Chapter 10: Analytical Methods

If an investment can be expected to return 8%, using the rule of 72, what is the present value needed to have $50,000 for a child's education in 18 years?

$12,500 Under the rule of 72, dividing 72 by the expected return shows the number of years it will take for a deposited sum to double. 72 divided by 8 equals 9 years. Over an 18-year period, there will be 2 doublings. So, dividing the future value ($50,000) by 4 solves for the present value required. 72/8 = 9 years. 50,000/4=12,500

Which of the following statements regarding internal rate of return (IRR) is TRUE? A) IRR is a discount rate at which the net present value (NPV) of an investment is equal to zero. B) IRR ignores the time value of money. C) If the IRR is higher than the cost of borrowing to fund an investment, the investment is likely to be unprofitable. D) IRR cannot be used effectively to measure return on investments with even cash flows, such as bonds.

A) IRR is a discount rate at which the net present value (NPV) of an investment is equal to zero. Internal rate of return (IRR) is a discount rate at which the net present value (NPV) of an investment is equal to zero. IRR can be used to measure return on bonds because of their even cash flows and on those stocks that pay stable dividends for the same reason. IRR accounts for the time value of money. If the IRR is higher than the cost of borrowing to fund the investment, the investment should be profitable.

Which of the following statements best describes the risk-free rate of interest? A) The rate of interest earned on the 91-day U.S. Treasury bill B) The rate of interest in excess of the pure time value of money C) The arithmetic mean of the CPI over the past 12 months D) The rate of interest required to produce a net present value (NPV) of zero

A) The rate of interest earned on the 91-day U.S. Treasury bill The rate of interest earned on short-term U.S. Treasury securities, generally the 91-day T-bill (might be called the 13 week or 3 month bill on the exam), is referred to as the risk-free rate. The rate of interest in excess of the pure time value of money is called the risk premium, not the risk-free rate. CPI and NPV have nothing to do with the risk-free interest rate.

To make a quantitative evaluation using the present value computation, which of the following is NOT needed? A) Anticipated rate of return of the portfolio B) Time period involved C) Account value at the end of the period D) Account value at the beginning of the period

Account value at the beginning of the period

To calculate the future value of an investment, which of the following must be known?

Assumed interest rate duration of investment

An investor's portfolio has a beta coefficient of 0.85. If the overall market declined by 10% over the course of a year, the portfolio's value has likely A) decreased by 11.76% B) increased by 10.85% C) decreased by 8.5% D) increased by 8.5%

C) decreased by 8.5%

Last year, ABC Corporation had earnings per share of $5 and paid a quarterly dividend of $.75 per share. It has a current market value of $75. What is its price-earnings ratio? A) 25:1 B) 50:1 C) 15:1 D) 10:1

C) 15:1 The dividend information is irrelevant. The price-earnings ratio is the price of the stock ($75) divided by the earnings of the stock ($5), or 15:1.

Dividend payments are not a part of the computation for which of the following risk measurement tools? A) Dividend growth model B) Dividend discount model C) Correlation coefficient D) Net present value

C) Correlation coefficient

All of the following statements regarding an investment's internal rate of return (IRR) are true EXCEPT A)investments are acceptable when their internal rates of return exceed the investor's required rate of return B) IRR is the one rate of return that results in an investment having a net present value (NPV) of 0 C) IRR is most often used with growth stocks D) IRR expresses the rate of interest that matches the initial investment with the present value of future cash flows

C) IRR is more often used with growht stocks t is possible, although very difficult, to calculate IRR for investments with uneven cash flows such as growth stocks where dividends are generally not reliable. IRR is the rate of interest that equates the initial investment with the present value of future cash flows; it is the rate of return that results in an investment having a net present value of 0.

A measurement of investment return that takes the time value of money into consideration is A) real rate of return B) risk-adjusted rate of return C)internal rate of return (IRR) D)holding period return

C) Internal rate of return The internal rate of return compounds returns and takes into consideration the time value of money. Real rate of return considers the inflation rate and risk-adjusted return is another way of stating the Sharpe ratio.

In general, one would prefer to purchase a bond when its current market price is A) more than its present value B) less than its future value C) less than its present value D) the same as its present value Explanation

C) Less than its present value When a bond can be purchased for less than its present value, it has a positive net present value (NPV). For example, if the present value of a bond is $600 and it can be purchased for $565, it has an NPV of $35 and should be an attractive investment. Every bond selling at a discount has a market price that is less than its future value (par), so that doesn't tell us anything about its NPV.

Your client has $10,000 to invest and expects to earn an after-tax return of 8% to send his daughter to college in 12 years. Which of the following items will help determine whether the investment is likely to satisfy the client's goal? A)Present value B)Client's marginal federal income tax bracket C)Consumer Price Index D)The expected cost of college

D) To determine whether the investment will satisfy the goal, the investment adviser representative needs to know the amount needed to pay for college. While the investment will be worth $25,181.70, this may not be enough to pay for even one year of college 12 years from now.

Which of the following would best describe working capital? A)The value per share available to shareholders in the event of bankruptcy B)The amount of money available to the corporation that is currently being held in cash or cash-equivalent positions C)A corporation's net worth D)The amount of money a corporation has available to work with if it liquidates its current assets and pays off all of its current liabilities

D) The amount of money a corporation has available to work with if it liquidates its current assets and pays off all of its current liabilities

A client owns an investment-grade bond with a coupon of 7%. If similarly rated bonds are being issued today with coupons of 5%, and the market is efficient, it would be expected that the client's bond A) has a positive net present value B) will be selling at a discount from par C) has a negative net present value D) has a zero net present value

D) has a zero net present value With a discount rate of 5% (the discount rate in a present value computation is the current market interest rate), a debt instrument with a 7% coupon rate will be selling at a premium (interest rates down, prices up). If the market is efficiently pricing that bond, its market price should be equal to its present value, resulting in an NPV of zero.

An analyst attempting to determine the extent to which financial leverage is being employed by a company would examine the company's

Debt-to-equity ratio

When a company's debt-to-equity ratio is higher than typical for that industry, it might be said that the company is

Highly leveraged

Rule of 72

How long it will take for an investment return to double.

One measure of a corporation's liquidation value is its book value per share. When performing this computation, the value of which of the following would normally be subtracted from the corporation's net worth? Cash Wages payable Patents Preferred stock

Patents Preferred stock The computation of book value per share is basically net tangible worth per share of common stock. Therefore, we subtract both the par value of the preferred stock and the value listed on the balance sheet for the intangible assets, such as patents.

The statistical measurement that indicates how much an investment's returns have fluctuated, compared to its average return, over a given period of time is known as

Standard deviation

A stock's beta coefficient is a measure of the stock's

Volativity relative to the market Beta measures a stock's volatility relative to the overall market. A beta above 1 indicates a more volatile stock, while a beta below 1 describes a stock less volatile than the market.

A company's working capital equals its

current assets minus its current liabilities

A bond's yield to maturity reflects its

internal rate of return

The price-to-earnings ratio

shows how much investors value the stock as a function of earnings to the company's market price

Investment risk may broadly be categorized as either unsystematic or systematic risk; both types of risk together constitute total, or absolute, risk. Total risk is measured by

standard deviation Unlike beta, which only measures systematic risk, standard deviation reflects both systematic and unsystematic risk, revealing the total risk of the investment.

In portfolio theory, the alpha of a security or a portfolio is

the difference in the expected return of the portfolio, given the portfolio's beta, and the actual return the portfolio achieved Alpha is the difference in the expected return of the portfolio, given the portfolio's beta and the actual return the portfolio achieved. The higher the alpha, the better the portfolio has done in achieving excess or abnormal returns. The risk of the portfolio associated with the macroeconomic factors that affect all risky assets is systematic risk. The portfolio's average return in excess of the risk-free rate divided by the standard deviation in returns of the portfolio is the Sharpe ratio or measure. The measure of the variance in returns of a portfolio around its average return is the standard deviation.

The future value of an invested dollar is dependent on

the rate of return it earns the time period over which it is invested

An investment adviser representative is looking for a suitable investment for a client. The IAR wishes to find something that will offer an attractive return commensurate with its systematic risk. The choices have been narrowed to Security C and Security L, and the selection will be based on alpha. C has a beta of 1.0 and earned 13%, while L has a beta of 0.8 and earned 10.1%. The alpha of Security L is

−0.3

Assume Frank has a portfolio with an actual return of 10.50% for the past year. The portfolio beta equals 1.25, the return on the market equals 9.75%, and the risk-free rate of return equals 3%. Based on this information, what is the alpha for Frank's portfolio and did it out outperform or underperform the market?

−0.9375%, underperform (total portfolio return - risk free rate) - (portfolio beta x [market return - risk free])