CFA® Level 2 Progress Test – Solutions
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TUTOR TIP: Please take your time de-briefing these questions. If you cannot understand the logic behind a question then consult your study notes and if still unsure then please log a help-desk query. Please make sure you know why every question is correct and why the wrong choices are wrong. Watch out for time-traps! Equity questions can often seem very long to do however in many cases there are short-cuts. Remember if you have a constant growth in sales and nothing else is changing then you will get a constant growth in FCF. Thus it may look like a long question but often it just involves calculating the first year FCF and then just growing this value! Finally please make sure you understand ALL aspects of each question. Sometimes you can get a question correct by just calculating one part of the question, however please ensure you can derive the other elements of the question.
ANSWER TO QUESTION 1 1.1
C
The annual equal instalments are: Rick’s Housing Finance Company = $ 771.04 [N = 360, PV = 100,000, FV = 0, I/Y = 8.53%/12] 7city Tutor Tip: Make sure that you can do the above computation on your calculator! Also ‘Level paying’ is another term for a flat rate of interest as opposed to an annual compounded rate 1.2
A
Lake View Housing Finance Company = $ 771.82 [N = 300, PV = 100,000, FV = 0, I/Y = 8%/12] Mortgage rate Payment Number 1
8.00% =0.667%pm Initial Principal 100,000.00
Monthly Payment 771.82
Interest Component 666.67
Reduction of Principal 105.15
Outstanding Principal 99,894.85
Interest is 0.00667 x 100,000 and the principal component is the difference between the mortgage payment and the interest component.
1.3
B (see table below)
The table is shown for completeness. For this question we can jump straight to month 25, (last row) since we are given the pool factor. Opening Interest Payment Scheduled Bala Prepayment Closing balance CPR 100000.00 666.67 -771.82 99894.85 66.84 99828.01 0.008 99828.01 665.52 -771.30 99722.23 133.95 99588.28 0.016 99588.28 663.92 -770.26 99481.94 201.19 99280.75 0.024 99280.75 661.87 -768.71 99173.92 268.42 98905.49 0.032 98905.49 659.37 -766.63 98798.24 335.52 98462.71 0.04 98462.71 656.42 -764.02 98355.11 402.35 97952.76 0.048 97952.76 653.02 -760.90 97844.88 468.77 97376.12 0.056 97376.12 649.17 -757.25 97268.04 534.63 96733.41 0.064 96733.41 644.89 -753.09 96625.21 599.81 96025.39 0.072 96025.39 640.17 -748.41 95917.15 664.17 95252.98 0.08 95252.98 635.02 -743.23 95144.77 727.56 94417.21 0.088 94417.21 629.45 -737.55 94309.11 789.86 93519.25 0.096 93519.25 623.46 -731.37 93411.34 850.93 92560.41 0.104 92560.41 617.07 -724.71 92452.77 910.64 91542.13 0.112 91542.13 610.28 -717.57 91434.84 968.87 90465.97 0.12 90465.97 603.11 -709.97 90359.11 1025.48 89333.63 0.128 89333.63 595.56 -701.91 89227.28 1080.36 88146.92 0.136 88146.92 587.65 -693.41 88041.16 1133.40 86907.76 0.144 86907.76 579.39 -684.48 86802.66 1184.47 85618.19 0.152 85618.19 570.79 -675.14 85513.83 1233.49 84280.34 0.16 84280.34 561.87 -665.41 84176.81 1280.33 82896.47 0.168 82896.47 552.64 -655.28 82793.83 1324.92 81468.91 0.176 81468.91 543.13 -644.80 81367.24 1367.16 80000.08 0.184 80000.08 533.33 -633.96 79899.45 1406.97 78492.48 0.192 78492.48 523.28 -622.80 78392.97 1444.27 76948.70 0.2
SMM N 0.0006691 300 0.0013432 299 0.0020223 298 0.0027066 297 0.0033961 296 0.0040908 295 0.0047909 294 0.0054965 293 0.0062076 292 0.0069244 291 0.0076469 290 0.0083752 289 0.0091095 288 0.0098498 287 0.0105962 286 0.0113489 285 0.012108 284 0.0128735 283 0.0136456 282 0.0144244 281 0.01521 280 0.0160026 279 0.0168023 278 0.0176092 277 0.0184235 276
The pool factor is the opening balance for month 25 divided by the original balance (100,000) hence we know the opening balance must be 78,492.48. Interest is 0.08/12 x 78,492.48 PMT is 276N 78,492.48PV, 8/12 I/Y CPT PMT Scheduled balance = Opening + Interest – PMT CPR is 0.2 x 25 x 4 = 20% SMM = 1 – (1-CPR) 1/12 SMM = 1- (1-0.2) 1/12 = 0.018423 Prepayment = SMM x Scheduled Balance Please make sure you can derive all of these values. Even though in this question you actually only needed to calculate the PMT amount, the next question could be different! 1.4
B
Contraction risk is the risk that a bond’s average life will fall due to a rise in prepayments. Extension risk is the risk that cash flows will be lower than expected due to lower prepayment speed and thus the average life increases. A PAC bond provides some protection against both of these risks so long as the prepayment speed is within the PAC collar.
1.5
1.6
C Mortgages are loans that are collateralized by real estate property The lenders or mortgage owners pool together the mortgages to form a pool. The pool is then ‘sold’ to investors through issue of shares or participating certificates, which are the mortgage pass through certificates A mortgage pass through therefore represents a claim against a pool of mortgages So the collateral in case of mortgages is a real estate asset, while with mortgage pass through certificates the collateral is the pool of mortgages B
7city Tutor Tip: The conditional prepayment rate (CPR) is one convention used for describing the pattern of prepayments every month. Remember with PSA the CPR stops increasing once we hit month 30 hence 0.2%x30 =6% SMM = 1 – (1-CPR) 1/12 SMM = 1- (1-0.06) 1/12 = 0.005143 Prepayment = SMM x (mortgage balance – scheduled payment) Prepayment = 0.005143 x (300,000,000 – 5,000,000) = 1,517,189
ANSWER TO QUESTION 2 2.1
B ROE (Three stage analysis) NET INCOME SALES ASSETS EQUITY NET NET PROFIT INCOME/SALES MARGIN ASSET SALES/ASSETS TURNOVER EQUITY ASSETS/EQUITY MULTIPLIER
2.2
3,969 20,092 22,417 11,366 19.75% 0.896 1.972
C
ROE = 3969/11366 = 34.9% Alternatively we could use Dupont: ROE = Profit margin x Asset turnover x Financial Leverage = 19.75 x 0.896 x 1.972 = 34.9% 2.3
A (see below)
2.4
C 800 is closest to 794
Free Cash Flow Model Actual X002 19.16% 3,969.00 803.00
Growth Rate Net Income Net Income (I/S) Add: Depreciation (C/F) Less: Capital Expenditure (C/F) -1,188.00 Add/Less: Working Capital (C/F) -662.00 Add: Net Borrowings -926.00 (C/F) FCF Equity 1,996.00 No of Shares 2,487.00 FCF Equity / No. of Shares 0.80 Required Rate of Return (10.50%) Discounted FCF Equity
Forecast Forecast Forecast Forecast X003 X004 X005 X006 20.00% 20.00% 20.00% 8.00% 4,762.80 5,715.36 6,858.43 7,407.11 900.00 900.00 900.00 900.00 -1,000.00 -1,000.00 -1,000.00 -1,000.00 -794.40
-953.28 -1,143.94 -1,235.45
-1,111.20 -1,333.44 -1,600.13 -1,728.14 2,757.20 3,328.64 4,014.37 4,343.52 2,487.00 2,487.00 2,487.00 2,487.00 1.11 0.9050 1.00
1.34 0.8190 1.10
1.61 0.7412 1.20
1.74 0.6707
7city Tutor’s Tip: working capital changes in line with the growth in net income. For the questions asked you do not actually need to fill in all of the table, it is shown here for completeness.
2.5
C
Stage 1 PV for 20X3 -20X5
3.30
Stage 2 FCF Equity /No. of Shares Required Rate of Return (r) Sustainable Growth Rate (g) r-g Terminal Value 20X6 Discount Rate Terminal Value as of Today
1.74 0.105 0.08 0.025 69.60 0.74 51.58
Value / Share (Stage 1+2)
54.88
Tutor’s Tip: The answers shown above have been rounded at each stage to aid the presentation of the solution and as such your answers may be slightly different. The difference should not be significant. 2.6
A
FCFE is best if The company has an unstable dividend policy FCFE can be forecasted for a reasonable period and is positive If the capital structure has fluctuated over time then FCFF is more appropriate. Free Cash flow models are generally more appropriate for valuing majority holdings whereas dividend models are more appropriate for minority valuations.
ANSWER TO QUESTION 3 Question 1 and 2 see solution below 3.1
A
TUTOR TIP: the short-cut here is to calculate FCFE for year 1 and then grow it by the rate of sales growth, thus year 3 FCFE = 0.34 x1.3x1.3. This is because all relationships are driven by sales and hence the change is sales will drive FCF. 3.2
B
€m
Yr1
Yr2
Yr3
Yr4
Yr5
SALES (30% growth pa) NET INCOME (35% of sales) CAPEX (40% of sales) DEPRECIATION (10% of sales) WORKING CAPITAL INVESTMENT(6% of sales) NEW DEBT 20% D/TA
5.50 1.93 2.20 0.55 0.33
7.15 2.50 2.86 0.72 0.43
9.30 3.25 3.72 0.93 0.56
12.08 4.23 4.83 1.21 0.73
15.71 5.50 6.28 1.57 0.94
0.40
0.51
0.67
0.87
1.13
FCFE= NI +Dep-WC-Capex +new debt
0.34
0.44
0.58
0.75
0.97
FCFE = NI - (1-0.2)(Capex - Dep + WC inv)
0.34
0.44
0.58
0.75
0.97
PV OF FCFE (at 15%)
0.30
0.34
0.38
0.43
0.48
TERMINAL VALUE (20 X E5) PV OF TERMINAL VALUE
109.96 54.67
VALUE OF FIRM
56.59
SHARE PRICE
2.83
Remember the new debt will be D/TA % x Change in TA thus for year 1, total assets rise by Capex – Depreciation + Increase in Working capital giving us 0.2 x (2.2 – 0.55 + 0.33) = 0.396
3.3
A
see workings below
D/E of 0.667 translates to a D/TA of 0.4 e.g. assume debt is 6.67 and equity is 10, then D/TA must be 6.67/16.67 = 0.4 Table below is shown for completeness. €m
Yr1
Yr2
Yr3
Yr4
Yr5
SALES (30% growth pa) NET INCOME (35% of sales) CAPEX (40% of sales) DEPRECIATION (10% of sales) WORKING CAPITAL INVESTMENT(6% of sales) NEW DEBT 40% D/TA
5.50 1.93 2.20 0.55
7.15 2.50 2.86 0.72
9.30 3.25 3.72 0.93
12.08 4.23 4.83 1.21
15.71 5.50 6.28 1.57
0.33 0.79
0.43 1.03
0.56 1.34
0.73 1.74
0.94 2.26
FCFE= NI +Dep-WC-Capex +new debt
0.74
0.96
1.25
1.62
2.10
FCFE = NI - (1-0.4)(Capex - Dep + WC inv)
0.74
0.96
1.25
1.62
2.10
PV OF FCFE (at 15%)
0.64
0.72
0.82
0.93
1.05
TERMINAL VALUE (20 X E5) PV OF TERMINAL VALUE VALUE OF FIRM SHARE PRICE
109.96 54.67 58.83 2.94
Higher level of debt financing will increase FCFE and assuming no change in the required return, a higher valuation. 3.4
A
Assuming a FCFF figure for year 1 is €0.5m, for the items below calculate how a €200,000 change in the value would impact on FCFF. Assume where relevant a tax rate of 20% Change 1. Depreciation +40,000 2. Accounts receivables -200,000 3. Interest expense No impact FCFF is before interest so of course there is no impact from this change Depreciation is a non-cash cost so has no direct impact on FCF however it does affect the tax paid, thus the tax benefit (which is cash) is Depreciation x Tax rate. 3.5
C
Where CAPEX is very high it will cause FCF to be negative.
3.6
B
If the stock options were expected to be ongoing then we would adjust the cashflow but since it is a one-off event we would not make any adjustment.
ANSWER TO QUESTION 4 4.1
A
R^2 is SSR/TSS i.e. explained variation divided by total variation; thus 2287/4487. Degrees of freedom on the sum of squared errors (SSE) = n-k-1. K =number of independent variables, in this case k = 3. The total degrees of freedom is n-1, thus n=30 and therefore n-k-l = 26. The SEE is square root of the mean sum of squares due to error, where the mean is the sum of squares divided by the appropriate degrees of freedom; thus √[2200/26] = 9.198 4.2
C
The global test is an f-test. It is calculated as the mean sum of squares for regression divided by the mean sum of squared errors i.e. MSSR/MSSE = 762.5/84.62 = 9.01. Please note that when using the f test to test multiple coefficients it is always a one-tailed test thus our critical stat will be 7.98. Since the test stat exceeds the critical stat we can reject the null. (Please note these F critical stat were made up for the purposes of this question and are not the actual correct values) The mean values are the sum of squares divided by the degrees of freedom. MSSR = 2287/3 and the MSSE= 2200/26 where 3 is the number of independent variables (k) and 26 is n-k-1. 4.3
C
First we calculate the t stat: (b1-0)/SE. This gives us -1.43; 5.77 and 2.5 for the coefficients of A, B and C respectively. Only if the absolute value is greater than 2 can we reject the null (the null being that the coefficient is equal to zero). Thus we cannot reject coefficient A. 4.4
B
Autocorrelation (also called serial correlation) causes incorrect t-scores. These t scores appear to be higher than they really are, thus they can make regression parameters appear to be significant when in fact they are not. 4.5
B
Durbin Watson is a test for serial correlation. 4.6
A
B is wrong on two counts, firstly the lag coefficient needs to be less than one and second the test is wrong. C is the description for identifying a MA(q) model not an AR model.
ANSWER TO QUESTION 5 5.1
A
Plant and equipment = 850 + 380 + 40 = 1270 (in thousands) Given that $440,000 consideration represented 80% of the company we can calculate that the fair value of the whole company must be $550,000 Minority Interest = 0.2 x Fair value = 0.2 x 550 = 110 (Under IFRS the minority interest is recognized based on fair value of the net assets and not on the fair value of the whole business but under US GAAP you must use the fair value of the whole entity ie it will include an element of goodwill. Where goodwill is zero the two approaches will be the same). 5.2
B (see working 1)
5.3
C (see working 2)
5.4
C (see working 4)
5.5
C (see notes below working 2)
5.6
A
The equity method recognizes the net equity income but does not recognize individual line items such as any sales, cost of good sold etc… Therefore the net profit margin will be higher under the equity method as revenue will be lower than under the other methods.
Workings Working 1: Consolidated Income Statement for the year following investment:
Revenue COGS Gross Profit Expenses Depreciation Net Income Minority Interest Retained
Consolidated Income Statement Acquisition Method $ (000’s) 113 (47) 66 (23) (17)* 26 (1.2)** 24.8
Consolidated Income Statement Pooling Method $ (000’s) 113 (47) 66 (23) (13) 30 30
*The depreciation includes the additional depreciation due to the difference between the book value and fair value of Elm’s plant and equipment. The difference was $40,000 which is expensed over 10 years (the remaining useful economic life of the asset). Therefore the additional depreciation is $4,000 ** Minority interest will share the impact of the extra depreciation thus 0.2 x (NI – extra depreciation) giving us 0.2 x (10-4) TUTOR TIP Net income is the same for equity method and also consolidation under the acquisition method. You might find it easier to calculate the net income using the equity method. See working 3 for overview of net income using the equity method.
Working 2: If Elm is treated as a joint venture, US GAAP requires the use of the Equity method Balance Sheet of Oak using the Equity method (note the answers have been rounded to the nearest whole number)
Oak’s Balance at date of acquisition $ (000’s) Cash Receivables Inventory Total Current assets Land Plant and Equipment (net) Investment in Elm Total assets
272 260 220 752 1250 850 440 3292
Current Liabilities Non Current Liabilities Total Liabilities Common Stock Additional Paid in Capital Retained earnings Total Liabilities and Equity
300 780 1080 860 452 900 3292
Under the equity method the initial investment in Elm is the acquisition cost, i.e. $440,000. The investment in Elm one year later (question 5) s calculated as follows: Original cost + $440,000 Oak’s share of net income + $8,000 (80% x $10,000) Less additional depreciation (80% x $4,000) - $3,200 = Year balance sheet value = $444,800 Note: cash is reduced to reflect the investment price i.e. 400 – 128 (given in question)
Working 3: Oak’s income statement for the year after investing in Elm, using the equity approach: Oak’s Income Statement Revenue COGS Gross Profit Expenses Depreciation Income from Elm Net Income
$ (000’s) 80 (35) 45 (15) (13.2)* 8 24.8
*The depreciation expense includes the additional depreciation on the plant and equipment due to the difference between the book value and fair value. The total depreciation expense is different to working 1 because under the equity method we do not include Elm’s expenses on a line-by-line basis. Oak’s share of the net income of Elm is included as one line (income from Elm) Note: net income is the same as under the acquisition method.
Working 4: The net income would be the same as the equity method and the full consolidation (acquisition method). *The depreciation is calculated as follows: Income Statement using Proportionate Consolidation Revenue COGS Gross Profit Expenses Depreciation Net Income
Oak’s depreciation + $10,000 80% of Elm’s depreciation + $2,400 Additional depreciation (80% x 4000) + £3,200 Total depreciation expense = $15,600
$ (000’s) 106.4 (44.6) 61.8 (21.4) (15.6)* 24.8
ANSWER TO QUESTION 6 6.1
A
4156 + 312 + 42 + 623 + 249 (interest cost) – 215 (benefits paid) = 5167 Interest cost is calculated as: Opening PBO x discount rate, giving us 4,156 x 0.06 = 249 6.2
B
Service cost + Interest cost + amortization of actuarial loss – expected returns: 312 + 249 + 195 - 245 6.3
B
Answer A is very nearly correct except if says “required”. Neither IFRS nor US GAAP require the use of the corridor test. Both allow faster recognition if preferred. Answer C relates to the IFRS treatment for past service costs 6.4
A
There are two ways to calculate the economic expense; we can either take the change in the funded status and then deduct employer contributions or by summing each item that affect the pension obligation and deducting the actual return on plan assets. In the first case, benefits paid affect equally the PBO and the Plan assets so therefore they have no impact on the funded status. Using the second approach, if the service cost increases (which it should with higher assumed pay rises) then the PBO will increase and thus the economic expense. Improving the terms of the pension will give rise to a Prior Service Cost which will also increase the PBO. 6.5
B
Higher discount rate will lower PBO and thus lower service costs and interest costs. This will give us a lower pension expense. The lower expected future pay rises will also lower the PBO due to the final salary being lower. This will reinforce the effect of the interest rate change. The lower expected return will have no effect on the PBO however, lower expected returns will give us a higher pension expense. We cannot of course know whether the impact from the expected return will counter the impact from the interest rate and salary changes thus we cannot say overall what the impact will be on the pension expense.
6.6
C
Under IFRS the pension position is smoothed out number unlike US GAAP’s funded status. Given we are told actual returns have been significantly low in recent years then under US GAAP this would translate to lower asset value and therefore a lower funded status. However, under IFRS this is reduced since in general we use expected and not actual returns. Thus, we would make a positive adjustment to the funded status to reverse out these “temporary” effects. There are no significant differences between the two accounting standards with regard to the pension expense so A is incorrect. Answer B is just nonsense.
