Chapter 6: Discounted Cash Flow Valuation

Theresa adds $1,500 to her savings account on the first day of each year. Marcus adds $1,500 to his savings account on the last day of each year. They both earn 6.5 percent annual interest. What is the difference in their savings account balances at the end of 35 years? a. $12,093 b. $12,113 c. $12,127 d. $12,211 e. $12,219

a. $12,093

You are scheduled to receive annual payments of $3,600 for each of the next 12 years. The discount rate is 8 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. $2,170.39 b. $2,511.07 c. $2,021.18 d. $2,027.94 e. $2,304.96

a. $2,170.39

Racing Engines wants to save $750,000 to buy some new equipment four years from now. The plan is to set aside an equal amount of money on the first day of each quarter starting today. The firm can earn 4.75 percent on its savings. How much does the firm have to save each quarter to achieve its goal? a. $42,337.00 b. $42,969.70 c. $43,192.05 d. $43,419.29 e. $43,911.08

a. $42,337.00

You are paying an effective annual rate of 15.33 percent on your credit card. The interest is compounded monthly. What is the annual percentage rate on this account? a. 14.35 percent b. 13.90 percent c. 14.10 percent d. 13.75 percent e. 14.00 percent

a. 14.35 percent

Your father helped you start saving $20 a month beginning on your fifth birthday. He always made you deposit the money into your savings account on the first day of each month just to "start the month out right." Today completes your 17th year of saving and you now have $6,528.91 in this account. What is the rate of return on your savings? a. 5.15 percent b. 5.30 percent c. 5.47 percent d. 5.98 percent e. 6.12 percent

a. 5.15 percent percentCALCULATOREnter N (17X12), I/Y (/12), PMT -20BGN, FV 6528.91, CPT I/Y --> 5.15

You have been investing $250 a month for the last 13 years. Today, your investment account is worth $73,262. What is your average rate of return on your investments? a. 8.94 percent b. 9.23 percent c. 9.36 percent d. 9.41 percent e. 9.78 percent

a. 8.94 percent

Which one of the following compounding periods will yield the lowest effective annual rate given a stated future value at year 5 and an annual percentage rate of 10 percent? a. Annual. b. Semi-annual. c. Monthly. d. Daily. e. Continuous.

a. Annual.

You are going to loan a friend $6,000 for one year at an interest rate of 4.5 percent, compounded annually. How much additional interest could you have earned if you had compounded the rate continuously rather than annually? a. $5.84 b. $.6.17 c. $6.10 d. $5.93 e. $6.28

b. $.6.17

Your grandmother is gifting you $150 a month for four years while you attend college to earn your bachelor's degree. At a 4.8 percent discount rate, what are these payments worth to you on the day you enter college? a. $6,201.16 b. $6,539.14 c. $5,589.19 d. $6,608.87 e. $6,870.23

b. $6,539.14 PVA = $150 × [(1 - {1 / [1 + (.048 / 12)](4 × 12)}) / (.048 / 12)] = $6,539.14

The Distribution Point plans to save $2,000 a month for the next 3 years for future emergencies. The interest rate is 4.5 percent compounded monthly. The first monthly deposit will be made today. What would today's deposit amount have to be if the firm opted for one lump sum deposit that would yield the same amount of savings as the monthly deposits after 3 years? a. $70,459.07 b. $67,485.97 c. $69,068.18 d. $69,333.33 e. $67,233.84

b. $67,485.97

Your local pawn shop loans money at an annual rate of 23 percent and compounds interest weekly. What is the actual rate being charged on these loans? a. 25.16 percent b. 25.80 percent c. 26.49 percent d. 26.56 percent e. 26.64 percent

b. 25.80 percent EAR = [1 + (.23 / 52)]52 - 1 = .2580, or 25.80 percent

Troy will receive $7,500 at the end of Year 2. At the end of the following two years, he will receive $9,000 and $12,500, respectively. What is the future value of these cash flows at the end of Year 5 if the interest rate is 8 percent? a. $38,418 b. $32,907 c. $33,445 d. $36,411 e. $35,255

c. $33,445

You want to start your own consulting business and believe it could produce cash flows of $5,600, $48,200, and $125,000 at the end of each of the next three years, respectively. At the end of three years you think you can sell the business for $450,000. At a 14 percent discount rate, what is this business idea worth today? a. $311,406 b. $514,545 c. $430,109 d. $345,738 e. $478,901

c. $430,109 PV = $5,600 / 1.14 + $48,200 / 1.142 + ($125,000 + 450,000) / 1.143 = $430,109

Today, you borrowed $6,200 on your credit card to purchase some furniture. The interest rate is 14.9 percent, compounded monthly. How long will it take you to pay off this debt assuming that you do not charge anything else and make regular monthly payments of $120? a. 5.87 years b. 6.40 years c. 6.93 years d. 7.23 years e. 7.31 years

c. 6.93 years

The banks in your area offer the following rates of interest on their savings accounts. If you want to open one of these accounts, which bank should you select? Bank A: .75 percent APR with daily compounding. Bank B: .85 percent APR with monthly compounding. Bank C: .8725 percent APR with annual compounding. Bank D: .87 percent APR with quarterly compounding. Bank E: .775 percent APR with semi-annual compounding. a. Bank A b. Bank B c. Bank C d. Bank D e. Bank E

d. Bank D

You need some money today and the only friend you have that has any is your miserly friend. He agrees to loan you the money you need, if you make payments of $30 a month for the next six months. In keeping with his reputation, he requires that the first payment be paid today. He also charges you 2 percent interest per month. How much money are you borrowing? a. $164.09 b. $168.22 c. $169.50 d. $170.68 e. $171.40

e. $171.40 PVA Due = $30 × ({1 - [1 / (1 + .02)6]} / .02) × (1 + .02) = $171.40

You are borrowing $21,800 to buy a car. The terms of the loan call for monthly payments for five years at 8.25 percent interest. What is the amount of each payment? a. $387.71 b. $391.40 c. $401.12 d. $439.76 e. $444.64

e. $444.64

What is the effective annual rate of 14.9 percent compounded continuously? a. 15.59 percent b. 15.62 percent c. 15.69 percent d. 15.84 percent e. 16.07 percent

e. 16.07 percent

You are comparing two annuities that offer quarterly payments of $2,500 for five years and pay .75 percent interest per month. You will purchase one of these today with a single lump sum payment. Annuity A will pay you monthly, starting today, while annuity B will pay monthly, starting one month from today. Which one of the following statements is correct concerning these two annuities? a. These annuities have equal present values but unequal future values. b. These two annuities have both equal present and future values. c. Annuity B is an annuity due. d. Annuity A has a smaller future value than annuity B. e. Annuity B has a smaller present value than annuity A.

e. Annuity B has a smaller present value than annuity A.

You just received an insurance settlement offer related to an accident you had three years ago. The offer provides you with three choices: Option A: $1,500 a month for 6 yearsOption B: $1,025 a month for 10 yearsOption C: $85,000 as a lump sum payment today You can earn 7.5 percent on your investments and do not care if you personally receive the funds or if they are paid to your heirs should you die within the settlement period. Which option should you select and why is that option justified? a. Option A: It provides the largest monthly payment. b. Option B: It pays the largest total amount. c. Option C: It is all paid today. d. Option B: It pays the greatest number of payments. e. Option A: It has the greatest value today.

e. Option A: It has the greatest value today.