Finance Sample Questions

Question One

Stock Valuation using Fama-French Three-Factor Model

An analyst has modeled the stock of a company using the Fama-French three-factor model. The risk-free rate is 5%, the market return is 9%, the return on the SMB portfolio is 3.2%, and the return on the HML portfolio is 4.8%. If a = 0, b = 1.1, c = -0.3, and d=1.2, what is the stock’s predicted return?

Expected Return = + b +c (SMB) +d (HML) +a

Where;

• R_f ​ is the risk-free rate.
• R_m ​is the market return.
• SMB (Small Minus Big) is the return on the size factor portfolio.
• HML (High minus Low) is the return on the value factor portfolio.
• a is the stock’s alpha (a measure of the stock's return that is not explained by the three factors; in this case, a=0a = 0a=0).
• b, c, and d mare the sensitivities of the stock to the respective factors.
• R_f​=5%
• R_m=9%
• SMB=3.2%
• HML=4.8%
• a = 0
• b =1.1
• c=−0.3
• d=1.2

Expected Return = 5% +1.1 (9%−5%) + (−0.3) (3.2%) +1.2(4.8%)

=5% +4.4% −0.96% +5.76%

=14.2%

Question Two

Expected Return and Standard Deviation Calculation

A stock’s return has the following distribution:

Demand for Products Probability of Occurrence of Demand Return if

Demand Occurs

Weak 0.1 -40%

Below Average 0.2 -5

Average 0.4 12

Above Average 0.2 21

Strong 0.1 50

Calculate the stock’s expected return and standard deviation.

Expected return (μ)

μ=∑ (P_i×R_i)

μ is the expected return

P_i is the probability of occurrence of demand for each scenario

R_i​ is the return if demand occurs for each scenario

μ = (0.1×−40%) + (0.2×−5) + (0.4×12) + (0.2×21) + (0.1×50)

= -0.04 + -1 + 4.8 + 4.2 + 5

= 12.96%

Standard deviation (σ) =
σ =
σ =

σ =

σ = 17.4257%

Question Three

Standard Deviation of Stock Returns

A company has annual returns for three different stocks (Stock A, Stock B, and Stock C) over the past five years as follows:

• Stock A: 8%, 12%, 15%, 5%, 10%
• Stock B: 10%, 14%, 9%, 13%, 11%
• Stock C: 7%, 9%, 8%, 11%, 12%

Calculate the standard deviation of returns for each stock to determine which stock has the most volatile returns.

Stock A

Mean Return

=

=

= 10%

Deviations from Mean

8%−10% =−2%

12%−10%=2%

15%−10%=5%

5%−10%=−5%

10%−10% = 0%

​Squared Deviations

(−2%) ² = 4

(2%) ² =4

(5%) ² =25

(−5%) ² = 25

(0%) ² =0

​Variance

Variance =

=

= 11.6

Standard Deviation

=

= 3.406%

Stock B

Mean Return

=

=

= 11.4%

Deviations from Mean

10%−11.4% =−1.4%

14%−11.4%=2.6%

9%−11.4%=-2.4%

13%−11.4%=1.6%

11%−11.4% = -0.4%

​Squared Deviations

(−1.4%) ² = 1.96

(2.6%) ² =6.76

(-2.4%) ² =5.76

1.6%) ² = 2.56

(0.4%) ² =0.16

​Variance

Variance =

​

=

= 3.44

Standard Deviation

=

= 1.855%

Stock C

Mean Return

Mean =

=

= 9.4%

Deviations from Mean

7%−9.4% =−2.4%

9%−9.4%=-0.4%

8%−9.4%=-1.4%

11%−9.4%=1.6%

12%−9.4% = 2.6%

​Squared Deviations

(−2.4%) ² = 5.76

(-0.4%) ² =0.16

(-1.4%) ² =1.96

(1.6%) ² = 2.56

(2.6%) ² =6.76

​Variance

=

​

=

= 3.44

Standard Deviation

=

= 1.855%

Question Four

Net Present Value (NPV) Calculation

ABC Manufacturing Company is considering purchasing a new piece of equipment that will improve its production process. The equipment costs $500,000 and has an estimated useful life of 5 years with no salvage value. The company expects the new equipment to generate additional revenue of $200,000 per year and reduce operating costs by $50,000 per year. The company's required rate of return is 10%.

Calculate the Net Present Value (NPV) of the investment.

Initial investment = 500,000

r (required rate of return) =10%

Discount Factor =

Discount Factors

Year 1 = = 0.9091

Year 2 = = 0.8264

Year 3 = = 0.7513

Year 4 = = 0.6830

Year 5 = = 0.6209

Year 1 = 250,000 × 0.9091 = 227,272.73

Year 2 = 250,000 × 0.8264 = 206,611.57

Year 3 = 250,000 × 0.7513 = 187,828.70

Year 4 = 250,000 × 0.6830 = 170,753.36

Year 5 = 250,000 × 0.6209 = 155,230.33

Total Present Value of Cash Flows

= 227,272.73+206,611.57+187,828.70+170,753.36+155,230.33

= 947,696.69

NPV

NPV=Total Present Value of Cash Flows−Initial Investment

NPV =947,696.69−500,000

=447,696.69

Question Five

Depreciation Calculation

A company purchases machinery for $120,000. It has a useful life of 10 years and a salvage value of $10,000. Using the straight-line method, calculate the annual depreciation expense.

Annual Depreciation Expense =

Cost of the Asset = $120,000

Salvage Value = $10,000

Useful Life = 10 years

Annual Depreciation Expense

=

=

= 11,000

Question Six

Weighted Average Cost of Capital (WACC) Calculation

Turnbull Co. is considering a project that requires an initial investment of $270,000. The firm will raise the $270,000 in capital by issuing $100,000 of debt at a before-tax cost of 11.1%, $30,000 of preferred stock at a cost of 12.2%, and $140,000 of equity at a cost of 14.7%. The firm faces a tax rate of 25%. What will be the WACC for this project?

After-tax cost of debt

r_d×(1−T)

=11.1 %× (1−0.25)

=11.1%×0.75

=8.325%

Weights

Weight of debt (w_d​)

Weight of debt (w_d​) =

=

​ = 0.3704

= 37.04%

Weight of preferred stock (w_ps)

Weight of preferred stock (w_ps) =

=

= 0.1111

= 11.11%

Weight of equity (w_e)

Weight of equity (w_e) =

=

= 0.5185

= 51.58%

WACC

WACC=(w_d​×r_d​×(1−T))+(w_ps​×r_ps​)+( w_e ​×r_e​)

w_d​ = 0.3704

r_d×(1−T) = 8.325%

w_ps​= 0.1111

r_ps​= 12.2%

w_e​= 0.5185

r_e​= 14.7%

WACC= (0.3704×0.08325) + (0.1111×0.122) + (0.5185×0.147)

= 0.0256 + 0.0136 + 0.0758

= 0.115

= 11.5%

Question Seven

Retained Earnings Breakpoint Calculation

Alpha Moose Transporters Co.’s addition to earnings for this year is expected to be $745,000. Its target capital structure consists of 50% debt, 5% preferred, and 45% equity. Determine Alpha Moose Transporter’s retained earnings breakpoint

Retained Earnings Breakpoint =

Addition to Earnings = $745,000

Proportion of Equity in Capital Structure = 45%

Question Eight

Inflation Rate and Implied Exchange Rate Calculation

Big Mac prices in the UK have increased from £4.50 to £4.90 over the past year. During the same timeframe, US Big Mac prices have increased from $3.45 to $3.55. What are estimates of the inflation rates for the US and UK given these “consumption baskets”. What is the implied exchange rate from last year and this year for GBPUSD?

United Kingdom

The initial price of a Big Mac (last year) = £4.50

Final price of a Big Mac (this year) = £4.90

= × 100

= × 100

= 8.89%

United States

The initial price of a Big Mac (last year) = $3.45

Final price of a Big Mac (this year) = $3.55

Inflation rate in the US

= × 100

× 100

= 2.9%

Initial implied exchange rate (last year)

GBP price of Big Mac last year = £4.50

USD price of Big Mac last year = $3.45

Implied exchange rate last year

=

=1.3043

Final implied exchange rate (this year):

GBP price of Big Mac this year = £4.90

USD price of Big Mac this year = $3.55

Implied exchange rate this year

=

= 1.3803

Question Nine

Cost of Preferred Stock Calculation

Barton Industries can issue perpetual preferred stock at a price of $60 per share. The stock would pay a constant annual dividend of $3.23 per share. If the firm's marginal tax rate is 25%, what is the company's cost of preferred stock?

r_p​=

D_p​=3.23 (annual dividend per share)

P_p=60 (price per share)

=

= 0.05383

= 5.383%