ch 4
17. All else equal, the future value of a lump-sum amount invested today will increase if the a. interest rate that is earned is lowered. b. number of compounding periods is increased. c. investment time period is shortened. d. amount initially invested is lowered. e. Two or more of the above answers are correct.
ANS: B DIF: Medium OBJ: TYPE: Conceptual TOP: Time value concepts
A perpetuity is an annuity with perpetual payments.
ANS: T DIF: Easy TOP: Perpetuity
What is the effective annual return (EAR) for an investment that pays 10 percent compounded annually? a. equal to 10 percent b. greater than 10 percent c. less than 10 percent d. This question cannot be answered without knowing the dollar amount of the investment. e. None of the above is correct.
ANS: A DIF: Easy OBJ: TYPE: Conceptual TOP: Effective annual rate
What is the term used to describe an annuity with an infinite life? a. perpetuity b. infinuity c. infinity due d. There is no special term for an infinite annuity.
ANS: A DIF: Easy OBJ: TYPE: Conceptual TOP: Perpetuity
20. You plan to invest an amount of money in five-year certificate of deposit (CD) at your bank. The stated interest rate applied to the CD is 12 percent, compounded monthly. How much must you invest if you want the balance in the CD account to be $8,500 in five years? a. $4,678.82 b. $4,823.13 c. $13,600.00 d. $14,979.90 e. $7,589.29
ANS: A DIF: Medium OBJ: TYPE: Conceptual TOP: PV of a lump sum
15. All else equal, if you expect to receive a certain amount in the future, say, $500 in ten (10) years, the present value of that future amount will be lowest if the interest earned on such investments is compounded a. daily b. weekly c. monthly d. quarterly e. annually
ANS: A DIF: Medium OBJ: TYPE: Conceptual TOP: Time value concepts
23. At approximately what rate would you have to invest a lump-sum amount today if you need the amount to triple in six years? Assume interest is compounded annually. a. 20% b. 12% c. 24% d. Not enough information is provided to answer the question. e. None of the above is a correct answer.
ANS: A DIF: Medium OBJ: TYPE: Conceptual TOP: Time value concepts
Suppose someone offered you your choice of two equally risky annuities, each paying $5,000 per year for 5 years. One is an annuity due, while the other is a regular (or deferred) annuity. If you are a rational wealth-maximizing investor which annuity would you choose? a. The annuity due. b. The deferred annuity. c. Either one, because as the problem is set up, they have the same present value. d. Without information about the appropriate interest rate, we cannot find the values of the two annuities, hence we cannot tell which is better. e. The annuity due; however, if the payments on both were doubled to $10,000, the deferred annuity would be preferred.
ANS: A DIF: Medium OBJ: TYPE: Conceptual TOP: Annuities
Why is the present value of an amount to be received (paid) in the future less than the future amount? a. Deflation causes investors to lose purchasing power when their dollars are invested for greater than one year. b. Investors have the opportunity to earn positive rates of return, so any amount invested today should grow to a larger amount in the future. c. Investments generally are not as good as those who sell them suggest, so investors usually are not willing to pay full face value for such investments, thus the price is discounted. d. Because investors are taxed on the income received from investments they never will buy an investment for the amount expected to be received in the future. e. None of the above is a correct answer.
ANS: B DIF: Easy OBJ: TYPE: Conceptual TOP: Time value concepts
By definition, what type of annuity best describes payments such as rent and magazine subscriptions (assuming the costs do not change over time)? a. ordinary annuity b. annuity due c. nonconstant annuity d. annuity in arrears
ANS: B DIF: Easy OBJ: TYPE: Conceptual TOP: Annuities
Given some amount to be received several years in the future, if the interest rate increases, the present value of the future amount will a. Be higher. b. Be lower. c. Stay the same. d. Cannot tell. e. Be variable.
ANS: B DIF: Easy OBJ: TYPE: Conceptual TOP: PV of a sum
24. Sarah is thinking about purchasing an investment from HiBond Investing. If she buys the investment, Sarah will receive $100 every three months for five years. The first $100 payment will be made as soon as she purchases the investment. If Sarah's required rate of return is 16 percent, to the nearest dollar, how much should she be willing to pay for this investment? a. $1,359 b. $1,413 c. $1,112 d. $1,519 e. $1,310
ANS: B DIF: Medium OBJ: TYPE: Conceptual TOP: PV of an annuity
18. Susan just signed a long-term lease on a townhouse in New York City (near Central Park) that requires her to make equal monthly payments for the next five years. The payments Susan has promised to make represent a(n) __________ for the landlord. a. ordinary annuity b. annuity due c. series of uneven cash flows d. perpetuity
ANS: B DIF: Medium OBJ: TYPE: Conceptual TOP: Annuities
As the discount rate increases without limit, the present value of the future cash inflows a. Gets larger without limit. b. Stays unchanged. c. Approaches zero. d. Gets smaller without limit, i.e., approaches minus infinity. e. Goes to ern.
ANS: C DIF: Easy OBJ: TYPE: Conceptual TOP: PV and discount rate
19. Suppose that the present value of receiving a guaranteed $450 in two years is $385.80. The opportunity rate of return on similar risk investments is 8 percent. According to this information, all else equal, which of the following statements is correct? a. It always would be preferable to wait two years to receive the $450 because this value is greater than the present value. b. Risk averse investors always would prefer to take the $385.80 today because it is a guaranteed amount whereas there is uncertainty as to whether the future amount will be paid. c. No investor should be willing to pay more than $385.80 for such an investment. d. It is apparent the present value was computed incorrectly because the present value of a future amount always should be greater than the future value. e. None of the above is a correct answer.
ANS: C DIF: Medium OBJ: TYPE: Conceptual TOP: Time value concepts
Which of the following statements is correct? a. Other things held constant, an increase in the number of discounting periods per year increases the present value of a given annual annuity. b. Other things held constant, an increase in the number of discounting periods per year increases the present value of a lump sum to be received in the future. c. The payment made each period under an amortized loan is constant, and it consists of some interest and some principal. The later we are is the loan's life, the smaller the interest portion of the payment. d. There is an inverse relationship between the present value interest factor of an annuity and the future value interest factor of an annuity, (i.e., one is the reciprocal of the other). e. Each of the above statements is true.
ANS: C DIF: Medium OBJ: TYPE: Conceptual TOP: Time value concepts
14. Which of the following statements is correct? a. Simple rates can't be used in present value or future value calculations because they fail to account for compounding effects. b. The periodic interest rate can be used directly in calculations as long as the number of payments per year is greater than or equal to the number of compounding periods per year. c. In all cases where interest is added or payments are made more frequently than annually, the periodic rate is less than the annual rate. d. Generally, the APR is greater than the EAR as a result of compounding effects. e. If the compounding period is semiannual then the periodic rate will equal the effective annual rate divided by two.
ANS: C DIF: Medium OBJ: TYPE: Conceptual TOP: Types of interest rates
16. Which of the following payments (receipts) would probably not be considered an annuity due? Based on your knowledge and using logic, think about the timing of the payments. a. rent payments associated with a five-year lease b. payments for a magazine subscription for a two-year period where the payments are made annually c. interest payments associated with a corporate bond that was issued today d. annual payments associated with lottery winnings that are paid out as an annuity
ANS: C DIF: Medium OBJ: TYPE: Conceptual TOP: Annuities
22. Alice's investment advisor is trying to convince her to purchase an investment that pays $250 per year. The investment has no maturity; therefore the $250 payment will continue every year forever. Alice has determined that her required rate of return for such an investment should be 14 percent and that she would hold the investment for 10 years and then sell it. If Alice decides to buy the investment, she would receive the first $250 payment one year from today. How much should Alice be willing to pay for this investment? a. $1,304.03, because this is the present value of an ordinary annuity that pays $250 a year for 10 years at 14 percent. b. $1,486.59, because this is the present value of an annuity due that pays $250 a year for 10 years at 14 percent. c. $1,785.71, because this is the present value of a $250 perpetuity at 14 percent. d. There is not enough information to answer this question, because the selling price of the investment in 10 years is not known today. e. None of the above is correct.
ANS: C DIF: Medium OBJ: TYPE: Conceptual TOP: Perpetuity
Which of the following statements is most correct? a. If annual compounding is used, the effective annual rate equals the simple rate. b. If annual compounding is used, the effective annual rate equals the periodic rate. c. If a loan has a 12 percent simple rate with semiannual compounding, its effective annual rate is equal to 11.66 percent. d. Both answers a and b are correct. e. Both answers a and c are correct.
ANS: D Statement d is correct. The equation for EAR is as follows:EAR=((1+r_simple)/m)^m-1 If annual compounding is used, m = 1 and the equation above reduces to EAR = rSIMPLE. The equation for the periodic rate is: r_periodic=r_simple/m If annual compounding is used then m = 1 and rPER = rSIMPLE and since EAR = rSIMPLE then rPER = EAR. DIF: Easy OBJ: TYPE: Conceptual TOP: Effective annual rate
Everything else equal, which of the following conditions will result in the lowest present value of an amount to be received in the future? a. annual compounding b. quarterly compounding c. monthly compounding d. daily compounding
ANS: D DIF: Easy OBJ: TYPE: Conceptual TOP: PV and effective annual rate
21. Vegit Corporation needs to borrow funds to support operations during the summer. Vegit's CFO is trying to decide whether to borrow from the Bank of Florida or the Bank of Georgia. The loan offered by Bank of Florida has a 12.5 percent simple interest rate with annual interest payments, whereas the loan offered by the Bank of Georgia has a 12 percent simple interest rate with monthly payments. Which bank should Vegit use for the loan? a. Bank of Georgia, because the 12 percent simple interest is cheaper than the 12.5 percent simple interest at Bank of Florida. b. Bank of Georgia, because the effective interest rate on the loan is less than 12 percent, whereas the effective interest rate on the loan at the Bank of Florida is greater than 12.5 percent. c. Bank of Florida, because the simple interest rate is higher, which means that Vegit will be able to invest the proceeds from the loan at a higher rate of return. d. Bank of Florida, because the effective interest rate on the loan is 12.5 percent, which is less than the 12.7 percent effective interest rate on the loan offered by the Bank of Georgia. e. There is not enough information to answer this question.
ANS: D DIF: Medium OBJ: TYPE: Conceptual TOP: Effective annual rate
11. Which of the following statements is correct? a. For all positive values of k and n, FVIFr, n ≥ 1.0 and PVIFAr, n ≥ n. b. You may use the PVIF tables to find the present value of an uneven series of payments. However, the PVIFA tables can never be of use, even if some of the payments constitute an annuity (for example, $100 each year for Years 3, 4, and 5), because the entire series does not constitute an annuity. c. If a bank uses quarterly compounding for saving accounts, the simple rate will be greater than the effective annual rate. d. The present value of a future sum decreases as either the simple interest rate or the number of discount periods per year increases. e. All of the above statements are false.
ANS: D DIF: Medium OBJ: TYPE: Conceptual TOP: Time value concepts
25. Which of the following statements is most correct? a. The first payment under a 3-year, annual payment, amortized loan for $1,000 will include a smaller percentage (or fraction) of interest if the interest rate is 5 percent than if it is 10 percent. b. If you are lending money, then, based on effective interest rates, you should prefer to lend at a 10 percent simple, or quoted, rate but with semiannual payments, rather than at a 10.1 percent simple rate with annual payments. However, as a borrower you should prefer the annual payment loan. c. The value of a perpetuity (say for $100 per year) will approach infinity as the interest rate used to evaluate the perpetuity approaches zero. d. Statements a, b, and c are all true. e. Only statements b and c are true.
ANS: D DIF: Tough OBJ: TYPE: Conceptual TOP: Time value concepts
13. A $10,000 loan is to be amortized over 5 years, with annual end-of-year payments. Given the following facts, which of these statements is correct? a. The annual payments would be larger if the interest rate were lower. b. If the loan were amortized over 10 years rather than 5 years, and if the interest rate were the same in either case, the first payment would include more dollars of interest under the 5-year amortization plan. c. The last payment would have a higher proportion of interest than the first payment. d. The proportion of interest versus principal repayment would be the same for each of the 5 payments. e. The proportion of each payment that represents interest as opposed to repayment of principal would be higher if the interest rate were higher.
ANS: E If the interest rate were higher, the payments would all be higher, and all of the increase would be attributable to interest. So, the proportion of each payment that represents interest would be higher. Note that statement b is false because interest during Year 1 would be the interest rate times the beginning balance, which is $10,000. With the same interest rate and the same beginning balance, the Year 1 interest charge will be the same, regardless of whether the loan is amortized over 5 or 10 years. DIF: Medium OBJ: TYPE: Conceptual TOP: Time value concepts
Cash flow time lines are used primarily for decisions involving paying off debt or investing in financial securities. They cannot be used when making decisions about investments in physical assets.
ANS: F DIF: Easy TOP: Cash flow time lines
The coupon rate is the rate of return you could earn on alternative investments of similar risk.
ANS: F DIF: Easy TOP: Coupon rate
Of all the techniques used in finance, the least important is the concept of the time value of money.
ANS: F DIF: Easy TOP: Time value concepts
When a loan is amortized, the largest portion of the periodic payment goes to reduce principal in the early years of the loan such that the accumulated interest can be spread out over the life of the loan.
ANS: F DIF: Medium TOP: Amortization
The greater the number of compounding periods within a year, the greater the future value of a lump sum invested initially, and the greater the present value of a given lump sum to be received at maturity.
ANS: F DIF: Medium TOP: Compounding
The effective annual rate is always greater than the simple rate as a result of compounding effects.
ANS: F DIF: Medium TOP: Effective and simple rates
The effective annual rate is less than the simple rate when we have monthly compounding.
ANS: F DIF: Medium TOP: Effective annual rate
Because we usually assume positive interest rates in time value analyses, the present value of a three-year annuity will always be less than the future value of a single lump sum, if the annuity payment equals the original lump sum investment.
ANS: F DIF: Medium TOP: Lump sum and annuity
Compounding is the process of converting today's values, which are termed present value, to future value.
ANS: T DIF: Easy TOP: Compounding
One of the potential benefits of investing early for retirement is that an investor can receive greater benefits from the compounding of interest.
ANS: T DIF: Easy TOP: Retirement and compounding
An annuity is a series of equal payments made at fixed equal-length intervals for a specified number of periods.
ANS: T DIF: Medium TOP: Annuities
The difference between an ordinary annuity and an annuity due is that each of the payments of the annuity due earns interest for one additional year (period).
ANS: T DIF: Medium TOP: Annuities
The difference between the PV of an annuity due and the PV of an ordinary annuity is that each of the payments of the annuity due is discounted by one more year.
ANS: T DIF: Medium TOP: Annuities
Suppose an investor can earn a steady 5% annually with investment A, while investment B will yield a constant 12% annually. Within 11 years time, the compounded value of investment B will be more than twice the compounded value of investment A (ignore risk).
ANS: T DIF: Medium TOP: Comparative compounding
All else equal, a dollar received sooner is worth more than a dollar received at some later date, because the sooner the dollar is received the more quickly it can be invested to earn a positive return.
ANS: T DIF: Medium TOP: Time value concepts
Solving for the interest rate associated with a stream of uneven cash flows, without the use of a calculator, usually involves a trial and error process.
ANS: T DIF: Medium TOP: Uneven cash flows and interest
You have determined the profitability of a planned project by finding the present value of all the cash flows form that project. Which of the following would cause the project to look more appealing in terms of the present value of those cash flows? a. The discount rate decreases. b. The cash flows are extended over a longer period of time, but the total amount of the cash flows remains the same. c. The discount rate increases. d. Answers b and c above. e. Answers a and b above.
ANS: A DIF: Easy OBJ: TYPE: Conceptual TOP: PV and discount rate
An amortized loan is a loan that requires equal payments over its life; its payments include both interest and repayment of the debt.
ANS: T DIF: Easy TOP: Amortization