CFA Problems - Everyday

Using the DDM if the required rate of return is 10% and the stock's current market price is $50, the stock is overvalued, undervalued, or correctly valued? Year 1 Dividend (D1) = 4 Year 2 divided = 4.40 Stock price at the end of y2 = 50

4/(1.10) + 4.4/(1.1) ^2 = 7.27 Current price today is 50/(1.1) ^2 = 41.322 Intrinsic Value = 7.27 + 41.322 = 48.60 Vs market value of 50, stock is overvalued

the 2 year implied spot rate is closet to? Time Period:/Forward Rate 0y1y: 2.31% 1y1y: 2.82% 2y1y: 2.97%

A. 2.56 (2.31 + 2.82)/2 = 2.56

An analyst gathers the following information about the forward curve for one-year rates: Time Period Forward Rate 0y1y 1.20% 1y1y 1.88% 2y1y 2.46% 3y1y 2.93% The price of a three-year, 5% annual-pay bond is closest to: A.107.42. B.109.18. C.111.73.

Correct because the bond also can be valued using the forward curve. 5 / 1.012 + 5 / (1.012 × 1.0188) + 105 / (1.012 × 1.0188 × 1.0246) = 4.94 + 4.85 + 99.39 = 109.18 ≈ 109.2.

An analyst gathers the following information about a company's common stock: Dividend per share - Year 1 $2.00 Dividend per share - Year 2 $2.10 Annual dividend per share - Year 3 and beyond $2.21 If the required rate of return is 10%, the intrinsic value per share is closest to: A.$21.82. B.$22.10. C.$27.31.

**Correct** because it is the present value of all future dividends. The present value of the perpetual level dividends, three year from now, is: $2.21 / (0.10 - 0) = $22.10. The present value of the perpetual level dividends now is: $22.10 / (1.10)^3 = $16.604. The present of dividends in the first three years is: $2.00 / 1.10 + $2.10 / (1.10) ^ 2 + $2.21 / (1.10) ^ 3 = $1.818 + $1.736 + $1.660 = $5.214 . So, the intrinsic value of the stock is closest to: $16.604 + $5.214 = $21.818 ≈ $21.82

An analyst gathers the following information about a portfolio: Year 1, 2, 3 Returns: Equity: 7.20% 9.60% -14.20% Fixed Income: 2.10% -4.60% 4.70% If the equity weighting is 70%, the fixed-income weighting is 30% and the portfolio is rebalanced annually, the portfolio's annual geometric mean return is _closest_ to: 1. A.0.60%. 2. B.0.83%. 3. C.1.82%.

**Correct** because the first step is to calculate the portfolio's annual returns as a weighted mean of the equity and fixed-income returns with 70% equity and 30% fixed-income weighting. Year 1: (0.7 ´ 0.072) + (0.3 ´ 0.021) = 0.0567 = 5.67% Year 2: (0.7 ´ 0.096) + (0.3 ´ -0.046) = 0.0534 = 5.34% Year 3: (0.7 ´ -0.142) + (0.3 ´ 0.047) = -0.0853 = -8.53% Next, the portfolio's geometric mean annual return is calculated as: [(1 + 0.0567) ´ (1 + 0.0534) ´ (1 - 0.0853)]^(1/3) - 1 = [1.01818]^(1/3) - 1 = 0.00602 » 0.60%.

An investor purchases 1,000 shares of a non-dividend paying stock on margin and sells them after one year as follows: | | | |---|---| |Purchase price per share|$25| |Sale price per share|$20| |Annual call money rate|5%| |Leverage ratio|2| Ignoring commissions, the investor's holding period return is _closest_ to: 1. A.-45%. 2. B.-40%. 3. C.-23%.

**Correct** because this is the return on investment to the investor. Total purchase price = $25/share × 1,000 shares = $25,000 Leverage ratio of 2 indicates buyer's equity of 1/2 Buyer's equity = 1/2 × $25,000 = $12,500 Borrowed money = $25,000 - $12,500 = $12,500 Interest on borrowed money = 5% × $12,500 = $625 Sale proceeds = $20/share × 1,000 shares = $20,000 Net return to buyer = Sale proceeds - purchase price - interest payment = $20,000 - $25,000 - $625 = -$5,625 Return on investment to the buyer = -$5,625 / $12,500 = -45%

A bond has a modified duration of 5 and a convexity statistic of 75. If the bond's yield-to-maturity decreases 50 bps, the expected percentage price change is _closest_to: 1. A.2.41%. 2. B.2.59%. 3. C.2.69%.

**Correct** because: %△𝑃𝑉𝐹𝑢𝑙𝑙≈(𝐴𝑛𝑛𝑀𝑜𝑑𝐷𝑢𝑟×△𝑌𝑖𝑒𝑙𝑑)+[1/2×𝐴𝑛𝑛𝐶𝑜𝑛𝑣𝑒𝑥𝑖𝑡𝑦×(△𝑌𝑖𝑒𝑙𝑑)^2]=(−5×−0.005)−[12×75×(−0.005)^2] = 0.025 + 0.00094 = 0.02594 ~ 2.59%.

Calculate the value of a stock that paid a $1 dividend last year, if next year's dividend will be 5% higher and the stock will sell for $13.45 at year-end. The required return is 13.2%.

**Example: One-period DDM valuation** Calculate the value of a stock that paid a $1 dividend last year, if next year's dividend will be 5% higher and the stock will sell for $13.45 at year-end. The required return is 13.2%. **Answer:** The next dividend is the current dividend increased by the estimated growth rate. In this case, we have: D1 = D0 × (1 + dividend growth rate) = $1.00 × (1 + 0.05) = $1.05 The present value of the expected future cash flows is: dividend: $1.05/1.132=$0.93 year-end price: $13.45/1.132=$11.88 The current value based on the investor's expectations is: stock value = $0.93 + $11.88 = $12.81

Calc the bill's discount rate: FV: 1mm PV: 950k Number of days to maturity: 340 Number of days in the year: 360 1. A.4.72%. 2. B.5.29%. 3. C.5.57%.

. **Correct** because the DR = {year/days} × {(FV - PV)/FV} where: PV = present value, or the price of the money market instrument FV = future value paid at maturity, or the face value of the money market instrument Days = number of days between settlement and maturity; Year = number of days in the year; DR = discount rate, stated as an annual percentage rateDR = {360/340} × {(1,000,000 - 950,000)/1,000,000} DR = 1.05882 × 0.05 = 0.052941 ≈ 5.29%.

For a sample size of 10 and sum of squared differences in ranks of 118, the Spearman rank correlation is closest to: 1. A.0.28. 2. B.0.72. 3. C.0.93.

A. A. R = 1- [6(118)/10(10^2-1)]= 6x118 = 708/990 = 0.715 > 1-.71515 = 0.2848

Prob | Earnings The standard deviation of the company's earnings is closest to: A.$115 million. B.$134 million. C.$375 million.

A. Correct because the expected value is calculated as E(X) = P(X1)X1 + P(X2)X2 + ... + P(Xn)Xn = 0.25×100 + 0.70×300 + 0.05×600 = 25 + 210 + 30 = 265 and the variance is calculated as σ2(X) = E{[X − E(X)]2 } = 0.25×(100 - 265)2 + 0.70×(300 - 265)2 + 0.05×(600 - 265)2 = 6,806.25 + 857.50 + 5,611.25 = 13,275 and the standard deviation is the positive square root of variance, i.e. 13,2751/2 ≈ $115.22 ≈ $115 million.

An analyst gathers the following information about an equally weighted portfolio comprised of 500 assets: Average variance of the returns of the assets = 0.04 Average covariance between the returns of the assets = 0.01 The variance of the portfolio returns is closest to: A.0.01. B.0.04. C.0.05.

A. For portfolios with a large number of assets, covariance among the assets accounts for almost all of the portfolio's risk The variance of the portfolio = (0.04/500) + [(500 - 1)/500] × 0.01 = 0.00008 + 0.00998 = 0.01006 ≈ 0.01 (average covariance of returns)

An analyst gathers the following information about three securities: Total Variance of Returns Nonsystematic Variance of Returns Security 1 0.20 0.05 Security 2 0.30 0.25 Security 3 0.35 0.22 According to capital market theory, which security has the highest expected return? A.Security 1 B.Security 2 C.Security 3

A. Security 1 has systematic variance = 0.20 - 0.05 = 0.15; Security 2 has systematic variance = 0.30 - 0.25 = 0.05; Security 3 has systematic variance = 0.35 - 0.22 = 0.13.

An account has a stated annual interest rate of 3.6% with monthly compounding. The number of years it will take for an initial investment in the account to double is _closest_ to: 1. A.19.3. 2. B.19.6. 3. C.20.0

A. because with more than one compounding period per year, the future value formula can be expressed as FV lower N = PV[1 + (_rs/m)]^mN where rs is the stated annual interest rate, m is the number of compounding periods per year, and N_stands for the number of years. Moreover, we can identify rs = 0.036 and m= 12, and for the initial investment to double we must have FV lower N/PV = 2. Hence, the number of years, N, must satisfy 2 = [1 + (0.036/12)]12_N_, which can be solved as _N_ = ln(2)/[12 × ln(1.003)] = 19.2830 ≈ 19.3 years.

An analyst gathers the following information about three securities: Security 1: Total Variance: 0.20 Non systematic Variance of returns: 0.05 Security 2: Total Variance: 0.30 Non systematic Variance of Returns: 0.25 Security 3: Total Variance: 0.35 Nonsystematic Variance of Returns: 0.22 According to capital market theory, which security has the highest expected return? A.Security 1 B.Security 2 C.Security 3

A. A.Security 1Correct because according to the capital market theory investors should not be compensated for taking on nonsystematic risk. In contrast, investors must be compensated for accepting systematic risk because that risk cannot be diversified away. In summary, systematic or non-diversifiable risk is priced and investors are compensated for holding assets or portfolios based only on that investment's systematic

Based on the below, the covariance between the returns of the portfolio and the market is closet to? Portfolio Standard Deviation of Returns: 10%, Beta 0.5Market Standard Deviation of Returns: 20%, Beta 1.0 A.0.005. B.0.010. C.0.020.

A. Correct because the portfolio's beta is calculated as βp = Cov(Rp,Rm)/σ^2m, where Cov(Rp,Rm) is the covariance between the returns of portfolio p and the market index m, and σm2 is the market's variance of returns. Therefore, Cov(Rp,Rm) = βp × σm2 = 0.5 × 0.22 = 0.020.

Give examples of the below: A.timing option. B.flexibility option. C.fundamental option. D. Sizing option

A. Timing option = ex. project sequencing B. Flexibility option = ex. Price setting C. Fundamental Option = ex. the entire project is in itself an option D. Sizing option = ex. Option to abandon a cap investment at a future date

An analyst calculates a portfolio's target semideviation of returns over twelve consecutive months, including seven months of below-target returns. The sum of the squared deviations below the target is 42%2. The target semideviation is _closest_ to: 1. A.1.87%. 2. B.1.95%. 3. C.2.65%.

B. 1.95 —> 42/12-1 = 42/11 and then square root it = 1.95

When estimating a target capital structure, the equity weight associated with a debt-to-equity ratio of 0.6 is closest to: A.37.5% B.40.0%. C.62.5%.

Answer C. D/E / (1+D/E) = .6/1+.6 = 37.50%

A company has a fixed $1,100 capital budget and has the opportunity to invest in the four independent projects listed in the table: |**Project**|**Investment Outlay**|**NPV**| |---|---|---| |1|$600|$100| |2|$500|$100| |3|$300|$50| |4|$200|$50| The combination of projects that provides the _best_ choice is: 1. A.1 and 2. 2. B.1, 3, and 4. 3. C.2, 3, and 4

Answer C. Key is to figure out which investment provides the higher NPV for the lowest capital invested

Two mutually exclusive projects have the following cash flows (€) and internal rates of return (IRR): | ** <br>IRR** | **Year 0** | **Year 1** | **Year 2** | **Year 3** | **Year 4** | | | ------------- | ---------- | ---------- | ---------- | ---------- | ---------- | ----- | | Project 1 | 27.97% | -2,450 | 345 | 849 | 635 | 3,645 | | Project 2 | 28.37% | -2,450 | 345 | 849 | 1,051 | 3,175 | Assuming a discount rate of 8% annually for both projects, the _best_ decision for the firm to make is to accept: 1. A.Project 1 only 2. B.Project 2 only 3. C.Both Project 1 and Project 2

Answer. A A. Key is to figure out which one has the higher NPV since both projects IRR's are above the discount rate

An analyst collects the following information: Current stock price: €26 Gross return from an up move: 1.10 Gross return from a down move 0.75 Call and put exercise price: €22 Based on a one-period binomial pricing model, which of the following has the largest payoff? 1. A.Put option following an up move 2. B.Put option following a down move 3. C.Call option following a down move

B Put option up move pay off = 26(1.10) = 28.60 > 22-28.60 = 0 pay off Put option down move pay off = 26(.75) = 19.50 > (22-19.50) = 2.50 Call option down move = 26(.75) = 19.50 > (19.50-22) = 0

An analyst gathers the following information about a bond: Clean (per 100 of par value): 114.75 Annual modified duration: 4.8250 Macaulay duration (years): 4.9469 Accrued interest (per 100 of par value): 1.6250 The bond's money duration (per 100 of par value) is _closest_ to: 1. A.553.67. 2. B.561.51. 3.) 575.70

B. *Correct** because the money duration equals the product of modified duration and full price. Full price = Clean price + Accrued interest = 114.75 + 1.625 = 116.375; Money duration = Modified duration × Full Price = 116.375 × 4.8250 = 561.5094 ≈ 561.51.

An analyst gathers the following information about a fund's returns: If the target return is 4%, the target downside deviation is closet to: Year 1: 2% Year 2: 5% Year 3: 3% Year 4: 6% Year 5: 2% A. 1.34% B. 1.50% C. 1.87%

B. 1.50% Subtract each number by 4 and cross out any positive numbers. Will leave you with -2, -1, and -2. Square each one and sum = 9 > (9/5-1) ^.5 = 1.50%

An analyst gathers the following information about an underlying: Current price of underlying asset $16.0 End of period upward price $22.0 End of period downward price $12.0 Risk-free rate 4.0% Using a one-period binomial model, the risk-neutral probability of a price increase is _closest_ to: 1. A.0.38 2. B.0.46 3. C.0.54

B. 1 + r - Rd / Ru - Rd Rd = 22/16 = 1.375 Ru = 12/16= 0.75 1 + 0.04 - 0.75) / (1.375 - 0.75) = 0.29/0.625 = 0.464 ≈ 0.46. **note if you wanted to find the risk neutral prob of a decrease in the underlying price you would need to subtract 1-0.46 = 0.54

A bond is selling for 98.2. It is estimated that the price will fall to 96.6 if yields rise 30 bps and that the price will rise to 100.1 if yields fall 30 bps. Based on these estimates, the effective duration of the bond is _closest to_: 1. A.1.78. 2. B.5.94. 3. C.11.88

B. EffDur = (𝑃𝑉−)−(𝑃𝑉+)2×(𝛥Curve)×(𝑃𝑉0) where _PV_-, _PV_0, and _PV_+ are the values of the bond when the yield falls, under the current yield, and when the yield rises, respectively, and ∆Curve is the change in the benchmark yield curve. EffDur = 100.1−96.62×98.2×0.003=5.94

Calc discount margin for this FRN Time to maturity = 3 years Current price = 98 Reference rate = 1.5% Quote margin = 0.5% Payment basis = qty

B. Using a financial calculator: N = 12, PV = 98, PMT = 0.5, FV = 100 ⇒ r = 0.0067406. We can now solve for DM: 0.0067406 = (0.015 + DM)/4 ⇒ DM = 0.01196 ≈ 1.20%.

Company Val ($billions) = 1.5 Value of debt ($ billions) 0.6 Marginal tax rate = 30% Based on Modigliani and Miller's Proposition I with taxes, if the company issues common stock to repay outstanding debt, the value of the unlevered company will be closest to:

B. Correct because the value of the levered company is greater than that of the all-equity company by an amount equal to the tax rate multiplied by the value of the debt, also termed the debt tax shield. VL = VU + tD, where VL = the value of the levered company, VU = the value of the unlevered company, t is the marginal tax rate and tD is the debt tax shield. Therefore, $1.5 billion = VU + 0.30 × $0.6 billion and VU = $1.32 billion ≈ $1.3 billion.

An analyst gathers the following information about two similarly rated 8% semiannual coupon payment bonds: Bond 1 Bond 2 Price 114.243 112.691 Years to maturity 3 5 Yield to maturity 3% 5% Using matrix pricing, the price per 100 of par value of a 4-year semiannual coupon payment bond with similar credit quality and a 7.6% annual coupon is closest to: A.113.07. B.113.19. C.113.47.

B. Correct because the price is calculated on the basis of an interpolated yield-to-maturity: (3% + 5%)/2 = 4%, or 2% per semi-annual period. Price of 4-year bond: PMT=3.8%; n=8; i = 2%; FV=100; calculate PV = 113.19.

A stock has a correlation of 0.45 with the market and a standard deviation of returns of 12.35%. If the market has a standard deviation of returns of 8.25%, then the beta of the stock is closest to: A.0.30. B.0.67. C.1.50.

B. One of beta's formulas is beta = corr of returns x (SD of asset/SD of market)

A company holds licenses with a net book value of 12,118 (in USD thousands) as of 31 December Year 1. The company reported the following data related to impairment losses and amortization on these licenses (in USD thousands): Accumulated impairment losses and amortization as of 31 December Year 1: 2,142 Exchange Movements: 212 Amortization charge for the year: 752 Impairment losses: 52 Disposals: —- Transfers to investments in associated undertakings: (7) The cost of licenses as of 31 December Year 2 was 16,435 (in USD thousands). Based on the data provided, the carrying value of licenses (in USD thousands) as of 31 December Year 2 is closest to: A.8,967. B.13,284. C.13,496.

B.13,284 Correct because to calculate the carrying value of licenses, first calculate the total amount of accumulated impairment losses and amortization based on the data provided as follows: (Accumulated impairment losses and amortization as of 31 December Year 1 + Exchange movements + Amortization charge for the year + Impairment losses + Disposals + Transfers to investments in associated undertakings) or (2,142 + 212 + 752 + 52 - 7) = 3,151. That amount is used to calculate the carrying value as of 31 December Year 2 as follows: (Cost of licenses as of 31 December Year 2 - Accumulated impairment losses and amortization) = (16,435 - 3,151) = 13,284 = carrying value as of December 31 Year 2.

An analyst gathers the following information: Standard Deviation of Returns Beta Portfolio 10% 0.5 Market 20% 1.0 The covariance between the returns of the portfolio and the market is closest to: A.0.005. B.0.010. C.0.020.

C. Beta = Cov(Pp, Rm)/variance of the market

The price of a fixed-rate corporate bond with an annual modified duration of 7.15 increases from 92 to 97 per 100 of par value. If the government benchmark yield increases by 5 bps, the estimated decline in the spread over the benchmark yield is closest to: A.71 bps. B.76 bps. C.81 bps.

C. Correct because given that the price increases to 97 from 92, the percentage price increase is (97 - 92)/(92) ≈ 0.05435. Using %ΔPVFull ≈ -AnnModDur × ΔYield, the change in the yield-to-maturity can be calculated as 0.05435 = -7.15 × ΔYield ⇒ ΔYield = -0.05435/7.15 ≈ -0.00760

An investment pays $1,000 at the end of each year in perpetuity, with the first payment occurring six years from today. If the discount rate is 9% per year, the present value of the investment today is _closest_ to: 1. A.$4,486. 2. B.$6,625. 3. C.$7,221.

C. PV of investment today = (PV of perpetuity in 5 years)/(1 + _r_)5, where PV of perpetuity in 5 years = _A_/_r_ = $1,000/0.09 = $11,111.11. Thus, PV of investment today = $11,111.11/(1 + 0.09)5 = $7,221.46 ≈ $7,221. Calculator solution: N = 5; I = 9%; FV = -11,111.11; compute PV = 7,221.46.

If the 1-year spot rate is 3% and the 2-year spot rate is 4.5%, the 1y1y implied forward rate is closest to: A.1.46%. B.3.75%. C.6.02%.

C. 2x 4.5 = 9-3 = 6

- What is CCC calc? - Explain Pull/Drag on CCC and give examples - What flags should you note for DOH/DSO/DPO directions - What are the formulas for DOH/Inventory turnover, DSO/Receivables turnover, and DPO/Payables turnover - What is LIFO/FIFO impact on DOH/Inventory turnover

CCC = DOH + DSO - DPO - drag = DOH + DSO up things not getting converted into cash fast enough ie. Obsolete inventory, increased diff collecting receivables - pull = cash paid to fast ie. Reduction in line of credit/early payment to suppliers Flags: DOH + DSO going up = BAD for CCC and DPO going down is BAD for CCC DOH = 365/inventory turnover Inventory Turnover = Cost of sales/average inventory DSO = 365/receiveables turnover Receivables turnover = Rev/average Receivables DPO = 365/payables turnover Payables turnover = Purchases or COGs/Average Accounts Payable Purchases = Cost of goods sold + Ending inventory - Beginning inventory Rising Prices? FIFO > Lower inventory turn over higher DOH LIFO > Higher inventory turn over lower DOH Declining Prices? Opposite

Commercial paper with a face value of $25,000,000 and a term of 120 days was issued 55 days ago. If the current market value is $24,855,000, the implied discount rate assuming a 360-day year is closest to: A.3.21%. B.3.23%. C.3.80%.

Correct because Discount rate (DR) = (Year/Days) x ((FV − PV)/FV) DR = (360/65) x ((25,000,000 − 24,855,000)/25,000,000) = 0.032123≈ 3.21%.

A stock recently paid a dividend of $1.50 which is expected to grow at 8% per year. The required rate of return of 12%. Calculate the value of this stock assuming that it will be priced at $51.00 three years from now.

D1 = $1.50(1.08) = $1.62 D2 = $1.50(1.08)2 = $1.75 D3 = $1.50(1.08)3 = $1.89 PV of dividends = $1.62 / 1.12 + $1.75 / (1.12)2 + $1.89 / (1.12)3 = $4.19 Find the PV of the future price: $51.00 / (1.12)3 = $36.30 Add the present values. The current value based on the investor's expectations is $4.19 + $36.30 = $40.49.

Net income: 200k Tax Rate: 15% Weighted average number of common shares outstanding: 125k 12% bond convertible into 3k common shares (potentially dilutive) 60k Given this information, the diluted EPS of the company is closest to: A.$1.51. B.$1.60. C.$1.61.

First find basic = ( net income/preferred dividends)/weighted average number of shares outstanding = 200k - 0 / 125k = 1.60 Diluted EPS = net income + after interest on convertible debt - preferred dividends / weighted average number of shares outstanding + additional common shares that would have been issued at conversion 200k + (60k x . 12(1-.015) - 0 ) / 125k + 3k = 1.61 which is higher than basic so must report basic of 1.60

Two years from now a client will receive the first of three annual payments of $20k. From a small business project. If she can earn 9% annually on her investments and plans to retire in 6 years, how much will the three business project payments be worth at the time of her retirement?

Step 1: n = 3 I/Y = 9 PMT = 20k PV CPT -> 50,625 Step 2: N =1 I/Y = A PMT = 0 FV = 50,625 CPT PV = 46,445 Step 3: n = 6 I/Y = 9 PMT = 0 PV = -46,445 CPT FV = 77,893

The price value of a basis point (PVBP) for a bond with a full price of 103.50 and a modified duration of 6.2 is _closest_ to: 1. A.0.0642. 2. B.0.6420. 3. C.6.4200

The PVBP is an estimate of the change in the full price given a 1 bp change in the yield-to-maturity. Here: 6.2 × 0.0001 = 0.00062 and PVBP = 0.00062 × 103.50 = 0.06417, rounded to 0.0642.

A fund initially has $50 million under management and earns 17% in Year 1. The fund receives additional investments of $125 million at the beginning of Year 2 and earns 12% in Year 2. The annualized money-weighted rate of return over the 2-year period is closest to: A.13.2%. B.14.5%. C.15.5%. A. 13.2% The value of the fund at the end of Year 2 is 50(1.17)(1.12) + 125(1.12) = 205.52. To find the IRR -- the money-weighted return -- using a calculator: CF0 = -50; CF1 = -125; CF2 = +205.52; compute IRR = 13.1785% ≈ 13.2%.

The value of the fund at the end of Year 2 is 50(1.17)(1.12) + 125(1.12) = 205.52. To find the IRR -- the money-weighted return -- using a calculator: CF0 = -50; CF1 = -125; CF2 = +205.52; compute IRR = 13.1785% ≈ 13.2%.