The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation.

### p_{0} = \frac{c_1}{r_{\text{eff}} - g_{\text{eff}}} ###

What is the discount rate '## r_\text{eff} ##' in this equation?

A stock pays annual dividends. It just paid a dividend of $5. The growth rate in the dividend is 1% pa. You estimate that the stock's required return is 8% pa. Both the discount rate and growth rate are given as effective annual rates.

Using the dividend discount model, what will be the share price?

A share just paid its semi-annual dividend of $5. The dividend is expected to grow at 1% every 6 months forever. This 1% growth rate is an effective **6 month** rate.

Therefore the next dividend will be $5.05 in six months. The required return of the stock 8% pa, given as an effective **annual** rate.

What is the price of the share now?

You own a nice suit which you wear once per week on nights out. You bought it one year ago for $600. In your experience, suits used once per week last for 6 years. So you expect yours to last for another 5 years.

Your younger brother said that retro is back in style so he wants to wants to borrow your suit once a week when he goes out. With the increased use, your suit will only last for another 4 years rather than 5.

What is the present value of the cost of letting your brother use your current suit for the next 4 years?

Assume: that bank interest rates are 10% pa, given as an effective annual rate; you will buy a new suit when your current one wears out and your brother will not use the new one; your brother will only use your current suit so he will only use it for the next four years; and the price of a new suit never changes.

Your poor friend asks to borrow some money from you. He would like $1,000 now (t=0) and every year for the next 5 years, so there will be 6 payments of $**1,000** from t=0 to t=5 inclusive. In return he will pay you $**10,000** in seven years from now (t=7).

What is the net present value (NPV) of lending to your friend?

Assume that your friend will definitely pay you back so the loan is risk-free, and that the yield on risk-free government debt is **10**% pa, given as an effective annual rate.

Which of the following is **NOT** a valid method to estimate future revenues or costs in a pro-forma income statement when trying to value a company?

A trader **sells** one crude oil **futures** contract on the CME expiring in one year with a locked-in futures price of $38.94 per barrel. The crude oil spot price is $40.33. If the trader doesn’t close out her contract before expiry then in one year she will have the:

An equity index fund manager controls a USD**1 billion** diversified equity portfolio with a beta of **1.3**. The equity manager fears that a global recession will begin in the next year, causing equity prices to tumble. The market does not think that this will happen. If the fund manager wishes to reduce her portfolio beta to **0.5**, how many S&P500 futures should she sell?

The US market equity index is the S&P500. One year CME futures on the S&P500 currently trade at **2,062** points and the spot price is **2,091** points. Each point is worth $**250**. How many one year S&P500 futures contracts should the fund manager sell?

Which form of production is **included** in the Gross Domestic Product (GDP) reported by the government statistics agency?