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Chapter 006 Discounted Cash Flow Valuation Multiple Choice Questions An annuity is a(n): a level stream of perpetual cash flows B level stream of cash flows occurring for a fixed period of time c increasing stream of perpetual cash flows d increasing stream of cash flows occurring for a fixed period of time e decreasing stream of cash flows occurring for a fixed period of time SECTION: 6.2 TOPIC: ANNUITY TYPE: DEFINITIONS Which one of the following is the annuity present value factor? a (1 + Present value factor) / r B (1 Present value factor) / r c Present value factor + (1 / r) d (Present value factor r) + (1 / r) e r (1 + Present value factor) SECTION: 6.2 TOPIC: PRESENT VALUE FACTOR FOR ANNUITIES TYPE: DEFINITIONS What is a consol? a a type of annuity issued by an insurance company B a name used in Canada for a perpetuity c an annuity stream of payments received as an inheritance d a decreasing stream of perpetual payments e an increasing stream of perpetual payments SECTION: 6.2 TOPIC: CONSOL TYPE: DEFINITIONS 7-1 Chapter 006 Discounted Cash Flow Valuation How is an annuity due defined? a a stream of cash flows occurring for less than one year b an annuity stream of payments that are disbursed rather than received c an annuity stream of payments that are received rather than disbursed d a set of equal cash flows occurring at the end of each period E a set of equal cash flows occurring at the beginning of each period SECTION: 6.2 TOPIC: ANNUITIES DUE TYPE: DEFINITIONS An annuity stream where the payments occur forever is called a(n): a annuity due b indemnity C perpetuity d amortized cash flow stream e ordinary annuity SECTION: 6.2 TOPIC: PERPETUITY TYPE: DEFINITIONS What is the interest rate that is expressed in terms of the interest payment made each period called? A stated interest b compound interest c effective annual d periodic interest e daily interest SECTION: 6.3 TOPIC: STATED INTEREST RATES TYPE: DEFINITIONS 7-2 Chapter 006 Discounted Cash Flow Valuation What is the interest rate that is expressed as if it were compounded once per year called? a stated interest b compound interest C effective annual d periodic interest e daily interest SECTION: 6.3 TOPIC: EFFECTIVE ANNUAL RATE TYPE: DEFINITIONS What is the interest rate charged per period multiplied by the number of periods per year called? a effective annual B annual percentage c periodic interest d compound interest e daily interest SECTION: 6.3 TOPIC: ANNUAL PERCENTAGE RATE TYPE: DEFINITIONS A loan where the borrower receives money today and repays a single lump sum on a future date is called a(n) _ loan a amortized b continuous c balloon D pure discount e interest-only SECTION: 6.4 TOPIC: PURE DISCOUNT LOAN TYPE: DEFINITIONS 7-3 Chapter 006 Discounted Cash Flow Valuation 10 A loan where the borrower pays interest each period and repays the entire principal of the loan at some point in the future is called a(n) _ loan a amortized b continuous c balloon d pure discount E interest-only SECTION: 6.4 TOPIC: INTEREST-ONLY LOAN TYPE: DEFINITIONS 11 A loan where the borrower pays interest each period, and repays some or all of the principal of the loan over time is called a(n) _ loan A amortized b continuous c balloon d pure discount e interest-only SECTION: 6.4 TOPIC: AMORTIZED LOAN TYPE: DEFINITIONS 12 A loan where the borrower pays interest each period, repays part of the principal of the loan over time, and repays the remainder of the principal at the end of the loan, is called a(n) _ loan a amortized b continuous C balloon d pure discount e interest-only SECTION: 6.4 TOPIC: BALLOON LOAN TYPE: DEFINITIONS 7-4 Chapter 006 Discounted Cash Flow Valuation 13 You are comparing two annuities which offer monthly payments of $500 for ten years and pay 0.5 percent interest per month Annuity A will pay you on the first of each month while annuity B will pay you on the last day of each month Which one of the following statements is correct concerning these two annuities? a Both annuities are of equal value today b Annuity B is an annuity due C Annuity A has a higher future value than annuity B d Annuity B has a higher present value than annuity A e Both annuities have the same future value as of ten years from today SECTION: 6.2 TOPIC: ORDINARY ANNUITY VERSUS ANNUITY DUE TYPE: CONCEPTS 14 You are comparing two investment options that pay percent interest annually Both options will provide you with $20,000 of income Option A pays five annual payments starting with $8,000 the first year followed by four annual payments of $3,000 each Option B pays five annual payments of $4,000 each Which one of the following statements is correct given these two investment options? a Both options are of equal value given that they both provide $20,000 of income B Option A is the better choice c Option B has a higher present value than option A d Option B is a perpetuity e Option A is preferable because it is an annuity due SECTION: 6.1 AND 6.2 TOPIC: UNEVEN CASH FLOWS AND PRESENT VALUE TYPE: CONCEPTS 7-5 Chapter 006 Discounted Cash Flow Valuation 15 You are considering two projects with the following cash flows: Which of the following statements are true concerning these two projects? I Both projects have the same future value at the end of year 4, given a positive rate of return II Both projects have the same future value given a zero rate of return III Both projects have the same future value at any point in time, given a positive rate of return IV Project B has a higher future value than project A, given a positive rate of return a II only b IV only c I and III only D II and IV only e I, II, and III only SECTION: 6.1 TOPIC: UNEVEN CASH FLOWS AND FUTURE VALUE TYPE: CONCEPTS 16 How does a perpetuity differ from an annuity? a perpetuity payments vary with the rate of inflation b perpetuity payments vary with the market rate of interest c perpetuity payments are variable while annuity payments are constant D perpetuity payments never cease e annuity payments are smaller in amount SECTION: 6.2 TOPIC: PERPETUITY VERSUS ANNUITY TYPE: CONCEPTS 7-6 Chapter 006 Discounted Cash Flow Valuation 17 Which one of the following statements concerning the annual percentage rate is correct? a The annual percentage rate considers interest on interest b The rate of interest you actually pay on a loan is called the annual percentage rate c The effective annual rate is lower than the annual percentage rate when an interest rate is compounded quarterly d When firms advertise the annual percentage rate they are violating U.S truth-in-lending laws E The annual percentage rate equals the effective annual rate when the rate on an account is designated as simple interest SECTION: 6.3 TOPIC: ANNUAL PERCENTAGE RATE TYPE: CONCEPTS 18 Which one of the following statements concerning interest rates is correct? a The stated rate is the same as the effective annual rate B The effective annual rate is the rate that applies if interest is compounded annually c The annual percentage rate increases as the number of compounding periods per year increases d Borrowers prefer more frequent compounding on their loan accounts given a stated annual percentage rate e For any positive rate of interest, the effective annual rate will always exceed the annual percentage rate SECTION: 6.3 TOPIC: INTEREST RATES TYPE: CONCEPTS 7-7 Chapter 006 Discounted Cash Flow Valuation 19 Which of the following statements concerning the effective annual rate are correct? I When making financial decisions, you should compare effective annual rates rather than annual percentage rates II The more frequently interest is compounded, the higher the effective annual rate given a fixed annual percentage rate III A quoted rate of percent compounded continuously has a higher effective annual rate than if the rate were compounded daily IV When choosing which loan to accept, you should select the offer with the highest effective annual rate a I and II only b I and IV only C I, II, and III only d II, III, and IV only e I, II, III, and IV SECTION: 6.3 TOPIC: EFFECTIVE ANNUAL RATE TYPE: CONCEPTS 20 The highest effective annual rate that can be derived from an annual percentage rate of percent is computed as: a .09e b e.09 q c e (1 + 09) D e.09 e (1 + 09)q SECTION: 6.3 TOPIC: CONTINUOUS COMPOUNDING TYPE: CONCEPTS 7-8 Chapter 006 Discounted Cash Flow Valuation 21 A pure discount loan is a(n): A example of a present value problem b loan that is interest-free c loan that grants you a discount if you pay your payments on time d loan that requires all interest to be paid at the time the loan is made e loan that discounts the payments if you pay them in advance SECTION: 6.4 TOPIC: PURE DISCOUNT LOAN TYPE: CONCEPTS 22 The principle amount of an interest-only loan is: a never repaid b repaid in equal increments and included in each loan payment C repaid in full at the end of the loan period d repaid in equal annual payments even when the loan interest is repaid monthly e repaid in increasing increments and included in each loan payment SECTION: 6.4 TOPIC: INTEREST-ONLY LOAN TYPE: CONCEPTS 23 An amortized loan: a requires the principle amount to be repaid in even increments over the life of the loan B may have equal or increasing amounts applied to the principle from each loan payment c requires that all interest be repaid on a monthly basis while the principle is repaid at the end of the loan term d requires that all payments be equal in amount and include both principle and interest e repays both the principle and the interest in one lump sum at the end of the loan term SECTION: 6.4 TOPIC: AMORTIZED LOAN TYPE: CONCEPTS 7-9 Chapter 006 Discounted Cash Flow Valuation 24 Your parents are giving you $500 a month for five years while you attend college to earn both a bachelor's and a master's degree At a percent discount rate, what are these payments worth to you when you first enter college? a $22,681.13 b $24,601.18 C $25,251.00 d $27,209.17 e $30,000.00 AACSB TOPIC: ANALYTIC SECTION: 6.2 TOPIC: ORDINARY ANNUITY AND PRESENT VALUE TYPE: PROBLEMS 7-10 Chapter 006 Discounted Cash Flow Valuation 33 You are scheduled to receive annual payments of $15,000 for each of the next 13 years The discount rate is percent What is the difference in the present value if you receive these payments at the beginning of each year rather than at the end of each year? a $9,211.07 b $9,698.17 c $9,704.38 d $9,876.47 E $10,107.32 Difference = $122,410.88 $112,303.56 = $10,107.32 Note: The difference = 09 $112,303.5589 = $10,107.32 AACSB TOPIC: ANALYTIC SECTION: 6.2 TOPIC: ORDINARY ANNUITY VERSUS ANNUITY DUE TYPE: PROBLEMS 7-19 Chapter 006 Discounted Cash Flow Valuation 34 You are comparing two annuities with equal present values The applicable discount rate is 11.25 percent One annuity pays $6,000 on the first day of each year for 25 years How much does the second annuity pay each year for 25 years if it pays at the end of each year? a $6,350 b $6,408 C $6,675 d $6,921 e $7,100 Because each payment is received one year later, then the cash flow has to equal: $6,000 + 1125) = $6,675 AACSB TOPIC: ANALYTIC SECTION: 6.2 TOPIC: ORDINARY ANNUITY VERSUS ANNUITY DUE TYPE: PROBLEMS 7-20 (1 Chapter 006 Discounted Cash Flow Valuation 35 Betsy receives $600 on the first of each month Jen receives $600 on the last day of each month Both Betsy and Jen will receive payments for four years At a percent discount rate, what is the difference in the present value of these two sets of payments? a $135.40 b $137.46 c $138.09 d $141.41 E $146.16 Difference = $25,202.28 $25,056.12 = $146.16 Note: Difference AACSB TOPIC: ANALYTIC SECTION: 6.2 TOPIC: ORDINARY ANNUITY VERSUS ANNUITY DUE TYPE: PROBLEMS 7-21 Chapter 006 Discounted Cash Flow Valuation 36 What is the future value of $3,400 a year for years at a percent rate of interest? a $22,051.60 b $23,876.49 c $24,011.77 D $25,579.34 e $27,881.48 AACSB TOPIC: ANALYTIC SECTION: 6.2 TOPIC: ORDINARY ANNUITY AND FUTURE VALUE TYPE: PROBLEMS 37 What is the future value of $1,650 a year for years at a percent rate of interest? a $17,409.08 B $19,763.68 c $21,254.45 d $23,136.19 e $25,222.22 AACSB TOPIC: ANALYTIC SECTION: 6.2 TOPIC: ORDINARY ANNUITY AND FUTURE VALUE TYPE: PROBLEMS 7-22 Chapter 006 Discounted Cash Flow Valuation 38 Marcia plans on saving $6,000 a year and expects to earn an annual rate of 11.5 percent How much will she have in her account at the end of 40 years? A $4,007,098 b $4,467,914 c $5,911,408 d $6,221,009 e $6,347,238 AACSB TOPIC: ANALYTIC SECTION: 6.2 TOPIC: ORDINARY ANNUITY AND FUTURE VALUE TYPE: PROBLEMS 7-23 Chapter 006 Discounted Cash Flow Valuation 39 Christie adds $2,000 to her savings account on the first day of each year Todd adds $2,000 to his savings account on the last day of each year They both earn a percent rate of return What is the difference in their savings account balances at the end of 25 years? A $8,854.86 b $9,003.48 c $9,126.39 d $9,130.07 e $9,041.14 Difference = $135,352.94 $126,498.08 = $8,854.86 Note: Difference = $126,498.08 07 = $8,854.8656 AACSB TOPIC: ANALYTIC SECTION: 6.2 TOPIC: ANNUITY DUE VERSUS ORDINARY ANNUITY TYPE: PROBLEMS 7-24 Chapter 006 Discounted Cash Flow Valuation 40 You borrow $14,500 to buy a car The terms of the loan call for monthly payments for years at a 6.9 percent rate of interest What is the amount of each payment? a $238.87 b $240.27 C $246.51 d $249.08 e $252.50 AACSB TOPIC: ANALYTIC SECTION: 6.2 TOPIC: ORDINARY ANNUITY PAYMENTS TYPE: PROBLEMS 7-25 Chapter 006 Discounted Cash Flow Valuation 41 You borrow $187,500 to buy a house The mortgage rate is 7.25 percent and the loan period is 25 years Payments are made monthly If you pay for the house according to the loan agreement, how much total interest will you pay? a $186,408 B $219,079 c $227,001 d $264,319 e $291,406 Total interest = ($1,355.262871 25 12) $187,500 = $219,079 AACSB TOPIC: ANALYTIC SECTION: 6.2 AND 6.4 TOPIC: ORDINARY ANNUITY PAYMENTS AND COST OF INTEREST TYPE: PROBLEMS 7-26 Chapter 006 Discounted Cash Flow Valuation 42 The Home Improvement Center (HIC) has an employment contract with the newly hired CEO The contract requires a lump sum payment of $32.4 million be paid to the CEO upon the successful completion of her first five years of service HIC wants to set aside an equal amount of money at the end of each year to cover this anticipated cash outflow and will earn 7.25 percent on the funds How much must HIC set aside each year for this purpose? a $5,227,064 B $5,606,026 c $5,668,987 d $6,778,958 e $7,270,433 AACSB TOPIC: ANALYTIC SECTION: 6.2 TOPIC: ORDINARY ANNUITY PAYMENTS AND FUTURE VALUE TYPE: PROBLEMS 7-27 Chapter 006 Discounted Cash Flow Valuation 43 Pat retires at age 58 and expects to live to age 90 On the day she retires, she has $287,409 in her retirement savings account She is conservative and expects to earn 5.25 percent on her money during her retirement years How much can she withdraw from her retirement savings each month if she plans to die on the day she spends her last penny? a $1,359.79 b $1,364.18 c $1,540.01 D $1,546.75 e $1,702.11 AACSB TOPIC: ANALYTIC SECTION: 6.2 TOPIC: ORDINARY ANNUITY PAYMENTS AND PRESENT VALUE TYPE: PROBLEMS 7-28 Chapter 006 Discounted Cash Flow Valuation 44 The Chelsey Group purchased a piece of property for $4.8 million They paid a down payment of 25 percent in cash and financed the balance The loan terms require monthly payments for 25 years at an annual percentage rate of 8.65 percent compounded monthly What is the amount of each mortgage payment? a $27,804.13 b $27,989.62 c $28,406.23 d $29,142.91 E $29,352.98 Amount financed = $4,800,000 (1 25) = $3,600,000 AACSB TOPIC: ANALYTIC SECTION: 6.2 TOPIC: ORDINARY ANNUITY PAYMENTS AND PRESENT VALUE TYPE: PROBLEMS 7-29 Chapter 006 Discounted Cash Flow Valuation 45 You estimate that you will have $31,870 in student loans by the time you graduate The interest rate is 5.45 percent If you want to have this debt paid in full within four years, how much must you pay each month? a $737.11 b $738.82 c $739.34 D $740.46 e $741.09 AACSB TOPIC: ANALYTIC SECTION: 6.2 TOPIC: ORDINARY ANNUITY PAYMENTS AND PRESENT VALUE TYPE: PROBLEMS 7-30 Chapter 006 Discounted Cash Flow Valuation 46 You are buying a previously owned car today at a price of $4,950 You are paying $750 down in cash and financing the balance for 42 months at 8.45 percent What is the amount of each loan payment? a $108.54 b $115.05 C $115.86 d $135.60 e $136.55 Amount financed = $4,950 $750 = $4,200 AACSB TOPIC: ANALYTIC SECTION: 6.2 TOPIC: ORDINARY ANNUITY PAYMENTS AND PRESENT VALUE TYPE: PROBLEMS 7-31 Chapter 006 Discounted Cash Flow Valuation 47 The Helping Hand Insurance Company wants to sell you an annuity which will pay you $2,750 per quarter for 20 years You want to earn a minimum rate of return of 6.25 percent What is the most you are willing to pay as a lump sum today to buy this annuity? A $125,085.43 b $127,039.89 c $179,544.36 d $193,573.08 e $198,747.27 AACSB TOPIC: ANALYTIC SECTION: 6.2 TOPIC: ORDINARY ANNUITY PAYMENTS AND PRESENT VALUE TYPE: PROBLEMS 7-32 Chapter 006 Discounted Cash Flow Valuation 48 Your car dealer is willing to lease you a new car for $199 a month for 72 months Payments are due on the first day of each month starting with the day you sign the lease contract If your cost of money is 5.45 percent, what is the current value of the lease? a $11,708.18 b $11,297.60 c $12,197.74 D $12,253.14 e $13,008.31 7-33 ... purchased a piece of property for $4.8 million They paid a down payment of 25 percent in cash and financed the balance The loan terms require monthly payments for 25 years at an annual percentage... each mortgage payment? a $27,804.13 b $27,989.62 c $28,406.23 d $29,142.91 E $29,352.98 Amount financed = $4,800,000 (1 25) = $3,600,000 AACSB TOPIC: ANALYTIC SECTION: 6.2 TOPIC: ORDINARY ANNUITY... What is the amount of each loan payment? a $108.54 b $115.05 C $115.86 d $135.60 e $136.55 Amount financed = $4,950 $750 = $4,200 AACSB TOPIC: ANALYTIC SECTION: 6.2 TOPIC: ORDINARY ANNUITY PAYMENTS