# Eight of the hardest CFA questions, and how to answer them

The CFA exams are approaching fast. You need to do at least 300 hours of study to pass each one. You can always follow our guide to prepping for the CFA exams. Even so, the questions have a reputation for being extremely difficult.

We’ve spoken to training companies who coach candidates embarking on the CFA exams. These eight questions – in their opinions – are the toughest questions you are likely to encounter on CFA levels I, II, and III. Helpfully, they have also provided solutions.

#### Questions for CFA Level I:

1. Beth Knight, CFA, and David Royal, CFA, are independently analyzing the value of Bishop, Inc. stock. Bishop paid a dividend of \$1 last year. Knight expects the dividend to grow by 10% in each of the next three years, after which it will grow at a constant rate of 4% per year. Royal also expects a temporary growth rate of 10% followed by a constant growth rate of 4%, but he expects the supernormal growth to last for only two years. Knight estimates that the required return on Bishop stock is 9%, but Royal believes the required return is 10%. Royal’s valuation of Bishop stock is approximately:

A. \$5 less than Knight’s valuation

B. Equal to Knights valuation

C. \$5 greater than Knights valuation

You can select the correct answer without calculating the share values. Royal is using a shorter period of supernormal growth and a higher required rate of return on the stock. Both of these factors will contribute to a lower value using the multistage DDM.

Royal’s valuation is \$5.10 less that Knight’s valuation.”

2. A semi-annual pay floating-rate note pays a coupon of Libor + 60 bps, with exactly three years to maturity. If the required margin is 40 bps and Libor is quoted today at 1.20% then the value of the bond is closest to:

A. 99.42

B. 100.58

C. 102.33

Floating rate bonds are pretty difficult to value accurately (in fact we will see this again in Level II Derivatives, as they are an essential component to swaps). However, there is an approximation provided in the CFA curriculum, and a rather neat Quartic short-cut too.

A floating-rate note can be (roughly) valued on a coupon date by discounting current Libor + quoted margin (think of this as the regular coupon) at current Libor + required margin (think of this as the discount rate). In other words, we discount what we get (PMT) at the rate that we need (I/Y).

On the calculator: N = 6, I/Y = (1.2 + 0.4) ÷ 2 = 0.8, PMT = (1.2 + 0.6) ÷ 2 = 0.9, FV = 100 è PV = 100.58.

Quartic shortcut: first note that if a bond is paying exactly what is required (i.e. quoted margin = required margin) then the bond will trade at par on each coupon date. In this question, the bond is paying 20 bps per year more than required. This means that we should pay a 20 bp premium per year. Three year maturity means a 60 bp premium. Hence our quick “guess” is that the bond should trade at 100 plus a 60 bp premium, or 100.60. Answer B is the only possible answer.

3. The following details (all annual equivalent) are collected from Treasury securities:

Years to maturity            Spot rate

2.0                                 1.0%

4.0                                 1.5%

6.0                                 2.0%

8.0                                 2.5%

Which of the following rates is closest to the two-year forward rate six years from now (i.e. the “6y2y” rate)?

A   2.0%
B   3.0%
C   4.0%

Calculating forward rates from spot rates and spots from forwards can be done easily, and quite accurately, with the banana method, described below.

Note that the six-year spot rate (say, z6) is 2% and the eight-year spot rate (z8) is 2.5%. Let’s call the 6y2y rate F, to keep notation easy.

To solve this, draw a horizontal timeline from 0 to 8, marking time 6 on the top. To avoid arbitrage, investing for six years at z6 then two years at F must be the same as investing for eight years at the z8rate. Mark above your timeline “z6 = 2%” (between T = 0 and T = 6) and “F = ?” (between T = 6 and T = 8), and below the timeline “z8 = 2.5%”.

Algebraically we can say that: (1 + z6)6 x (1 + F)2 = (1 + z8)8.

With a bit of effort, this solves as: F = [(1 + z8)8 ÷ (1 + z6)6]0.5 – 1 = [1.0258 ÷ 1.026]0.5 – 1 = 4.01%.

Quartic banana method: just below the timeline you have drawn, write down how many bananas (or any other inanimate object) you have received if you get 2.5 per year for eight years. Answer: 20. Now write down, above the timeline, how many you get in the first six years, at 2 per year. Answer: 12. Now calculate how many bananas you must have got in the last two years. Answer: 20 – 12 = 8. This is over two years, hence 4 per year, answer C. Banana method gives 4.00%; accurate method gives 4.01%. Close enough!

#### Questions for CFA Level II:

4. Sudbury Industries expects FCFF in the coming year of 400 million Canadian dollars (\$), and expects FCFF to grow forever at a rate of 3 percent. The company maintains an all-equity capital structure, and Sudbury’s required rate of return on equity is 8 percent.

Sudbury Industries has 100 million outstanding common shares. Sudbury’s common shares are currently trading in the market for \$80 per share.

Using the Constant-Growth FCFF Valuation Model, Sudbury’s stock is:

A. Fairly-valued.

B. Over-valued

C. Under-Valued

Based on a free cash flow valuation model, Sudbury Industries shares appear to be fairly valued.

Since Sudbury is an all-equity firm, WACC is the same as the required return on equity of 8%.

The firm value of Sudbury Industries is the present value of FCFF discounted by using WACC. Since FCFF should grow at a constant 3 percent rate, the result is:

Firm value = FCFF1 / WACC−g = 400 million / 0.08−0.03 = 400 million / 0.05 = \$8,000 million

Since the firm has no debt, equity value is equal to the value of the firm. Dividing the \$8,000 million equity value by the number of outstanding shares gives the estimated value per share:

V0 = \$8,000 million / 100 million shares = \$80.00 per share

Beecher Tuttle – Read more on efinancialcareers.com