatively low/stable inflation and strong/stable currency, the United States typically is viewed as a good investment. · Risk-adjusted returns are returns on financial instruments adjusted for the associated risk with the financial instrument. One classic example of risk-adjusted returns is the adjustment of government issued bonds for default risk. Bonds issued by the US government have virtually no default risk and are considered risk-free because the United States has never defaulted on its bonds. Thus, if an investor in a foreign country can purchase local bonds with a 10 percent real rate of return with a default risk of 4 percent, the risk-adjusted return is 6 percent. If the investor can buy U.S. Treasury bonds with a 7 percent real rate of return and a 0 percent default risk, the risk-adjusted return in the United States is 7 percent. Given these options and all else being the same, a rational investor would choose to invest in the U.S. Treasury bonds. |
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The Power of Compound Interest |
The Power of Compound Interest This video illustrates the power of compound interest. Follow along and see for yourself why so many people underestimate the incredible miracle of compounding. Click to watch The Power of Compound Interest. |
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TVM: Annuities, Mortgages, and Pensions |
Question 1: Explain the TVM concept of the present value of an annuity due. Answer 1: The present value of an annuity due is an annuity contract that is due at the beginning of the period. For instance, if your mortgage starts on 1/1/06, and your first mortgage payment is due 1/1/06, that is an annuity due. It is due at the beginning of your mortgage month. Consider this example: Suppose that a company has signed a $125,000 capital lease of equipment for 5 years at the current prime rate of 6%. Payment is due on the first day of the lease. The rental payments are determined by plugging payments into the future value of an annuity due calculator until the future value is $125,000. The payments are approximately $27,885 per year. Computing the value of an annuity due is a trial-and-error process. A starting point would be to divide the $125,000 by 5 years to get $25,000. Because you are also paying interest, you know it is greater than $25,000; so you would put in $26,000 next. You would continue doing this until the PV becomes $125,000. Question 2: Is it better to finance a home using a fixed or variable-rate mortgage? Answer 2: Ed is planning to purchase a new home. He has the option of a fixed-rate mortgage at 5.7% or an adjustable-rate mortgage at 3.75%. The home price is $275,000. The fixed-rate mortgage is for a term of 30 years with 15% down. The adjustable rate mortgage has a 3.75% interest rate that is capped at 7.5%. The maximum first rate increase is 1.25%, with subsequent increases of 0.25%. The adjustable-rate mortgage rate will remain constant for 18 months before the first increase. Subsequent increases can occur every 12 months. Ed will pay over the term of the mortgage $254,655 with the fixed rate and $298,638 with the adjustable-rate mortgage. He will be $43,983 ahead with the fixed rate. This is because the early payments (during the first 10 years) are primarily interest, whereas the later payments (during the last 10 years) are principle. With the adjustable rate, the interest rate will exceed the 5.7% in 4.5 years (3.75 + 1.25 + 0.25 + 0.25 + 0.25). Ed is basically financing his house for 25.5 years at a rate in excess of his fixed mortgage rate of 5.7%. During the first 4.5 years, very little principle has been paid on his original mortgage. Question 3: How does the TVM relate to pension contributions? Answer 3: BC Corporation hires two additional customer service people, Brad and Jenny, whom the company wants to add to BC's pension plan. Brad is 42 years old and plans to work until he turns 60. Jenny is 19, and she wants to work until age 55. They each will need $700,000 when they retire. Sally and Ed will need to determine the amount of money that must be contributed to the pension plan each year by BC Corporation to be able to fund Jenny and Brad's pension upon retirement. The CFO of BC Corporation, Antonio, explains that determining the annual pension deposit is calculated by the future value of an ordinary annuity. The company typically uses a 5% discount rate. By using a time value of money calculator, he enters the payment amount of $700,000 at an interest rate of 5% over the number of years Brad and Jenny will be working at BC Corporation. This takes some trial and error. Once Antonio gets the numbers close to $700,000, he knows that BC must contribute $59,900 annually for Brad and $42,300 annually for Jenny. |
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Activity: Future Value of an Uneven Cash Flow |
Future Value of an Uneven Cash Flow This video tutorial explains how to calculate the future value of an uneven cash flow using the compounding formula. Click to watch Future Value of an Uneven Cash Flow. |
Resource Links |
Investopedia Present Value Calculator (http://www.investopedia.com/calculator/PVCal.aspx) Provides a tool for calculating present value of future cash flows. |
"Discounted Cash Flows Calculator" (http://www.moneychimp.com/articles/valuation/dcf.htm) This calculator finds the fair value of a stock investment the theoretically correct way, as the present value of future earnings. |
Annuity Information (http://www.moneyinstructor.com/art/annuities101.asp) Basics on understanding how annuities work. |
The Present and Future Value of an Annuity (http://thismatter.com/money/investments/present-value-future-value-of-annuity.htm) Definitions and step-by-step calculations for Present and Future Value. |
Time Value of Money (http://www.moneychimp.com/articles/finworks/fmfutval.htm) This article explains formulas and concepts of various investment planning topics including compound interest, present value, bond yields, annuity, and stock valuation. |
Time Value of Money Study (http://www.studyfinance.com/lessons/timevalue/index.mv) This overview covers an introduction to simple interest and compound interest, illustrates the use of time value of money tables, shows a matrix approach to solving time value of money problems and introduces the concepts of intrayear compounding, annuities due, and perpetuities. A simple introduction to working time value of money problems on a financial calculator is included as well as additional resources to help understand time value of money, including an Excel worksheet. |
Time Value of Money (http://www.econedlink.org/lessons/index.cfm?lesson=EM37) This site describes the concept of the Time Value of Money (TVM) with a concrete example |
Annuities (http://web.utk.edu/~jwachowi/annuity1.html) The purpose of this tutorial is to help you better identify, understand, and calculate future and present values of both ordinary annuities and annuities due. The tutorial assumes that you have a basic understanding of the time value of money, but might still need a little extra help with annuities. |
Understanding the Time Value of Money (http://www.investopedia.com/articles/03/082703.asp) This is an online tutorial for understanding the time value of money. |