A student won $1m in a lottery. Currently the money is in a bank account which pays interest at 6% pa, given as an APR compounding per month.
She plans to spend $20,000 at the beginning of every month from now on (so the first withdrawal will be at t=0). After each withdrawal, she will check how much money is left in the account. When there is less than $500,000 left, she will donate that remaining amount to charity.
In how many months will she make her last withdrawal and donate the remainder to charity?
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?
Which of the following is NOT a valid method for estimating the beta of a company's stock? Assume that markets are efficient, a long history of past data is available, the stock possesses idiosyncratic and market risk. The variances and standard deviations below denote total risks.
A trader sells one crude oil European style put option contract on the CME expiring in one year with an exercise price of $44 per barrel for a price of $6.64. The crude oil spot price is $40.33. If the trader doesn’t close out her contract before maturity, then at maturity she will have the:
Question 708 continuously compounding rate, continuously compounding rate conversion
Convert a 10% continuously compounded annual rate ##(r_\text{cc annual})## into an effective annual rate ##(r_\text{eff annual})##. The equivalent effective annual rate is:
Use the below information to value a mature levered company with growing annual perpetual cash flows and a constant debt-to-assets ratio. The next cash flow will be generated in one year from now, so a perpetuity can be used to value this firm. The firm's debt funding comprises annual fixed coupon bonds that all have the same seniority and coupon rate. When these bonds mature, new bonds will be re-issued, and so on in perpetuity. The yield curve is flat.
| Data on a Levered Firm with Perpetual Cash Flows | ||
| Item abbreviation | Value | Item full name |
| ##\text{OFCF}_1## | $12.5m | Operating free cash flow at time 1 |
| ##\text{FFCF}_1 \text{ or }\text{CFFA}_1## | $14m | Firm free cash flow or cash flow from assets at time 1 |
| ##\text{EFCF}_1## | $11m | Equity free cash flow at time 1 |
| ##\text{BondCoupons}_1## | $1.2m | Bond coupons paid to debt holders at time 1 |
| ##g## | 2% pa | Growth rate of OFCF, FFCF, EFCF and Debt cash flow |
| ##\text{WACC}_\text{BeforeTax}## | 9% pa | Weighted average cost of capital before tax |
| ##\text{WACC}_\text{AfterTax}## | 8.25% pa | Weighted average cost of capital after tax |
| ##r_\text{D}## | 5% pa | Bond yield |
| ##r_\text{EL}## | 13% pa | Cost or required return of levered equity |
| ##D/V_L## | 50% pa | Debt to assets ratio, where the asset value includes tax shields |
| ##n_\text{shares}## | 1m | Number of shares |
| ##t_c## | 30% | Corporate tax rate |
Which of the following statements is NOT correct?