For a price of $95, Nicole will sell you a 10 year bond paying semi-annual coupons of 8% pa. The face value of the bond is $100. Other bonds with the same risk, maturity and coupon characteristics trade at a yield of 8% pa.
Question 96 bond pricing, zero coupon bond, term structure of interest rates, forward interest rate
An Australian company just issued two bonds paying semi-annual coupons:
- 1 year zero coupon bond at a yield of 8% pa, and a
- 2 year zero coupon bond at a yield of 10% pa.
What is the forward rate on the company's debt from years 1 to 2? Give your answer as an APR compounding every 6 months, which is how the above bond yields are quoted.
Your credit card shows a $600 debt liability. The interest rate is 24% pa, payable monthly. You can't pay any of the debt off, except in 6 months when it's your birthday and you'll receive $50 which you'll use to pay off the credit card. If that is your only repayment, how much will the credit card debt liability be one year from now?
A method commonly seen in textbooks for calculating a levered firm's free cash flow (FFCF, or CFFA) is the following:
###\begin{aligned} FFCF &= (Rev - COGS - Depr - FC - IntExp)(1-t_c) + \\ &\space\space\space+ Depr - CapEx -\Delta NWC + IntExp(1-t_c) \\ \end{aligned}###
Question 418 capital budgeting, NPV, interest tax shield, WACC, CFFA, CAPM
| Project Data | ||
| Project life | 1 year | |
| Initial investment in equipment | $8m | |
| Depreciation of equipment per year | $8m | |
| Expected sale price of equipment at end of project | 0 | |
| Unit sales per year | 4m | |
| Sale price per unit | $10 | |
| Variable cost per unit | $5 | |
| Fixed costs per year, paid at the end of each year | $2m | |
| Interest expense in first year (at t=1) | $0.562m | |
| Corporate tax rate | 30% | |
| Government treasury bond yield | 5% | |
| Bank loan debt yield | 9% | |
| Market portfolio return | 10% | |
| Covariance of levered equity returns with market | 0.32 | |
| Variance of market portfolio returns | 0.16 | |
| Firm's and project's debt-to-equity ratio | 50% | |
Notes
- Due to the project, current assets will increase by $6m now (t=0) and fall by $6m at the end (t=1). Current liabilities will not be affected.
Assumptions
- The debt-to-equity ratio will be kept constant throughout the life of the project. The amount of interest expense at the end of each period has been correctly calculated to maintain this constant debt-to-equity ratio.
- Millions are represented by 'm'.
- All cash flows occur at the start or end of the year as appropriate, not in the middle or throughout the year.
- All rates and cash flows are real. The inflation rate is 2% pa. All rates are given as effective annual rates.
- The project is undertaken by a firm, not an individual.
What is the net present value (NPV) of the project?
Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling $105 million. A scrip offer will be made that pays the fair price for the target's shares plus 75% of the total synergy value.
| Firms Involved in the Takeover | ||
| Acquirer | Target | |
| Assets ($m) | 6,000 | 700 |
| Debt ($m) | 4,800 | 400 |
| Share price ($) | 40 | 20 |
| Number of shares (m) | 30 | 15 |
Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money.
Calculate the merged firm's share price and total number of shares after the takeover has been completed.
How much more can you borrow using an interest-only loan compared to a 25-year fully amortising loan if interest rates are 4% pa compounding per month and are not expected to change? If it makes it easier, assume that you can afford to pay $2,000 per month on either loan. Express your answer as a proportional increase using the following formula:
###\text{Proportional Increase} = \dfrac{V_\text{0,interest only}}{V_\text{0,fully amortising}} - 1###Question 794 option, Black-Scholes-Merton option pricing, option delta, no explanation
Which of the following quantities from the Black-Scholes-Merton option pricing formula gives the Delta of a European call option?
Where:
###d_1=\dfrac{\ln[S_0/K]+(r+\sigma^2/2).T)}{\sigma.\sqrt{T}}### ###d_2=d_1-\sigma.\sqrt{T}=\dfrac{\ln[S_0/K]+(r-\sigma^2/2).T)}{\sigma.\sqrt{T}}###Which derivatives position has the possibility of unlimited potential gains?
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: