Business Finance Chapter 6 Notes

Business Finance Chapter 6 Notes 1. Most investments involve multiple cash flows. 2. When valuing cash flows, you can either value multiple cash flows or a single sum, also known as a(n) lump sum. 3. One method of calculating future values for multiple cash flows is to compound the accumulated balance forward one year at a time. 4. The present value of a series of future cash flows is the amount you would need today to exactly duplicate those future cash flows. 5. In almost all multiple cash flow calculations, it is implicitly assumed that the cash flows occur at the end of each period. 6. A typical investment has a large cash outflow at the beginning and then a cash inflow for many years. 7. The formula for the annuity present value is C × [(1 − Present value factor)/r]. 8. A single cash flow is also known as a: lump sum 9. The formula for the present value interest factor of an annuity is {1–[1/(1+r)^t]/r}. 10. Which of the following processes can be used to calculate future value for multiple cash flows? a. Compound the accumulated balance forward one year at a time b. Calculate the future value of each cash flow first and then add them up 11. The formula for the annuity present value factor for a 30-year annuity with an interest rate of 10 percent per year is [1 − (1/1.10 30 )]/.10] . 12. In the standard present and future value tables, and in all the default settings on a financial calculator, the assumption is that cash flows occur at the end of each period. 13. The annuity future value factor is found by taking the future value factor and subtracting one, then dividing this number by the interest rate. 14. Ralph has $1,000 in an account that pays 10 percent per year. Ralph wants to give this money to his favorite charity by making three equal donations at the end of the next 3 years. Which of the following formulas show how much Ralph will give to the charity each year? $1,000/[(1 − 1/1.10 3 )/0.10] 15. True: The formula for the present value interest factor for annuities is Annuity present value factor = {1–[1/(1+r)t]}r. 16. The APR is also called the stated rate and it differs from the EAR. 17. The present value interest factor for an annuity with an interest rate of 8 percent per year over 20 years is [1 − (1/1.08 20 )]/.08 . 18. Which of the following is the formula for the future value of an annuity? FV = ((1+r)t−1/r) 19. Which compounding interval will result in the lowest future value assuming everything else is held constant? Annual 20. Which of the following is the simplest form of loan? A pure discount loan 21. Which of the following are annuities? a. Monthly rent payments in a lease b. Installment loan payments 22. False: The APR is always the same as the EAR. 23. What is the present value of an ordinary annuity that pays $100 per year for 20 years if the interest rate is 10 percent per year? $100{[1 - (1/(1.10) 20 )]/0.10} 24. How frequently does continuous compounding occur? Every instant 25. You will receive a bonus of $5,000 in one year's time, and would like to take a loan against it now. What is the formula that shows how much you can borrow if you plan to use the entire amount to pay back the loan and your interest rate is 3%? $5,000/1.03 26. Which of the following are real-world examples of annuities? a. Mortgages b. Pensions Reason: Common stock dividends are not annuities - they are not required to be paid and when they are paid the amount cannot be known in advance for certain. 27. To find the present value of an annuity of $100 per year for 5 years at 10 percent per year using the tables, look up the present value interest factor which is 3.7908 and multiply that by $100. 28. When using the spreadsheet (Excel) function for finding the PV of an annuity, it's a good idea to enter the payment as a negative value. 29. Which formula shows the present value of an ordinary annuity that pays $100 per year for three years if the interest rate is 10 percent per year? $100{[1 − (1/(1.10) 3 )]/0.10} 30. An annuity due is an annuity for which the cash flows occur at the beginning of each period. 31. A perpetuity is a constant stream of cash flows for a(n) infinite period of time. 32. To use a present value of an annuity table to find the present value of an annuity factor, search the row for the number of periods and the column for the rate. 33. Which of the following spreadsheet (Excel) functions will calculate the $614.46 present value of an ordinary annuity of $100 per year for 10 years at 10 percent per year? =PV(.10,10,-100,0,) 34. A growing annuity has a(n) finite number of growing cash flows. 35. Because of tradition and legislation, interest rates are often quoted in many different ways. 36. An annuity due is a series of payments that are made at the beginning of each period. 37. Interest paid twice a year is known as semiannual compounding. 38. Which of the following is a perpetuity? A constant stream of cash flows forever 39. Which of the following is equal to an effective annual rate of 12.36 percent? 12%, compounded semiannually 40. Which of the following is true about a growing annuity? a. The cash flows grow for a finite period. b. The cash flows grow at a constant rate. 41. False: There is only one way to quote interest rates. 42. The annual percentage rate is the interest rate charged per period multiplied by the number of periods in a year. 43. The original loan amount is called the principal. 44. Given the same APR, more frequent compounding results in higher EARs. 45. APR - The interest rate per period multiplied by the number of periods in the year. 46. EAR - The interest rate stated as though it were compounded once per year. 47. With interest-only loans that are not perpetuities, the entire principal is repaid at some point in the future. 48. Amortization is the process of paying off loans by regularly reducing the principal. 49. Which of the following should be valued using a perpetuity formula? a. Cash flows from a product whose sales are expected to remain constant forever b. Preferred stock c. A consol (bond that pays interest only and does not mature) 50. An effective annual rate of 7.12 percent is equal to 7 percent compounded semiannually. 51. Which of the following are ways to amortize a loan? a. Pay the interest each period plus some fixed amount of the principal. b. Pay principal and interest every period in a fixed payment. c. Fixed payments that result in a zero loan balance d. Interest plus fixed amount 52. True: A fixed payment loan is most common for consumers. 53. Which of the following are true about the amortization of a fixed payment loan? a. The amount of interest paid decreases each period. b. The principal amount paid increases each period. 54. Amortization is the process of paying off loans by regularly reducing the principal. 55. The most common way to repay a loan is to pay interest plus a fixed principal amount every period. 56. Which type of amortization is most commonly used in the real world for mortgages and car loans? Fixed payment 57. The payments in a partial amortization loan are NOT based on the life of the loan. 58. With a fixed payment loan, the amount of interest paid decreases each period. 59. The loan balance on partial amortization loans declines so slowly because the payments are mostly interest. 60. Payments in a partial amortization loan are based on the amortization period, not the loan period. The remaining balance is then paid off in a lump sum bullet payment. 61. The variables in a future value of a lump sum problem include all of the following, except: payments 62. How would a decrease in the interest rate effect the future value of a lump sum, single amount problem (all other variables remain the same)? Decrease the future value 63. What is the future value of $1,000 invested for 15 years at a rate of 5%? $2,079 64. The variables in a present value of a lump sum problem include all of the following, except: 65. The variables in a present value of a lump sum problem include all of the following, except: free cash flow 66. The variable that you are solving for in a present value of a lump sum problem is: present value 67. What is the present value of $1,000 to be received in 12 years invested at a rate of 8%? $397 68. The variables in a future value of an annuity problem include all of the following, except: volatility 69. The variable that you are solving for in a future value of an annuity problem is: future value 70. The variables in a future value of an annuity problem include all of the following, except: usage 71. A common error made when solving a future value of an annuity problem is: Multiplying the annual deposit and the number of years before calculating the problem. 72. What is the future value of $400 invested each year for 15 years at a rate of 6%? $9,310 73. The variables in a present value of an annuity problem include all of the following, except: risk profile 74. The variable that you are solving for in a present value of an annuity problem is: the present value 75. What is the present value of $500 invested each year for 10 years at a rate of 5%? $3,861 76. The variables in a present value of an annuity problem include all of the following, except: source of funds 77. How would an increase in the interest rate effect the present value of an annuity problem (all other variables remain the same)? Decrease the present value 78. What is the present value of $400 invested each year for 12 years at a rate of 6%? $3,354 79. Which loan type requires the borrower to repay a single lump sum payment at some time in the future with interest? Pure discount 80. Which loan type requires calls for the borrower to pay interest each period and to repay the entire principal at some point in the future? Interest-only 81. Suppose a business takes out a $7,000, five-year loan at 6 percent that will be paid annually with a single, fixed payment each period. How much will be the annual payment? $1,661.88 82. What is the future value of $500 invested each year for 20 years at a rate of 10%? $28,637