Question 24 implicit interest rate in wholesale credit, effective rate
A bathroom and plumbing supplies shop offers credit to its customers. Customers are given 60 days to pay for their goods, but if they pay within 7 days they will get a 2% discount.
What is the effective interest rate implicit in the discount being offered? Assume 365 days in a year and that all customers pay on either the 7th day or the 60th day. All rates given in this question are effective annual rates.
The following is the Dividend Discount Model (DDM) used to price stocks:
### P_0 = \frac{d_1}{r-g} ###Assume that the assumptions of the DDM hold and that the time period is measured in years.
Which of the following is equal to the expected dividend in 3 years, ## d_3 ##?
What is the net present value (NPV) of undertaking a full-time Australian undergraduate business degree as an Australian citizen? Only include the cash flows over the duration of the degree, ignore any benefits or costs of the degree after it's completed.
Assume the following:
- The degree takes 3 years to complete and all students pass all subjects.
- There are 2 semesters per year and 4 subjects per semester.
- University fees per subject per semester are $1,277, paid at the start of each semester. Fees are expected to remain constant in real terms for the next 3 years.
- There are 52 weeks per year.
- The first semester is just about to start (t=0). The first semester lasts for 19 weeks (t=0 to 19).
- The second semester starts immediately afterwards (t=19) and lasts for another 19 weeks (t=19 to 38).
- The summer holidays begin after the second semester ends and last for 14 weeks (t=38 to 52). Then the first semester begins the next year, and so on.
- Working full time at the grocery store instead of studying full-time pays $20/hr and you can work 35 hours per week. Wages are paid at the end of each week and are expected to remain constant in real terms.
- Full-time students can work full-time during the summer holiday at the grocery store for the same rate of $20/hr for 35 hours per week.
- The discount rate is 9.8% pa. All rates and cash flows are real. Inflation is expected to be 3% pa. All rates are effective annual.
The NPV of costs from undertaking the university degree is:
Stocks in the United States usually pay quarterly dividends. For example, the retailer Wal-Mart Stores paid a $0.47 dividend every quarter over the 2013 calendar year and plans to pay a $0.48 dividend every quarter over the 2014 calendar year.
Using the dividend discount model and net present value techniques, calculate the stock price of Wal-Mart Stores assuming that:
- The time now is the beginning of January 2014. The next dividend of $0.48 will be received in 3 months (end of March 2014), with another 3 quarterly payments of $0.48 after this (end of June, September and December 2014).
- The quarterly dividend will increase by 2% every year, but each quarterly dividend over the year will be equal. So each quarterly dividend paid in 2015 will be $0.4896 (##=0.48×(1+0.02)^1##), with the first at the end of March 2015 and the last at the end of December 2015. In 2016 each quarterly dividend will be $0.499392 (##=0.48×(1+0.02)^2##), with the first at the end of March 2016 and the last at the end of December 2016, and so on forever.
- The total required return on equity is 6% pa.
- The required return and growth rate are given as effective annual rates.
- All cash flows and rates are nominal. Inflation is 3% pa.
- Dividend payment dates and ex-dividend dates are at the same time.
- Remember that there are 4 quarters in a year and 3 months in a quarter.
What is the current stock price?
Stocks in the United States usually pay quarterly dividends. For example, the software giant Microsoft paid a $0.23 dividend every quarter over the 2013 financial year and plans to pay a $0.28 dividend every quarter over the 2014 financial year.
Using the dividend discount model and net present value techniques, calculate the stock price of Microsoft assuming that:
- The time now is the beginning of July 2014. The next dividend of $0.28 will be received in 3 months (end of September 2014), with another 3 quarterly payments of $0.28 after this (end of December 2014, March 2015 and June 2015).
- The quarterly dividend will increase by 2.5% every year, but each quarterly dividend over the year will be equal. So each quarterly dividend paid in the financial year beginning in September 2015 will be $ 0.287 ##(=0.28×(1+0.025)^1)##, with the last at the end of June 2016. In the next financial year beginning in September 2016 each quarterly dividend will be $0.294175 ##(=0.28×(1+0.025)^2)##, with the last at the end of June 2017, and so on forever.
- The total required return on equity is 6% pa.
- The required return and growth rate are given as effective annual rates.
- Dividend payment dates and ex-dividend dates are at the same time.
- Remember that there are 4 quarters in a year and 3 months in a quarter.
What is the current stock price?
Question 419 capital budgeting, NPV, interest tax shield, WACC, CFFA, CAPM, no explanation
| Project Data | ||
| Project life | 1 year | |
| Initial investment in equipment | $6m | |
| Depreciation of equipment per year | $6m | |
| Expected sale price of equipment at end of project | 0 | |
| Unit sales per year | 9m | |
| Sale price per unit | $8 | |
| Variable cost per unit | $6 | |
| Fixed costs per year, paid at the end of each year | $1m | |
| Interest expense in first year (at t=1) | $0.53m | |
| Tax rate | 30% | |
| Government treasury bond yield | 5% | |
| Bank loan debt yield | 6% | |
| Market portfolio return | 10% | |
| Covariance of levered equity returns with market | 0.08 | |
| Variance of market portfolio returns | 0.16 | |
| Firm's and project's debt-to-assets ratio | 50% | |
Notes
- Due to the project, current assets will increase by $5m now (t=0) and fall by $5m at the end (t=1). Current liabilities will not be affected.
Assumptions
- The debt-to-assets 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 50% capital gains tax discount is not available since the project is undertaken by a firm, not an individual.
What is the net present value (NPV) of the project?
A stock is expected to pay its first dividend of $20 in 3 years (t=3), which it will continue to pay for the next nine years, so there will be ten $20 payments altogether with the last payment in year 12 (t=12).
From the thirteenth year onward, the dividend is expected to be 4% more than the previous year, forever. So the dividend in the thirteenth year (t=13) will be $20.80, then $21.632 in year 14, and so on forever. The required return of the stock is 10% pa. All rates are effective annual rates. Calculate the current (t=0) stock price.
Question 803 capital raising, rights issue, initial public offering, on market repurchase, no explanation
Which one of the following capital raisings or payouts involve the sale of shares to existing shareholders only?
A one year European-style put option has a strike price of $4. The option's underlying stock pays no dividends and currently trades at $5. The risk-free interest rate is 10% pa continuously compounded. Use a single step binomial tree to calculate the option price, assuming that the price could rise to $8 ##(u = 1.6)## or fall to $3.125 ##(d = 1/1.6)## in one year. The put option price now is:
The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.
A stock has a beta of 0.7.
What do you think will be the stock's expected return over the next year, given as an effective annual rate?