CFA Institute CFA Institute Certifications CFA-LEVEL-1 Questions & Answers

• Question 501:

  Assuming that the nominal risk-free rate of interest is currently at 4.90% per year, with the real inflationfree rate of return at 2.05% per year, what is the inflation premium? Further, assuming that the inflation premium is to fall by 130 basis points, what would be the adjusted nominal risk-free rate of interest?

  Assume that both the new inflation rate and the inflation-free rate of interest are considered small by historical standards.

  A. 2.85% per year, increase by 70 basis points

  B. 2.05% per year, increase by 130 basis points

  C. The answer cannot be calculated from the information provided.

  D. 2.85% per year, increase by 130 basis points

  E. None of these answers is correct.

  F. 2.05% per year, decrease by 130 basis points

  Correct Answer: E

  Remember that the nominal risk-free rate of interest is comprised of two components, the real "inflationfree" rate of interest and an inflation premium. The inflation premium is equal to the anticipated inflation rate.

  The equation for the calculation of the nominal interest rate when the real inflation-free rate of interest and/ or the inflation premium are significantly small is as follows:

  Risk-free rate of return = k* + IP

  where: k* = the real inflation-free rate of return and IP = the inflation premium

  In this example, the nominal risk-free interest rate is provided as 4.90%, and the inflation-free rate of return as 2.05%. Incorporating these values into the equation illustrated above will yield a value of 2.85% for the inflation premium.

  Increasing the inflation premium by 130 basis points will lead to a 130 basis point increase in the nominal risk-free interest rate. None of the answers correctly illustrate these findings.

  When either the real "inflation-free" interest rate or the expected inflation rate are significantly large, the calculation of the nominal risk-free rate differs from the equation used when these factors are significantly small. Specifically, the calculation of the nominal risk-free rate of interest when the inflation-free rate of interest and/or the inflation premium are significantly high, the calculation of the nominal risk-free rate is as follows:

  Nominal RFR = (1 + Real RFR)(1 + E(I)) - 1

  Where: Real RFR = the real inflation-free rate of interest and E(I) = the anticipated inflation rate

• Question 502:

  Consider the following transactional information for the investment account of a retail investor:

  1st Quarter Ending portfolio value: $65,000 Total amount invested: $59,000

  2nd Quarter Ending portfolio value: $63,500 Total amount invested: $65,000

  3rd Quarter Ending portfolio value: $60,900 Total amount invested: $63,500

  4th Quarter Ending portfolio value: $57,200 Total amount invested: $60,900

  Using this information, what is the annual time-weighted rate of return for this portfolio? Assume no taxes or transaction charges.

  A. (4.56%) per year

  B. (3.05%) per year

  C. 2.59% per year

  D. The calculation of the time-weighted rate of return cannot be calculated from the information provided

  E. (3.27%) per year

  F. None of these answers

  Correct Answer: B

  The time-weighted rate of return is the preferred method of return calculation in the investment

  management industry, primarily because this method is not sensitive to significant additions and

  withdrawals of funds from portfolios under examination. The calculation of the time-weighted rate of return

  involves three steps, which are illustrated as follows:

  Step 1:

  Price the portfolio immediately prior to any significant additions or withdrawals. Separate the portfolio into a

  series of subperiods based on the dates of cash inflows and outflows.

  Step 2:

  Calculate the holding period return for each subperiod.

  Step 3:

  Determine the annualized holding period return by linking or compounding the holding period return of

  each subperiod. If the investment is for more than one year, use the geometric mean of the annual returns

  as the time-weighted rate of return. If the investment is for less than one year, compound the subperiod

  returns to obtain an annualized measurement.

  To begin the process of determining the time-weighted rate of return, we would break the portfolio up into

  the following series of cash flows. However, in this example, the cash flows are already aggregated for us

  and we can move on to the next step: determining the holding period return for each subperiod. This

  process is detailed as follows:

  Quarter 1 holding period return = [($65,000 ending value - $59,000 invested) / $59,000 invested] =

  10.169%

  Quarter 2 holding period return = [($63,500 ending value - $65,000 invested) / $65,000 invested] =

  (2.308%)

  Quarter 3 holding period return = [($60,900 ending value - $63,500 invested) / $63,500 invested] = (4.094

  %)

  Quarter 4 holding period return = [($57,200 ending value - $60,900 invested) / $60,900 invested] =

  (6.076%)

  Now that the holding period return for each subperiod has been determined, we must annualize the return measure by taking the product of all four quarterly returns. This process is illustrated below:

  [(1 + .10169) * (1 - .02308) * (1 - .04094) * (1 - .06076) - 1] = (.0305) or (3.05%)

  When calculating the time-weighted rate of return, remember that the total amount invested is the relevant figure, not the beginning portfolio value. So said, whenever possible you should use the total amount invested rather than the beginning portfolio value in the calculation of the subperiod holding period return.

• Question 503:

  Consider the following annual growth forecasts for a common stock:

  Growth in years 1-2 = 25%

  Growth in years 3-4 = 15%

  Growth after year 4 = 10%

  Assuming that the last dividend was $1.30 per share, and that the required rate of return is 14% per year,

  what is the value of this common stock?

  A. $34.54

  B. $28.28

  C. $46.90

  D. The answer cannot be determined from the information provided.

  E. $49.90

  F. None of these answers is correct.

  Correct Answer: E

  To determine the value of a common stock experiencing temporary supernormal growth, use the following equation:

  {V = {[d0 * (1 + gs)^1] / k} + {[d1 * (1 + gs)^2} + ... {dn * (1 + gs)^n} + {[dn * (1 + gs)^n * (1 + gn] / (k - g)}/ (1

  + k)^n}}

  Where: V = the value of common stock at t0, d0 = the dividend at t0, d1 = the dividend at t1, dn = the dividend at tn, gs = the supernormal rate of growth, gn = the normal rate of growth, n = the time period "n", and k = the required rate of return.

  In this example, there is a transitional growth period of two years, during which the growth rate of this stock is expected to grow at 15% annually. This period will follow the two-year supernormal growth period, and would be denoted as "g subset t" if we were to reproduce the equation illustrated above. The calculation of the value of this common stock is illustrated as follows:

  {V = {[$1.30 * (1.25)^1] / (1.14)} + {[$1.30 * (1.25)^2] / (1.14)^2} + {[$1.30. * (1.25)^2 * (1.15)^1] / (1.14)^3}

  + {[$1.30 * (1.25)^2 * (1.15)^2] / (1.14)^4} + {{[$1.30 * (1.25)^2 * (1.15)^2 * (1.10)^1]/ (0.14 - 0.10)}/ (1.14) ^4}

  Which can be deduced to the following:

  {V = [$1.425439 + $1.562981 + $1.576691 + $1.590522 + $43.739352] = $49.89}

• Question 504:

  A preferred stock has a $100 par value and a dividend payout of $5 every 6 months. Your required rate of return is 10%. What is the value of the preferred stock?

  A. $50

  B. none of these answers

  C. $99

  D. $75

  Correct Answer: B

  The value of a preferred stock is the stated annual dividend divided by the required rate of return on preferred stock.

  In this case, V = $10 a year/.10 = $100

• Question 505:

  Earnings multipliers for series of stocks (such as the SandP 400) have been found to be

  A. more volatile than the earnings for series of stocks.

  B. less volatile than earnings for series of stocks.

  C. stable.

  D. approximately as volatile as earnings for series of stocks.

  Correct Answer: A

  The standard deviation of annual changes of the earnings multiplier for the SandP 400 is 28.2, while that for the annual earnings for the SandP 400 is 18.3. To value stock series, one needs to estimate both the earnings multiplier and the earnings. Although some analysts have tended to ignore the earnings multiplier on the assumption that it is stable over time, its high measured variability makes it hard to ignore.

• Question 506:

  Holding other things constant, a decrease in a firm's retention rate of earnings will

  A. increase the ROE.

  B. decrease the ROE.

  C. increase the firm's expected growth rate.

  D. decrease the earnings multiplier.

  Correct Answer: D

  A decrease in a firm's retention rate will decrease its expected growth rate of earnings and dividends. This, in turn, will decrease the earnings multiplier. Changes in a firm's retention rate should not affect its return on equity (ROE).

• Question 507:

  A preferred stock has a $100 par value and a dividend payout of $8 per year. Your required return is 9. What is the value of the preferred stock?

  A. not enough information to calculate it

  B. $88.89

  C. $92.24

  D. $85.67

  Correct Answer: B

  The value of a preferred stock is the stated annual dividend divided by the required rate of return on preferred stock.

  In this case, V = $8/.09 = $88.89

• Question 508:

  An analyst is attempting to value shares Kingdom Semiconductor, a large silicon distributor. Assume the following information for Kingdom shares:

  Required rate of return on equity: 16.25% per year Free cash flow to equity multiple at t4: 32 2,500,000 shares outstanding

  Additionally, the analyst has obtained the following estimates of free cash flow to equity for Kingdom over the next four years:

  Year 1: $2,000,000 Year 2: $3,500,000 Year 3: $4,500,000 Year 4: $5,000,000

  Using this information, what is the value per share of Kingdom Semiconductor according to the Free Cash Flow to Equity Model?

  A. $44.74

  B. $46.29

  C. None of these answers is correct.

  D. $35.69

  E. The answer cannot be calculated from the information provided.

  F. $39.02

  Correct Answer: F

  When determining the value of a common stock using the free cash flow to equity model, it is necessary to determine three things:

  1.

  The required rate of return on equity investments.

  2.

  The estimated free cash flow to equity multiple at time "k."

  3.

  The estimated free cash flows figures for the time periods leading up to "k."

  In this example, the calculation must begin with the discounting the free cash flow to equity figures for each of the four years provided. These figures are discounted each period by the required return on equity investments, and the final answer is converted to a per-share basis. This process is illustrated below:

  Year 1: ($2,000,000 / 1.1625) / 2,500,000 shares outstanding = $0.69 Year 2: [$3,500,000 / (1.1625)(1.1625)] / 2,500,000 shares outstanding = $1.04 Year 3: [$4,500,000 / (1.1625)(1.1625)(1.1625)] / 2,500,000 shares outstanding = $1.15 Year 4: [$5,000,000 / (1.1625)(1.1625)(1.1625)(1.1625)] / 2,500,000 shares outstanding = $1.10

  Now that the free cash-flow-to-equity figures have been discounted and converted to a per-share basis, the next step in the valuation process is to determine the value of the final cash flow, which is defined as:

  [(Free cash flow to equity multiple * Final free cash flow) / (1 + r)(1+r)...(1 + k)]

  In the body of this question, we were given the anticipated multiple of free cash to equity that shares of

  Intelligent Semiconductor will sell for at time period: specifically 32 times. Imputing this information into the

  terminal cash flow equation will yield the following:

  {[32 * ($5,000,000 / 2,500,000 shares outstanding)] / [(1.1625) (1.1625)(1.1625)(1.1625)]} = $35.04.

  Adding the answers from step 1 to the final year cash flow will yield the following:

  Value of Intelligent Semiconductor = [$0.69 + $1.04 + $1.15 + $1.10 + $35.04] = $39.02 per share.

• Question 509:

  Mutual fund A is a 7% load-fund, which you expect to have a rate of return of about 17%. Mutual fund B is a no-load fund, which is expected to have a rate of return of around 9%. If your investment horizon is 1 year, which fund should you invest in and what is your expected net rate of return?

  A. A; 8.8%

  B. A; 9.35%

  C. B; 9.0%

  D. none of these answers

  Correct Answer: C

  With fund A, a deposit of $100 will give you shares worth $93 after the load charge is taken into account. This amount is expected to grow to 93*(1+0.17) = $108.81. Thus, the net return with fund A is expected to be 8.8%. Hence, for a 1-year horizon, you should select fund B, which is expected to return 9%.

• Question 510:

  Which is a measure of profitability?

  A. Debt to Equity Ratio

  B. Price/Earnings Ratio

  C. Return on Assets

  D. Dividend Yield

  E. Payout Ratio

  Correct Answer: C

  Return on Assets = Net Income/Total Assets; With other things equal, firms with relatively large amounts of assets on their books (such as those in capital-intensive industries) will have low ROA figures.

  By contrast, service oriented firms having small amounts of capital on their books will have higher ROA figures.