# Corporate Finance MGMT 332 Chapter 5

 The effective annual rate (EAR) takes into account the —- of interest that occurs within a year. compounding Which of the following processes can be used to calculate the future value of multiple cash flows? Calculate the future value of each cash flow first and then add them up.Compound the accumulated balance forward on year at a time. Suppose you expect to receive \$5,000 in one year, \$4,300 more in two years, and an additional \$5,000 in three years. Match each present value amount to the corresponding cash flow assuming a discount rate of 17%. Present value of the Year 1 Cash Flow = 4,273.50 = \$5,000/1.17Present value of the Year 2 Cash Flow = 3,141.21 = 4300/(1.17)2ndPresent value of the Year 3 Cash Flow = 3,121.85 = \$5,000/(1.17)3rd An ordinary annuity consists of a —- stream of cash flows for a fixed period of time. level The present value interest factor for an annuity with an interest rate of 8 percent per year over 20 years is —-. 9.8181 True or false: When calculating the present value of an annuity using the financial calculator, you enter the cash flows of the annuity in the PMT key. True When finding the present or future value of an annuity using a spreadsheet (Excel), the —- should be entered as a decimal. Interest rate Which of the following is the formula for the future value of an annuity factor? FV = C{[(1+r)t-1] over r} An annuity with payments beginning immediately rather than at the end of the period is called an —-. Annuity due The difference between the present value of an ordinary annuity with payments of \$100 per year at 10% compounded annually for 10 years and an annuity due with payments of \$100 per year at 10% compounded annually for 10 years is: PV(annuity due – PV(ordinary annuity), or \$675.90 – \$614.45 = \$61.45 Which of the following is a perpetuity? A constant stream of cash flows forever What is the present value of a perpetuity paying \$150 at the end of each year at 8%? PV = 150/.08 = 1,875 The formula for the future value of an annuity factor is [(1+r)t-1]/r. True An annuity due is a series of payments that are made —-. at the beginning of each period It the interest rate is greater than zero, the value of an annuity due is always —- an ordinary annuity. greater than A perpetuity is a constant stream of cash flows for a —- period of time. infinite An investment offers a perpetual cash flow of \$100 every year. The required return on this investment is 10 percent. Which of the following is the value of this investment? \$100/.10 = \$1,000 Which of the following are ways to amortize a loan? Pay the interest each period plus some fixed amount of the principal.Pay principal and interest every period in a fixed payment. The interest rate charged per period multiplied by the number of periods per year is equal too — — — on a loan. annual percentage rate You borrow \$100 and agree to pay back your payday loan in 2 weeks for 10% interest over that 2-week period. What is your stated annual interest rate? 26 x (10%) = 260.00% You agree to pay back \$1,100 in 4 weeks for a \$1,000 payday loan. Your annual percentage rate (APR) to two decimal places is —- %. [(1100/1000)-1] x (52/4)(100) The general formula for —-is (1+quoted rate/m)m-1 The EAR Given an annuity that has a payment of \$35 per year, an annual interest rate of 3%, and a present value of \$130, it will last for —- . 4 years You have \$2,000 right now that you plan to invest in an account paying 8% interest. You plan to add \$1,000 to this account every year, beginning next year, for 10 years. What is the future value of this investment? Add the FV of the \$1000 annuity (\$1000 should be pmt) to the FV of the \$2,000 single sum. \$18,804.41 What is the present value of an annuity that makes payments of \$100 per year for ten years if the first payment is made immediately and the discount rate is 10 percent per year? \$100[(1-1/1.10 10th)/.10][1.10] = \$675.90 Find the future value of an annuity of \$100 per year for 10 years at 10 percent per year. \$100x[1.10 10th – 1]/.10 = \$1,593.74 The future value of an annuity due of \$100 per year for 10 years at 10% per year is: 100[(1.10 10th – 1)/.10][1.10] = \$1,753.12 Which of the following Excel functions will result in the correct answer for the following annuity problem:You plan to deposit \$100 per year for the next 10 years in an account paying 8%. How much will you have in this annuity? =FV(.08,10,-100,0) An interest rate expressed in terms of the interest payment made each period is called a —- . stated interest rate; quoted interest rate Which of the following is NOT a way to amortize a loan? Fixed interest payments only In the Excel setup of a loan amortization problem, which of the following occurs? The payment is found with = PMT(rate, nper, -pv, fv).To find the principal payment each month, you subtract the dollar interest payment from the fixed payment. Which of the following could NOT be evaluated as annuities or annuities due? Tips to a waiterMonthly electric bills Which of the following is the general formula for the EAR when m is the number of times interest is compounded in a year? (1+quoted rate/m)Mth -1 The present value of an annuity due is equal to the present value of a —- annuity multiplied by (1+r). ordinary In almost all multiple cash flow calculations, it is implicitly assumed that the cash flows occur at the —- of each period. end The interest rate expressed as if it were compounded once per year is called the effective annual rate Amortization is the process of paying off loans by regularly reducing the —-. principal Which of the following is the simplest form of loan? A pure discount loan Suppose you paid off a \$1,200 loan by paying \$400 in principal each year plus 10 percent annual interest over a 3-year period. What is the total payment (interest plus principal) in year 3? \$400 + (\$1,200-800) x .10 = \$440 With typical interest-only loans, the entire principal is: repaid at some point in the future The original amount of a loan is termed the loan —-. principal When finding the present or future value of an annuity using a financial calculator, the —- should be entered as a percentage. interest rate If the quoted interest rate is 2% per month (12 months in a year), what is the APR? 2%/month x 12 months = 24% A credit card charges a rate of 1.5 percent per month, compounded monthly. What is the EAR? (1.015)12th – 1 = 19.56% C/r is the formula for the present value of a —-. perpetuity The formula for the — value interest factor of an annuity is: [1-1/(1+r)t]/r. present Suppose you borrow \$1,000 at 5% interest per year for 10 years. The loan is an interest only loan so each year you will pay —-. 5% x \$1,000 = \$50 Suppose you paid a \$1,200 loan off by paying \$400 in principal each year plus 10% yearly interest. How much is the 2nd interest payment? (\$1,200 – \$400) x 0.10 = \$80 If the quoted interest rate is 2% per month (APR = 24%), what is the EAR? (1.02)12th -1 = 26.82% To find the present value of an annuity of \$100 per year for 10 years at 10% per year using the tables, find a present value factor of —- and multiply it by —-. 6.1446; \$100 Which of the following is the appropriate Excel function to convert a quoted rate of 12% compounded quarterly to an EAR? EFFECT(0.12,4) 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. How much will Ralph give to the charity each year? \$402.11 More frequent compounding leads to: higher EARs Because of —- and —-, interest rates are often quoted in many different ways. tradition; legislation
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