Exam 1 - Chapter 4

The present value of $1,000 discounted at the rate of 5% per year, to be received at the end of 3 years is equal to

$1,000/(1.05)3

The present value of $10,000 discounted at 5% per year and received at the end of 5 years is

$10,000/(1.05)5.

If you invest $2,000 at the end of each year for five years and you earn 7% interest compounded annually, how much will you have accumulated at the end of the fifth year?

$11,501

Over the long term, which one of the following has historically had the lowest risk and lowest average annual rate of return?

long-term government bonds

Which one following will lower required rates of return?

lower rates of inflation

David has purchased an investment that he expects to produce an annual cash flow of $3,000 for five years. He requires an 8% rate of return compounded annually. What is the maximum amount that David can pay and still earn the required rate of return?

$11,978

Justin invests $4,000 in a savings account for two years. The account pays 2% interest compounded annually. How much interest income will Justin earn on this investment?

$161.60

Kelly bought a stock at a price of $22.50. She received a $1.75 dividend and sold the stock for $24.75. What is Kelly's capital gain on this investment?

$2.25

Taylor has saved $400 at the end of every month for the last 4 years with the intention of paying cash for a new car. She has earned a fixed annual rate of 4% over the 4 year period; interest is compounded monthly. How much can she pay for her new car at the end of the fourth year?

$20,784

Zachary has purchased an investment that he expects to produce income of $3,000 at the end of the first year and $4,000 at the end of the second year. If he requires an 8% rate of return compounded annually, what is the maximum amount that he can pay and still earn the required rate of return?

$3,000/(1.08)1 + $4,000/(1.08)2 = $6,207.13

Zachary has purchased an investment that he expects to produce income of $3,000 at the end of the first year and $4,000 at the end of the second year. If he pays $5,800 for this investment, what is the internal rate of return?

$3,000/1.128 + $4,000/1.1282 = $5,800 Answer is approximately 12.8%. A more exact answer found with Excel is 12.8414%

Justin invests $4,000 in a savings account for two years. The account pays 2% interest compounded annually. How much money will be in the account at the end of the second year?

$4,161.60

Roy is going to receive a payment of $5,000 one year from today. He earns an average of 6% on his investments. What is the present value of this payment?

$4,717

Christopher invests $400 today at a 4% rate of return which is compounded annually. What is the future value of this investment after four years?

$468

When computing an investment's internal rate of return using a financial calculator or spreadsheet such as Excel, which of the following should be entered as a negative number?

) the initial cost of the investment

Christopher purchased 200 shares of ABC stock at $21.25 per share. After nine months, he sold all of his shares at a price of $19.88 a share. Christopher received a total of $0.55 per share in dividends during the time he owned the shares. Jake's holding period return is

-6.4%.

Alexis bought a stock for $34 a share two years ago. The stock does not pay any dividends. Today she sold the stock for $28.50 a share. What was her internal rate of return on this investment?

-8.44%

The required return on Beta stock is 14%. The risk-free rate of return is 4% and the real rate of return is 2%. How much are investors requiring as compensation for risk?

10%

The markets in general are paying a 2% real rate of return. Inflation is expected to be 3%. ABC stock commands a 6% risk premium. What is the expected rate of return on ABC stock?

11%

Lauren purchased a stock for $28 a share and sold it six months later for $31. While she owned the stock, Lauren received two quarterly dividends of $0.35 per share. Brittany's holding period return on this stock is

13.2%.

n investment costs $3,500 today. This investment is expected to produce annual cash flows of $1,200, $1,400, $1,300 and $1,100, respectively, over the next four years. What is the internal rate of return on this investment?

16.2%

Ashley purchased a stock at a price of $27 a share. She received quarterly dividends of $0.75 per share. After one year, Ashley sold the stock at a price of $29.25 a share. What is her percentage holding period return on this investment?

19.4%

Bob's house has doubled in value since he bought it 30 years ago. The house's value has increased by an annual rate of

2.34%

An investment produced annual rates of return of 4%, 8%, 14% and 6%, respectively, over the past four years. What is the standard deviation of these returns?

4.3%

The Sorka Corp. has paid annual dividends of $0.60, $0.63, $0.65, $0.68 and $0.72, respectively, over the past five years. What is the dividend growth rate?

4.7%

Josh purchased 100 shares of XOM for $76.63 per share at the beginning of 2011. He received dividends per share of $1.37 (2011), $1.55 (2012), $1.66 (2013), $1.74 (2014), $1.85 (2015). At the end of 2015 just after receiving the last dividend, he sold the stock for $84.76. What was his average annual rate of return form both dividends and capital gains? (Hint: compute the IRR, assume that all dividends were received at the end of the year.)

4.94%

Ryan purchased a bond for $980 at the beginning of 2011. He received annual interest payments of $55 at the end of each year through 2016 when the bond was redeemed at its face value of $1,000. Compute the yield (internal rate of return) Ryan earned on his bond purchase.

5.91%

The required rate of return on the Cosmos Corporation's common stock is 10%, the current real rate of return in the market is 1%, and the inflation rate is 3%. In this case, the risk premium associated with Cosmos stock is

6%.

Josh purchased 100 shares of XOM at the beginning of 2011. He received dividends per share of $1.37 (2011), $1.55 (2012), $1.66 (2013), $1.74 (2014), $1.85 (2015). At the end of 2015, just after receiving the last dividend, he sold the stock for $84.76. At what rate did the dividends grow from the end of 2011 to the end of 2015? Assume that all dividends were received at the end of the year.

7.8%

Six years ago, Miguel invested $3,500. Today his investment is worth $5659. The internal rate of return on this investment is

8.34%.

Table 1 A B 1 Year Cash Flow 2 1 $(5,000) 3 2 $4,000 4 3 $3,000 10) Given a spreadsheet similar to the one shown in Table 1, the command to compute the internal rate of return would be

=IRR(B2:B4).

The following investment cash flows have been entered into cells B5 through B9 of an EXCEL spreadsheet. B5 $(5,200 ), B6 $2,100, B7 $1,300, B8 $1,800, B9 $1,200, where $(5,200) is the cost of the investment and the following amounts are cash flows at the end of years one through four. The correct function for computing the yield on this investment is

=irr(B5:B9).

To compute the present value of $1,000 annuity received at the end of each of the next three years and discounted at the rate of 5% per year, you should enter the following variables into a financial calculator.

A) N=3, i=5, PMT=1000

Which of the following investments may be impacted by government actions?

A) stocks B) corporate bonds C) government bonds D) all of the above

Jason purchased ABC stock at $40 per share and DEF stock at $35 per share on the same day in 2015. Exactly 6 months later, the ABC stock is worth $42.00 per share and has not paid a dividend while the DEF stock is worth $36 per share and has paid 2 quarterly dividends of $0.50 each. The holding period returns are

ABC 5% and DEF 5.7%.

) Josh purchased 100 shares of XOM for $76.63 per share at the beginning of 2007. He received dividends per share of $1.37 (2007), $1.55 (2008), $1.66 (2009), $1.74 (2010), $1.85 (2011). At the end of 2011, just after receiving the last dividend, he sold the stock for $84.76. What was his average annual rate of return form both dividends and capital gains? (Hint: compute the IRR, assume that all dividends were received at the end of the year.)

Answer: Josh's cash flows on a per share basis were as follows: PV at 4.076% 2007 (beginning) -$76.63 -76.63 2007 (end) 1.37 1.32 2008 (end) 1.55 1.43 2009 (end) 1.66 1.47 2010 (end) 1.74 1.48 2011 (end) 1.85 + 84.76 70.93 Total 00.00

Which one of the following statements is correct The future value of $1 at the end of two years is equal to $1 plus the first year's interest times 1 plus the annual interest rate.concerning the time value of money?

As the interest rate increases for any given year, the future value interest factor will decrease.

Explain the similarities and differences between the holding period return and the internal rate of return.

Both measures take into account total return from both income and capital gains. The holding period of return does not adjust returns for the length of time that an investment is held. The internal rate of return computes an average compound annual rate of return and is suitable for comparing investments held for different periods of time.

The expected rate of return and standard deviations, respectively for four stocks are given below: ABC 9%, 3% CDE 11%, 9% FGH 12%, 8% IJK 14%, 10%

CDE

Briefly explain the holding period return (HPR) and give several characteristics of this measure.

HPR is the total return earned from holding an investment for a specified period of time. HPR =

Camille purchased a bond 5 years ago for $1,050. The bond paid $50 in annual interest and returned the $1,000 principal at the end of the fifth year. Camille used the interest payment to pay for college textbooks.

Her internal rate of return was less than 5%.

Which of the following statements are correct concerning the present value of $1.00 five years from today discounted at 5%? I. The present value is equal to $1.00 divided by 1.05 to the 5th power. II. If the discount rate were less than 5%, the present value would be smaller. III. If the discount rate were more than 5%, the present value would be smaller. IV. If the $1.00 were to be received 6 years from today, the present value would be larger.

I and III only

Which of the following statements about the standard deviation are correct? I. The standard deviation is a measure of relative dispersion. II. Standard deviations should be in conjunction with expected returns to compare investments. III. The standard deviation is calculated by taking the square root of the variance. IV. The higher the standard deviation of an investment, the lower its risk.

I, II and III only

Which of the following factors will increase the risk level of an investment? I. a firm's decision to use a high percentage of debt financing II. an economic situation in which consumer prices are rising at a rapid rate III. the ability to trade the investment in a broad market rather than in a thin market IV. unstable currency values

I, II and IV only

Which of the following should be considered when deciding among alternative investments? I. time value of money II. risks associated with each investment III. risk free rate of return IV. personal risk tolerance level

I, II and IV only

Which of the following is(are) issue characteristics of an investment? I. type of investment such as stocks or bonds II. financial condition of the issuer III. coupon or dividend payments IV. time to maturity

I, III and IV only

Which is most true of an annual rate of 4% compounded quarterly?

It is equivalent to 4.06% paid annually

Which types of risk can not be avoided by carefully researching a company's business prospects and financial statements?

Market risk is the risk that market forces can affect the return of an individual investment. Event risk is the risk that an unforeseeable event may have an immediate, significant effect on an investment's returns. Tax risk is the possibility that tax laws affecting an investment could change. All of these risks are caused by factors external to the company, so they cannot be avoided by researching internal factors. Although not firm related, we could also mention purchasing power risk tied to unanticipated changes in inflation and interest rate risk which could affect stock values.

To compute the present value of $1,000 annuity received at the end of each of the next three years and discounted at the rate of 5% per year, you should use which of the following EXCEL commands?

PV

Samantha bought a stock one year ago for $66 a share. She received a total of $2.00 in dividends. Today she sold the stock for $70 a share. Which one of the following statements is correct concerning this investment?

Samantha has a total return of 9.1%.

Historically, what is the correct ranking of the following securities from lowest rate of return to the highest?

Short-term government bills, long-term government bonds, stocks.

Explain the relationship between risk, the expected rate of return and the actual rate of return.

The higher the risk, real or perceived, of an investment the higher the expected rate of return. The higher the actual risk of an investment, the greater the probability that the actual rate of return will vary significantly from the expected rate of return.

Assume that $100 is deposited at the end of each year for five years at 10% compound interest and that no withdrawals are made over the five-year period. Based on this data, which one of the following statements is correct?

The present value can be determined by computing the present value of a $100 ordinary annuity for five years at 10%.

The expected rate of return and standard deviations, respectively for four stocks are given below: OPQ 11%, 8% RST 11%, 9% UVW 12%, 10% XYZ 12%, 8% Which stock is clearly most desirable?

XYZ

Jeremy purchased 100 shares of FB for $19 per share in September 2012 and sold them 3 years later at $91 per share. At what annual rate did the value of his investment grow?

about 69%

The risk-free rate is equal to the real rate of return plus

an expected inflation premium.

Which of the following will lower the rate of return on a stock whose price has doubled since you bought it?

an increase in the capital gains tax from 15% to 20%

Inflation tends to have a particularly negative impact on the price of

bonds.

As gasoline prices fell in 2015, sales of hybrid and electric vehicles dropped sharply. This is an example of

business risk.

The holding period return (HPR) can appropriately be used to

compare returns among investments that are held for the same period of time.

The maximum rate of return that can be earned for a given rate of interest occurs when interest is compounded

continuously.

When calculating the present value of either a future single sum or a future annuity, the applicable interest rate is usually called the

discount rate.

The most predictable component of stock returns is

dividend income

A petroleum refinery in the Gulf region is forced to shut down for several months because of hurricane damage. This is an example of

event risk.

The stock of Plomb Co. falls sharply on news that its CEO has drowned in a boating accident while on vacation. This is an example of

event risk.

Rational investor's are motivated to purchase an asset because of its

expected returns

In some markets it may take many months to sell a residential property. This is an example of

liquidity risk.

A business has strong sales and profits, but its stock price falls anyway because stock prices in general are declining. This is an example of

market risk

Liquidity risk is defined as the risk of

not being able to sell an investment conveniently and at a reasonable price.

Which of the following internal characteristics should cause investors to expect the highest rate of return?

poor management and excessive use of debt financing

Most investors are risk-averse, which means they

require an increase in return for any increase in risk.

If the present value of an investment's benefits equals the present value of the investment's costs, then the investor would earn a

return equal to the discount rate.

Over the past 4 years, the annual rates of return on stock of Brown & Warren Inc. have been -2%, 4%, 14% and 6%, respectively, over the past four years. Compute the standard deviation of these returns.

rt (rt-avg)2 -2.00% 0.56% 4.00% 0.02% 14.00% 0.72% 6.00% 0.00% 22.00% 1.31% 5.50% 0.44% 6.61%

A capital loss is computed by

subtracting the original cost of an investment from the proceeds received from the sale of that investment.

Congress considers a bill that would eliminate the mortgage interest deduction for individuals. For the housing industry, this is an example of

tax risk.

When the rate of return is equal to the discount rate

the cost of an investment equals the present value of its benefits.

If a stock is purchased at the beginning of a year, a single dividend is paid at the end of the year and the stock is sold immediately after the dividend has been received. In this case

the internal rate of return equals the holding period return.

Which one of the following is an example of an annuity?

the payment of $259 a month for three consecutive years

The closest approximation to the real, risk-free rate of interest is

the short-term Treasury bill rate minus the inflation rate.

The time value of money concept best supports the idea of

the sooner the better.

In which of the following circumstances would it be most appropriate to use the holding period return?

to compare the performance of several stocks, each of which was held throughout an entire year