# Fight Finance

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A credit card offers an interest rate of 18% pa, compounding monthly.

Find the effective monthly rate, effective annual rate and the effective daily rate. Assume that there are 365 days in a year.

All answers are given in the same order:

$$r_\text{eff monthly} , r_\text{eff yearly} , r_\text{eff daily}$$

Which of the following statements about short-selling is NOT true?

An old company's Firm Free Cash Flow (FFCF, same as CFFA) is forecast in the graph below.

To value the firm's assets, the terminal value needs to be calculated using the perpetuity with growth formula:

$$V_{\text{terminal, }t-1} = \dfrac{FFCF_{\text{terminal, }t}}{r-g}$$

Which point corresponds to the best time to calculate the terminal value?

There are many ways to calculate a firm's free cash flow (FFCF), also called cash flow from assets (CFFA). Some include the annual interest tax shield in the cash flow and some do not.

Which of the below FFCF formulas include the interest tax shield in the cash flow?

$$(1) \quad FFCF=NI + Depr - CapEx -ΔNWC + IntExp$$ $$(2) \quad FFCF=NI + Depr - CapEx -ΔNWC + IntExp.(1-t_c)$$ $$(3) \quad FFCF=EBIT.(1-t_c )+ Depr- CapEx -ΔNWC+IntExp.t_c$$ $$(4) \quad FFCF=EBIT.(1-t_c) + Depr- CapEx -ΔNWC$$ $$(5) \quad FFCF=EBITDA.(1-t_c )+Depr.t_c- CapEx -ΔNWC+IntExp.t_c$$ $$(6) \quad FFCF=EBITDA.(1-t_c )+Depr.t_c- CapEx -ΔNWC$$ $$(7) \quad FFCF=EBIT-Tax + Depr - CapEx -ΔNWC$$ $$(8) \quad FFCF=EBIT-Tax + Depr - CapEx -ΔNWC-IntExp.t_c$$ $$(9) \quad FFCF=EBITDA-Tax - CapEx -ΔNWC$$ $$(10) \quad FFCF=EBITDA-Tax - CapEx -ΔNWC-IntExp.t_c$$

The formulas for net income (NI also called earnings), EBIT and EBITDA are given below. Assume that depreciation and amortisation are both represented by 'Depr' and that 'FC' represents fixed costs such as rent.

$$NI=(Rev - COGS - Depr - FC - IntExp).(1-t_c )$$ $$EBIT=Rev - COGS - FC-Depr$$ $$EBITDA=Rev - COGS - FC$$ $$Tax =(Rev - COGS - Depr - FC - IntExp).t_c= \dfrac{NI.t_c}{1-t_c}$$

An investor owns an empty block of land that has local government approval to be developed into a petrol station, car wash or car park. The council will only allow a single development so the projects are mutually exclusive.

All of the development projects have the same risk and the required return of each is 10% pa. Each project has an immediate cost and once construction is finished in one year the land and development will be sold. The table below shows the estimated costs payable now, expected sale prices in one year and the internal rates of returns (IRR's).

 Mutually Exclusive Projects Project Costnow ($) Sale price inone year ($) IRR(% pa) Petrol station 9,000,000 11,000,000 22.22 Car wash 800,000 1,100,000 37.50 Car park 70,000 110,000 57.14

Which project should the investor accept?

Which of the following assets would you expect to have the highest required rate of return? All values are current market values.

Alice, Bob, Chris and Delta are traders in the futures market. The following trades occur over a single day in a newly-opened equity index future that matures in one year which the exchange just made available.

1. Alice buys 2 future from Bob.

2. Chris buys 5 futures from Delta.

3. Chris buys 9 futures from Bob.

Which of the following statements is NOT correct?

The risk-weight on "Margin lending against listed instruments on recognised exchanges" is 20% according to APRA's interpretation of the Basel 3 Accord in 'Prudential Standard APS 112 Capital Adequacy: Standardised Approach to Credit Risk, Attachment A: Risk-weights for on-balance sheet assets'.

A bank is considering lending a $100,000 margin loan secured by an ASX-listed stock. How much regulatory capital will the bank require to grant this loan under the Basel 3 Accord? Ignore the capital conservation buffer and the off-balance sheet exposure. A stock has a beta of 1.2. Its next dividend is expected to be$20, paid one year from now.

Dividends are expected to be paid annually and grow by 1.5% pa forever.

Treasury bonds yield 3% pa and the market portfolio's expected return is 7% pa. All returns are effective annual rates.

What is the price of the stock now?

Question 948  VaR, expected shortfall

Below is a historical sample of returns on the S&P500 capital index.

 S&P500 Capital Index Daily Returns Ranked from Best to Worst 10,000 trading days from 4th August 1977 to 24 March 2017 based on closing prices. Rank Date(DD-MM-YY) Continuously compounded daily return (% per day) 1 21-10-87 9.23 2 08-03-83 8.97 3 13-11-08 8.3 4 30-09-08 8.09 5 28-10-08 8.01 6 29-10-87 7.28 … … … 9980 11-12-08 -5.51 9981 22-10-08 -5.51 9982 08-08-11 -5.54 9983 22-09-08 -5.64 9984 11-09-86 -5.69 9985 30-11-87 -5.88 9986 14-04-00 -5.99 9987 07-10-98 -6.06 9988 08-01-88 -6.51 9989 27-10-97 -6.55 9990 13-10-89 -6.62 9991 15-10-08 -6.71 9992 29-09-08 -6.85 9993 07-10-08 -6.91 9994 14-11-08 -7.64 9995 01-12-08 -7.79 9996 29-10-08 -8.05 9997 26-10-87 -8.4 9998 31-08-98 -8.45 9999 09-10-08 -12.9 10000 19-10-87 -23.36 Mean of all 10,000: 0.0354 Sample standard deviation of all 10,000: 1.2062 Sources: Bloomberg and S&P.

Assume that the one-tail Z-statistic corresponding to a probability of 99.9% is exactly 3.09. Which of the following statements is NOT correct? Based on the historical data, the 99.9% daily: