EXAM 2 CONCEPTS
13) Define the following terms: (a) perpetuity
(a) A perpetuity is a stream of equal cash flows that occur at regular intervals and lasts forever.
13) Define the following terms: (b) annuity
(b) An annuity is a stream of N equal cash flows paid at regular intervals.
6) Which of the following statements regarding growing perpetuities is FALSE? A) We assume that r < g for a growing perpetuity. B) PV of a growing perpetuity C) To find the value of a growing perpetuity one cash flow at a time would take forever. D) A growing perpetuity is a cash flow stream that occurs at regular intervals and grows at a constant rate forever.
=Answer: A
7) Which of the following formulas is INCORRECT? A) PV of a growing annuity = C × B) PV of an annuity = C × C) PV of a growing perpetuity = D) PV of a perpetuity = need formulas
=Answer: A Explanation: A) PV of a growing annuity = C ×
12) Which of the following statements regarding annuities is FALSE? A) PV of an annuityC × B) The difference between an annuity and a perpetuity is that a perpetuity ends after some fixed number of payments. C) An annuity is a stream of N equal cash flows paid at regular intervals. D) Most car loans, mortgages, and some bonds are annuities.
=Answer: B Explanation: B) A perpetuity never ends.
7) Which of the following statements regarding perpetuities is FALSE? A) To find the value of a perpetuity by discounting one cash flow at a time would take forever. B) A perpetuity is a stream of equal cash flows that occurs at regular intervals and lasts forever. C) PV of a perpetuity D) One example of a perpetuity is the British government bond called a consol. need formuals
=Answer: C Explanation: C) PV of a perpetuity =
1) The present value (PV) of a stream of cash flows is just the sum of the present values of each individual cash flow.
=Answer: TRUE
1) The opportunity cost of capital is the best available expected return offered in the market on an investment of comparable risk and term to the cash flow being discounted.
Answer: TRUE
1) When you borrow money, the interest rate on the borrowed money is the price you pay to be able to convert your future loan payments into money today.
Answer: TRUE
3) Quality adjustments to changes in the CPI most often result in reductions to the inflation rate calculated from it.
Answer: TRUE
31) What is the general relationship between the absolute values of APR and EAR for an investment?
Answer: The APR of a project will either equal its EAR or be smaller than EAR. The APR will equal EAR with annual compounding for all other compounding intervals the APR will be smaller than EAR.
13) In which of the following situations would it not be appropriate to use the following formula: PV=C0 + C1/(1 + r) + C2/(1 + r)2 + . . . . + Cn/(1 + r)n when determining the present value (PV) of a cash flow stream? A) when yield curves are flat B) when short-term and long-term interest rates vary widely C) when the inflation rate is high D) when the discount rate is high
C0 + C1/(1 + r) + C2/(1 + r)2 + . . . . + Cn/(1 + r)n when determining the present value (PV) of a cash flow stream? A) when yield curves are flat B) when short-term and long-term interest rates vary widely C) when the inflation rate is high D) when the discount rate is high =Answer: B
EAR =
EAR = {(1 + APR) / m}m - 1;
13) Define the following terms: (c) growing perpetuity
(c) A growing perpetuity is a cash flow stream that occurs at regular intervals and grows at a constant rate forever.
13) Define the following terms: (d) growing annuity
(d) A growing annuity is a stream of N growing cash flows, paid at regular intervals.
4) What, typically, is used to calculate the opportunity cost of capital on a risk-free investment? A) the best expected return offered in any investment available in the market B) the interest rate on U.S. Treasury securities with the same term C) the interest rate of any investments alternatives that are available D) the best rate of return offered by U.S. Treasury securities
Answer: B
20) If the current inflation rate is 2.0%, then the nominal rate necessary for you to earn a(n) 7.3% real interest rate on your investment is closest to ________. A) 11.3% B) 9.4% C) 13.2% D) 15.1%
Answer: B Explanation: B) or 9.4%
14) How do you calculate (mathematically) the present value (PV) of a(n): (a) perpetuity (b) annuity (c) growing perpetuity (d) growing annuity need to add formulas
Answer: (a) PV of a perpetuity = (b) PV of an annuity = C × (c) PV of a growing perpetuity = (d) PV of a growing annuity = C ×
2) Investment X and Investment Y are both growing perpetuities with initial cash flow of $100. Both investments have the same interest rate (r) and cash flows. The present value of Investment X is $5,000, while the present value of Investment Y is $4,000. Which of the following is true? A) Investment X has a higher growth rate than Investment Y. B) Investment X has a lower growth rate than Investment Y. C) The answer cannot be determined without knowing the interest rate for both investments. D) With the same initial cash flow and the same interest rate, Investment X and Investment Y should have the same present value.
Answer: A
29) When computing a present value, which of the following is TRUE? A) You should adjust the discount rate to match the interval between cash flows. B) You should adjust the future value to match the present value. C) You should adjust the time period to match the present value. D) You should adjust the cash flows to match the time period of the discount rate.
Answer: A
5) What is the effective annual rate (EAR)? A) It is the interest rate that would earn the same interest with annual compounding. B) It is the ratio of the number of the annual percentage rate to the number of compounding periods per year. C) It is the interest rate for an n-year time interval, where n may be more than one year or less than or equal to one year (a fraction). D) It refers to the cash flows from an investment over a one-year period divided by the number of times that interest is compounded during the year.
Answer: A
6) Why, in general, do investment opportunities offer a rate greater than that offered by U.S. Treasury securities for the same horizon? A) Most investment opportunities bear far greater risk than those offered by U.S. Treasury securities. B) The return from U.S. Treasury securities generally attracts less tax than the returns from other investments. C) The opportunity cost of capital for a given horizon is generally based on U.S. Treasury securities with that same horizon. D) U.S. Treasury securities are generally considered to be the best alternative to most investments.
Answer: A
8) Which of the following is true about perpetuities? A) Since a perpetuity generates cash flows every period infinitely, the cash flow generated equals the PV times the interest rate. B) Since a perpetuity generates cash flows every period infinitely, initial cash outflow must be discounted to calculate the present value. C) Since a perpetuity generates cash flows every period infinitely, there is no way to solve for the cash flow using the present value and the interest rate. D) Since a perpetuity generates cash flows every period infinitely, its FV is the same as its PV.
Answer: A
10) Which of the following best describes the annual percentage rate? A) the quoted interest rate which, considered with the compounding period, gives the effective interest rate B) the effective annual rate, after compounding is taken into account C) the discount rate, when compounded more than once a year or less than once a year D) the discount rate, when effective annual rate is divided by the number of times it is compounded in a year
Answer: A
10) Which of the following situations would result in lowering of interest rates by the banking authority of a country? A) The economy is slowing down. B) Inflation is rising rapidly. C) The level of investment is quite high. D) The rate of savings is quite low.
Answer: A
14) In an effort to maintain price stability, it is expected that the European Central Bank will raise interest rates in the future. Which of the following is the most likely effect of such an action on short-term and long-term interest rates in Europe? A) Long-term interest rates will tend to be higher than short-term interest rates. B) Long-term interest rates will be about the same as short-term interest rates. C) Both long- and short-term interest rates would be expected to fall sharply. D) No relative change in short and long term interest rates could be predicted.
Answer: A
16) Term: _ 1 year 2 years 3 years 5 years 10 years 20 years Rate: 5.00% 5.20% 5.40% 5.50% 5.76% 5.9% Given the above term structure of interest rates, which of the following is most likely in the future? Option I. Interest rates will fall. Option II. Economic growth will slow. Option III. Long-term rates will rise relative to short term rates. A) Option I only B) Option II only C) Option III only D) Options I and II
Answer: A
2) You are given two choices of investments, Investment A and Investment B. Both investments have the same future cash flows. Investment A has a discount rate of 4%, and Investment B has a discount rate of 5%. Which of the following is true? A) The present value of cash flows in Investment A is higher than the present value of cash flows in Investment B. B) The present value of cash flows in Investment A is lower than the present value of cash flows in Investment B. C) The present value of cash flows in Investment A is equal to the present value of cash flows in Investment B. D) No comparison can be made—we need to know the cash flows to calculate the present value.
Answer: A
17) The effective annual rate (EAR) for a loan with a stated APR of 8% compounded monthly is closest to ________. A) 8.30% B) 9.13% C) 9.96% D) 10.79%
Answer: A Explanation: A)
21) Consider the following investment alternatives: Investment APR Compounding A 6.9030% Annual B 6.6992% Daily C 6.7787% Quarterly D 6.7643% Monthly Which alternative offers you the lowest effective rate of return? A) Investment A B) Investment B C) Investment C D) Investment D
Answer: A Explanation: A)
4) What is the real interest rate given a nominal rate of 8.9% and an inflation rate of 1.9%? A) 6.9% B) 8.2% C) 9.6% D) 11.0%
Answer: A Explanation: A)
14) The table above shows the rate of return (APR) for four investment alternatives. Which offers the highest EAR? Investment: A B C D Rate of Return: 6.0% 5.9% 5.8% 5.7% Compounding Yearly Semiannually Monthly Weekly A) Investment A B) Investment B C) Investment C D) Investment D
Answer: A Explanation: A) 1
26) In 2009, U.S. Treasury yielded 0.1%, while inflation was 2.7%. What was the real rate in 2009? A) -2.6% B) 2.6% C) -2.8% D) 2.8%
Answer: A Explanation: A) 0.1% - 2.7% = -2.6%
34) How do we handle a situation when both compounding period and cash flow interval are given to us but both are less than a year and not equal to each other?
Answer: Additional care should be taken when the compounding period is given to us and it does not equal the cash flow interval. This requires some additional steps in computing the applicable interest rate. The compounding interval has to match the cash flow interval to enable transformation to present value (PV) or future value (FV). In most cases, it should be possible to achieve this by calculating the effective annual rate from the given compounding interval and subsequently calculating the annual percentage rate and periodic interest rate for the cash flow interval.
30) Everything else remaining same, under what situation will APR and EAR be equal?
Answer: An APR will equal EAR only with annual compounding assuming everything else remains same.
28) The yield curve is typically ________. A) downward sloping B) upward sloping C) flat D) inverted
Answer: B
3) Which of the following investments has a higher present value, assuming the same (strictly positive) interest rate applies to both investments? Year Investment X Investment Y 1 $5,000 $11,000 2 $7,000 $9,000 3 $9,000 $7,000 4 $11,000 $5,000 A) Investment X has a higher present value. B) Investment Y has a higher present value. C) Investment X and Investment Y have the same present value, since the total of the cash flows is the same for both. D) No comparison can be made—we need to know the interest rate to calculate the present value.
Answer: B
28) Which of the following is/are TRUE? I. The EAR can never exceed the APR. II. The APR can never exceed the EAR. III. The APR and EAR can never be equal. A) Only I. is true. B) Only II. is true. C) Only II. & III. are true. D) Only I. & III. are true.
Answer: B
7) Given that the inflation rate in 2006 was about 3.24%, while a short-term municipal bond offered a rate of 2.9%, which of the following statements is correct? A) The purchasing power of investors in these bonds grew over the course of the year. B) The real interest rate for investors in these bonds was greater than the rate of inflation. C) Investors in these bonds were able to buy less at the end of the year than they could have purchased at the start of the year. D) The nominal interest rate offered by these bonds gave the true increase in purchasing power that resulted from investing in these bonds.
Answer: C
8) Which of the following statements is FALSE? A) The actual return kept by an investor will depend on how the interest is taxed. B) The equivalent after-tax interest rate is r(1 - τ). C) The highest interest rate for a given horizon is the rate paid on U.S. Treasury securities. D) It is important to use a discount rate that matches both the horizon and the risk of the cash flows.
Answer: C
9) A(n) 12% APR with monthly compounding is closest to ________. A) an EAR of 10.14% B) an EAR of 15.22% C) an EAR of 12.68% D) an EAR of 25.36%
Answer: C Explanation: C)
18) The effective annual rate (EAR) for a loan with a stated APR of 11% compounded quarterly is closest to ________. A) 12.61% B) 13.75% C) 11.46% D) 14.90%
Answer: C Explanation: C) or 11.46%
19) The effective annual rate (EAR) for a savings account with a stated APR of 5% compounded daily is closest to ________. A) 5.64% B) 6.15% C) 5.13% D) 6.66%
Answer: C Explanation: C) or 5.13%
5) Which of the following computes the growth in purchasing power? A) growth of money + growth of prices B) (1 + real rate) / (1 + nominal rate) C) (1 + inflation rate) / (1 + nominal rate) D) growth of money / growth of prices
Answer: D
8) Historically, why were high inflation rates associated with high nominal interest rates? A) Individuals will spend more when they expect their investments to increase in value. B) Growth in investment and savings is encouraged when consumers are judged to be overspending. C) High inflation leads to a decrease in purchasing power and thus increases the attractiveness of investment over consumption in the short term. D) The real interest rate needs to be high enough so that individuals can expect their savings to have greater purchasing power in the future than in the present.
Answer: D
16) Which of the following statements is FALSE about interest rates? A) As interest rates may be quoted for different time intervals, it is often necessary to adjust the interest rate to a time period that matches that of cash flows. B) The effective annual rate indicates the amount of interest that will be earned at the end of one year. C) The annual percentage rate indicates the amount of simple interest earned in one year. D) The annual percentage rate indicates the amount of interest including the effect of compounding.
Answer: D
17) Which of the following reasons for considering long-term loans inherently more risky than short-term loans is most accurate? A) There is a greater chance that inflation may fall in a longer time-frame. B) The penalties for closing out a long term loan early make them unattractive to many investors. C) Long-term loans typically have ongoing costs that accumulate over the life of the loan. D) The loan values are very sensitive to changes in market interest rates.
Answer: D
19) Which of the following statements is FALSE? A) The interest rates that banks offer on investments or charge on loans depend on the horizon of the investment or loan. B) The Federal Reserve determines very short-term interest rates through its influence on the federal funds rate. C) The interest rates that are quoted by banks and other financial institutions are nominal interest rates. D) Fundamentally, interest rates are determined by the Federal Reserve.
Answer: D
4) Which of the following would be LEAST likely to lower the interest rate that a bank offers a borrower? A) The number of borrowers seeking funds is low. B) The expected inflation rate is expected to be low. C) The borrower is judged to have a low degree of risk. D) The loan will be for a long period of time.
Answer: D
7) Which of the following statements is FALSE? A) The opportunity cost of capital is the best available expected return offered in the market on an investment of comparable risk and term of the cash flows being discounted. B) Interest rates we observe in the market will vary based on quoting conventions, the term of investment, and risk. C) The opportunity cost of capital is the return the investor forgoes when the investor takes on a new investment. D) For a risk-free project, the opportunity cost of capital will typically be greater than the interest rate of U.S. Treasury securities with a similar term.
Answer: D
9) When the costs of an investment come before that investment's benefits, what will be the effect of a rise in interest rates on the attractiveness of that investment to potential investors? A) It will make it more attractive, since it will increase the investment's net present value (NPV). B) It will make it more attractive, since it will decrease the investment's net present value (NPV). C) It will make it less attractive, since it will increase the investment's net present value (NPV). D) It will make it less attractive, since it will decrease the investment's net present value (NPV).
Answer: D
9) Which of the following is true about perpetuities? A) All else equal, the present value of a perpetuity is higher when the periodic cash flow is higher. B) All else equal, the present value of a perpetuity is higher when the interest rate is lower. C) If two perpetuities have the same present value and the same interest rate, they must have the same cash flows. D) All of the above are true statements.
Answer: D
20) Consider the following investment alternatives: Investment APR Compounding A 6.2200% Annual B 6.0583% Daily C 6.1277% Quarterly D 6.1204% Monthly Which alternative offers you the highest effective rate of return? A) Investment A B) Investment B C) Investment C D) Investment D
Answer: D Explanation: D)
21) If the current inflation rate is 3.6% and you have an investment opportunity that pays 10.9%, then the real rate of interest on your investment is closest to ________. A) 8.5% B) 9.9% C) 11.3% D) 7.0%
Answer: D Explanation: D) (1 + nominal rate) = (1 + inflation rate)(1 + real rate) or 7.05%
6) In 2007, interest rates were about 4.5% and inflation was about 2.8%. What was the real interest rate in 2007? A) 1.58% B) 1.61% C) 1.62% D) 1.65%
Answer: D Explanation: D) 1.045 / 1.028 = 1.0165; real rate = 1.65%
9) Emma runs a small factory that needs a vacuum oven for brazing small fittings. She can purchase the model she needs for $180,000 up front, or she can lease it for five years for $4,200 per month. She can borrow at 7% APR, compounded monthly. Assuming that the oven will be used for five years, should she purchase the oven or should she lease it? A) Lease, since the present value (PV) of the lease is $12,224 less than the cost of the oven. B) Lease, since the present value (PV) of the lease is $8,642 less than the cost of the oven. C) Lease, since the present value (PV) of the lease is $2,212 less than the cost of the oven. D) Buy, since the present value (PV) of the lease is $32,108 more than the cost of the oven.
Answer: D Explanation: D) Calculate PV lease payments = $212,108; subtract $180,000 to get $32,108.
24) Your firm needs to invest in a new delivery truck. The life expectancy of the delivery truck is five years. You can purchase a new delivery truck for an upfront cost of $350,000, or you can lease a truck from the manufacturer for five years for a monthly lease payment of $7000 (paid at the end of each month). Your firm can borrow at 9.00% APR with quarterly compounding. The effective annual rate on your firm's borrowings is closest to ________. A) 9.00% B) 7.45% C) 11.17% D) 9.31%
Answer: D Explanation: D) or 9.31%
15) If a few intermediate cash flows in valuing a stream of cash flows are zero can we delete those points on the timeline and squeeze the timeline to show only nonzero cash flows?
Answer: Every cash flow contains two pieces of information—the nominal value and the time stamp. If we decide to eliminate the zero cash flows from the timeline and concentrate only on the nonzero ones, we will be distorting the time stamp of some nonzero cash flows. Hence, we need to show the timeline in full, including all cash flows zero as well as nonzero.
1) Cash flows from an annuity occur every year in the future.
Answer: FALSE
1) Joe borrows $100,000 and agrees to repay the principal, plus 7% APR interest compounded monthly, at the end of three years. Joe has taken out an amortizing loan.
Answer: FALSE
2) The real interest rate is the rate of growth of one's purchasing power due to money invested.
Answer: FALSE
2) The term "opportunity" in opportunity cost of capital comes from the fact that any worthwhile opportunity for investment will have a cost: the risk to the capital invested.
Answer: FALSE
2) Trial and error is the only way to compute the internal rate of return (IRR) when interest is calculated over five or more periods.
Answer: FALSE
2) When there are large numbers of people looking to save their money and there is little demand for loans, one would expect interest rates to be high.
Answer: FALSE
3) For a free-risk investment, the opportunity cost of capital will generally be more than the interest rate offered by U.S. Treasury securities with a similar term.
Answer: FALSE
3) The annual percentage rate indicates the amount of interest, including the effect of any compounding.
Answer: FALSE
33) What care, if any, should be taken when cash flows occur in periodicities that are shorter than a year (e.g., quarterly or monthly cash flows)?
Answer: In the real world, cash flows can occur with any periodicity but interest rates are generally quoted in annual terms. As such, when cash flows occur at a shorter than annual time interval the interest rates have to be modified to correspond to the cash flow interval. One way to do that is to match the compounding period equal to cash flow interval.
1) A growing perpetuity, where the rate of growth is greater than the discount rate, will have an infinitely large present value (PV).
Answer: TRUE
1) Market forces determine interest rates based ultimately on the willingness of individuals, banks, and firms to borrow, save, and lend.
Answer: TRUE
1) The internal rate of return (IRR) is the interest rate that sets the net present value (NPV) of the cash flows equal to zero.
Answer: TRUE
34) How are interest and return of principal handled in an amortizing loan payment?
Answer: The amount of periodic payments, generally monthly, for most amortizing loans is held constant such that a part goes toward paying interest on the outstanding balance and the rest toward return of principal. Thus this ratio keeps changing over the life of the loan. Initially, when the principal is highest, a major part of the loan goes toward paying interest and a smaller part toward returning the principal. However, as the loan progresses the interest component of the payment increases and the principal component decreases till the loan is fully paid off.
32) What is the implied assumption about interest rates when using the built-in functions of a financial calculator to calculate the present value (PV) of an annuity?
Answer: The built-in functions for present value of ordinary annuity in a financial calculator assume that interest rates are the same for every maturity on the yield curve.
17) How do the growth perpetuity results differ with negative and positive growths of similar magnitude assuming everything else remains unchanged?
Answer: The denominator in the formula for growth perpetuity plays in important role on the results for negative and positive growths of similar magnitude. A positive growth results in a smaller denominator thereby increasing the present value (PV). Contrarily, a negative growth results in a larger denominator giving a smaller present value (PV).
33) What is the implied assumption about interest rates when the equation to calculate the present value (PV) of perpetuity is used?
Answer: The equation for computation of present value of perpetuity assumes that the interest rates are the same for every maturity on the yield curve.
29) Can the nominal interest rate ever be negative? Can the real interest rate ever be negative? Explain.
Answer: The nominal interest rate can never be negative since by just holding your money you are earning a 0% return (no negative) on your money. The real rate, however, can be negative anytime that the inflation rate exceeds the nominal rate.
Use the table for the question(s) below. Suppose the term structure of interest rates is shown below: Term 1 year 2 years 3 years 5 years 10 years 20 years Rate (EAR%) 5.00% 4.80% 4.60% 4.50% 4.25% 4.15% 30) After examining the yield curve, what predictions do you have about interest rates in the future? About future economic growth and the overall state of the economy?
Answer: This is an inverted yield curve, which implies that interest rates should be falling in the future. An inverted yield curve is often interpreted as a negative forecast for economic growth. Since each of the last six recessions in the United States were preceded by a period with an inverted yield curve it could be a leading indicator of a future recession.
9) How do we decide on opportunity cost when we have several opportunities that need to be foregone?
Answer: We rank all the foregone opportunities, and opportunity cost is the second best opportunity that we forego. Thus we select the best opportunity and rank all the alternative opportunities and use the cost of the second best opportunity as opportunity cost.
32) Is it possible to analyze cash flows that occur in time intervals that are not exactly equal to a year?
Answer: Yes, in real world cash flows may be between any intervals. They may be shorter than a year or longer than a year. Additional care needs to be taken in both cases. For cash flows that have an interval longer than one year, one should be careful to show the years with zero cash flows. Alternately, for those with shorter than a year, one should be careful about modifying the interest rate to match the time interval.
15) Can we apply the growing perpetuity equation for negative growth as well?
Answer: Yes, it is perfectly in order to apply the growth perpetuity for negative growth. A negative growth gives two negatives in the denominator making it larger than a positive growth thus reducing the valuation compared to a positive growth of similar magnitude.