- 1. Stathis Polyzos FIN308 Introduction to Finance
- 2. The Common Assessment will be on Blackboard, through Lockdown Browser Make sure you have access to BlackBoard and are comfortable using it You can only have your formula sheet The assessment duration is 60 minutes Date/Time: 5 October 2023, 12:30 (Common Break) Location: M1-0-026 You need to have a scientific calculator FIN308 Common Assessment Revision 2
- 3. Material will cover Chapter 5 (Time Value of Money) The assessment will consist of exercises relating to time value of money and some theoretical questions The assessment accounts for 15% of your course grade S. Polyzos - FIN308 Common Assessment Revision 3
- 4. Study all the slides, not only those in the revision Study all the material (read the book), not only that in the presentation slides Go through the examples we did in class and the examples in the book Remember to also read the theory, not only the exercises S. Polyzos - FIN308 Common Assessment Revision 4
- 5. You need to access the test using LockDown Browser Click here http://www.respondus.com/lockdown/download.php?id=399140242 S. Polyzos - FIN308 Common Assessment Revision 5
- 6. All assessments are going to be on campus On-Campus Exam Rules Mobile phones are not allowed in class during the exam Having a mobile phone on you will mean that you will be graded with 0 on this exam, as per College of Business instructions You will not be allowed to leave the classroom for any reason (bathroom, water, etc.) unless there is a medical certificate You will be allowed to use only your formula sheet. You will not be allowed to exchange calculators, pens, etc. Screen brightness for monitors should be set to 100% (make sure you have a charger or an extra battery) S. Polyzos - FIN308 Common Assessment Revision 6
- 7. All exams to be on-campus It is your responsibility to follow the announcements by the University regarding exam rules and campus access. Any deviations from the above will result in no points for the exam. S. Polyzos - FIN308 Common Assessment Revision 7
- 8. Please follow the steps below in order to open the exam and submit your responses: Step 1. Open Respondus LockDown Browser Step 2. Log in to Blackboard (https://learn.zu.ac.ae), using your Zayed credentials Step 3. Select your FIN308 course from the course list Step 4. From the menu on the left, select “Course Common Assessments” Step 5. Select “FIN 308_ Common Assessment_ Test" from the assessment list Step 6. Read the instructions and press Start the Test Step 7. Enter the password given S. Polyzos - FIN308 Common Assessment Revision 8
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- 10. Time value of money S. Polyzos - FIN308 Common Assessment Revision 10
- 11. Theoretical Motivation We prefer present consumption to future consumption, since we can enjoy (derive utility from) the goods for a greater period of time In the presence of inflation, the value of money decreases over time Uncertainty/risk reduces the value of a future cash flow S. Polyzos - FIN308 Common Assessment Revision 11
- 12. Present Value – earlier money on a timeline Future Value – later money on a timeline Interest rate – “exchange rate” between earlier money and later money Discount rate Cost of capital Opportunity cost of capital Required return Inflation S. Polyzos - FIN308 Common Assessment Revision 12
- 13. The three basic patterns of cash flows include: A single amount: A lump sum amount either held currently or expected at some future date. An annuity: A level periodic stream of cash flow. A mixed stream: A stream of unequal periodic cash flows. S. Polyzos - FIN308 Common Assessment Revision 13
- 14. Future value is the value at a given future date of an amount placed on deposit today and earning interest at a specified rate. Found by applying compound interest over a specified period of time. Compound interest is interest that is earned on a given deposit and has become part of the principal at the end of a specified period. Principal is the amount of money on which interest is paid. S. Polyzos - FIN308 Common Assessment Revision 14
- 15. We use the following notation for the various inputs: FVn = future value at the end of period n PV = initial principal, or present value r = annual rate of interest paid. (Note: On financial calculators, I is typically used to represent this rate.) n = number of periods (typically years) that the money is left on deposit The general equation for the future value at the end of period n is S. Polyzos - FIN308 Common Assessment Revision 15
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- 17. Present value is the current dollar value of a future amount—the amount of money that would have to be invested today at a given interest rate over a specified period to equal the future amount. It is based on the idea that a dollar today is worth more than a dollar tomorrow. Discounting cash flows is the process of finding present values; the inverse of compounding interest. The discount rate is often also referred to as the opportunity cost, the discount rate, the required return, or the cost of capital. S. Polyzos - FIN308 Common Assessment Revision 17
- 18. The present value, PV, of some future amount, FVn, to be received n periods from now, assuming an interest rate (or opportunity cost) of r, is calculated as follows: S. Polyzos - FIN308 Common Assessment Revision 18
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- 20. An annuity is a stream of equal periodic cash flows, over a specified time period. These cash flows can be inflows of returns earned on investments or outflows of funds invested to earn future returns. An ordinary (deferred) annuity is an annuity for which the cash flow occurs at the end of each period An annuity due is an annuity for which the cash flow occurs at the beginning of each period. An annuity due will always be greater than an otherwise equivalent ordinary annuity because interest will compound for an additional period. S. Polyzos - FIN308 Common Assessment Revision 20
- 21. You can calculate the future value of an ordinary annuity that pays an annual cash flow equal to CF by using the following equation: As before, in this equation r represents the interest rate and n represents the number of payments in the annuity (or equivalently, the number of years over which the annuity is spread). S. Polyzos - FIN308 Common Assessment Revision 21
- 22. You can calculate the present value of an ordinary annuity that pays an annual cash flow equal to CF by using the following equation: As before, in this equation r represents the interest rate and n represents the number of payments in the annuity (or equivalently, the number of years over which the annuity is spread). S. Polyzos - FIN308 Common Assessment Revision 22
- 23. You can calculate the present value of an annuity due that pays an annual cash flow equal to CF by using the following equation: As before, in this equation r represents the interest rate and n represents the number of payments in the annuity (or equivalently, the number of years over which the annuity is spread). The future value of an annuity due is always higher than the future value of an ordinary annuity. S. Polyzos - FIN308 Common Assessment Revision 23
- 24. You can calculate the present value of an ordinary annuity that pays an annual cash flow equal to CF by using the following equation: As before, in this equation r represents the interest rate and n represents the number of payments in the annuity (or equivalently, the number of years over which the annuity is spread). S. Polyzos - FIN308 Common Assessment Revision 24
- 25. A perpetuity is an annuity with an infinite life, providing continual annual cash flow. If a perpetuity pays an annual cash flow of CF, starting one year from now, the present value of the cash flow stream is S. Polyzos - FIN308 Common Assessment Revision 25 PV = CF ÷ r
- 26. Shrell Industries, a cabinet manufacturer, expects to receive the following mixed stream of cash flows over the next 5 years from one of its small customers. S. Polyzos - FIN308 Common Assessment Revision 26
- 27. If the firm expects to earn at least 8% on its investments, how much will it accumulate by the end of year 5 if it immediately invests these cash flows when they are received? This situation is depicted on the following timeline. S. Polyzos - FIN308 Common Assessment Revision 27
- 28. Frey Company, a shoe manufacturer, has been offered an opportunity to receive the following mixed stream of cash flows over the next 5 years. S. Polyzos - FIN308 Common Assessment Revision 28
- 29. If the firm must earn at least 9% on its investments, what is the most it should pay for this opportunity? This situation is depicted on the following timeline. S. Polyzos - FIN308 Common Assessment Revision 29
- 30. Compounding more frequently than once a year results in a higher effective interest rate because you are earning on interest on interest more frequently. As a result, the effective interest rate is greater than the nominal (annual) interest rate. Furthermore, the effective rate of interest will increase the more frequently interest is compounded. A general equation for compounding more frequently than annually S. Polyzos - FIN308 Common Assessment Revision 30
- 31. Continuous compounding involves the compounding of interest an infinite number of times per year at intervals of microseconds. A general equation for continuous compounding where e is the exponential function. S. Polyzos - FIN308 Common Assessment Revision 31
- 32. The nominal (stated) annual rate is the contractual annual rate of interest charged by a lender or promised by a borrower. The effective (true) annual rate (EAR) is the annual rate of interest actually paid or earned. In general, the effective rate > nominal rate whenever compounding occurs more than once per year S. Polyzos - FIN308 Common Assessment Revision 32
- 33. The following equation calculates the annual cash payment (CF) that we’d have to save to achieve a future value (FVn): Suppose you want to buy a house 5 years from now, and you estimate that an initial down payment of $30,000 will be required at that time. To accumulate the $30,000, you will wish to make equal annual end-of-year deposits into an account paying annual interest of 6 percent. S. Polyzos - FIN308 Common Assessment Revision 33
- 34. Loan amortization is the determination of the equal periodic loan payments necessary to provide a lender with a specified interest return and to repay the loan principal over a specified period. The loan amortization process involves finding the future payments, over the term of the loan, whose present value at the loan interest rate equals the amount of initial principal borrowed. A loan amortization schedule is a schedule of equal payments to repay a loan. It shows the allocation of each loan payment to interest and principal. S. Polyzos - FIN308 Common Assessment Revision 34
- 35. The following equation calculates the equal periodic loan payments (CF) necessary to provide a lender with a specified interest return and to repay the loan principal (PV) over a specified period: Say you borrow $6,000 at 10 percent and agree to make equal annual end-of-year payments over 4 years. To find the size of the payments, the lender determines the amount of a 4-year annuity discounted at 10 percent that has a present value of $6,000. S. Polyzos - FIN308 Common Assessment Revision 35 𝐶𝐹 = 𝑃𝑉 × 𝑟 ÷ 1 − 1 1 + 𝑟 𝑛
- 36. It is often necessary to calculate the compound annual interest or growth rate (that is, the annual rate of change in values) of a series of cash flows. The following equation is used to find the interest rate (or growth rate) representing the increase in value of some investment between two time periods. S. Polyzos - FIN308 Common Assessment Revision 36
- 37. 𝑛 = log 𝐹𝑉 𝑛 𝑃𝑉0 log 1 + 𝑟 S. Polyzos - FIN308 Common Assessment Revision 37
- 38. These exercises will be solved in class S. Polyzos - FIN308 Common Assessment Revision 38
- 39. Assume that Amaya Chidori makes a ¥2,500 deposit into an investment account in a bank in Sendai, Japan. If this account is currently paying 0.7% per annum, what will the account balance be after 1 year? S. Polyzos - FIN308 Common Assessment Revision 39
- 40. Paul Jackson has saved £2,235 and decides to invest in an individual savings account (ISA), which is a type of savings account that offers tax exemptions to residents of the United Kingdom. If the ISA pays 2% annual interest with monthly compounding, what will the account balance be after 4 years? S. Polyzos - FIN308 Common Assessment Revision 40
- 41. Marina Tra just won $1.3 million in the Hong Kong mega lottery. She is given the option of receiving a lump sum immediately or she can elect to receive an annual payment of $100,000 at the end of each year for the next 25 years. If Marina can earn 5% annually on her investments, which option should she take? S. Polyzos - FIN308 Common Assessment Revision 41
- 42. Yassir Ismail is discussing investing in a new machine for his metal fabrication business in Dubai. The machine will cost AED130,000. He estimates that the new machine will generate the cash inflows shown in the table to the right, over its 5- year life. If Yassir requires 9% return on his investments, should he invest in the new machine? Year Inflow Estimate 1 AED 35,000 2 50,000 3 45,000 4 25,000 5 15,000 S. Polyzos - FIN308 Common Assessment Revision 42
- 43. Year Inflow Estimate Discount Factor Present Value 1 AED 35,000 2 50,000 3 45,000 4 25,000 5 15,000 S. Polyzos - FIN308 Common Assessment Revision 43
- 44. Jack and Jill have just had their first child. If they expect that college will cost $150,000 per year in 18 years, how much should the couple begin depositing annually at the end of each of the next 18 years to accumulate enough funds to pay for the first year of tuition 18 years from now? Assume they can earn a 6% annual rate of return on their investment. S. Polyzos - FIN308 Common Assessment Revision 44
- 45. Peter just got his driver’s license and he wants to buy a new sports car for $70,000. He has $20,000 to invest as a lump sum today. Peter is a conservative investor and he only invests in safe products. After approaching different banks, he is offered the following investment opportunities: a) River Bank’s savings account with an interest rate of 10.8% compounded monthly. b) First State Bank’s savings account with an interest rate of 11.5% compounded annually c) Union Bank’s saving account with an interest rate of 11.2% compounded quarterly. How long will it take for Peter to accumulate enough money to buy the car in each of the three cases and which one should he choose? 45
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