Suppose that the US government recently announced that subsidies for fresh milk producers will be gradually phased out over the next year. Newspapers say that there are expectations of a 40% increase in the spot price of fresh milk over the next year.

Option prices on fresh milk trading on the Chicago Mercantile Exchange (CME) reflect expectations of this 40% increase in spot prices over the next year. Similarly to the rest of the market, you believe that prices will rise by 40% over the next year.

What option trades are likely to be profitable, or to be more specific, result in a positive Net Present Value (NPV)?

Assume that:

- Only the spot price is expected to increase and there is no change in expected volatility or other variables that affect option prices.
- No taxes, transaction costs, information asymmetry, bid-ask spreads or other market frictions.

A project has the following cash flows:

Project Cash Flows | |

Time (yrs) | Cash flow ($) |

0 | -400 |

1 | 200 |

2 | 250 |

What is the Profitability Index (PI) of the project? Assume that the cash flows shown in the table are paid all at once at the given point in time. The required return is **10**% pa, given as an effective annual rate.

Which firms tend to have **high** forward-looking price-earnings (PE) ratios?

**Question 398** financial distress, capital raising, leverage, capital structure, NPV

A levered firm has zero-coupon bonds which mature in one year and have a combined face value of $**9.9**m.

Investors are risk-neutral and therefore all debt and equity holders demand the same required return of **10**% pa.

In one year the firm's assets will be worth:

- $
**13.2**m with probability 0.5 in the good state of the world, or - $
**6.6**m with probability 0.5 in the bad state of the world.

A new project presents itself which requires an investment of $**2**m and will provide a certain cash flow of $**3.3**m in one year.

The firm doesn't have any excess cash to make the initial $2m investment, but the funds can be raised from shareholders through a fairly priced rights issue. Ignore all transaction costs.

Should shareholders vote to proceed with the project and equity raising? What will be the gain in shareholder **wealth** if they decide to proceed?

A European put option will mature in ##T## years with a strike price of ##K## dollars. The underlying asset has a price of ##S## dollars.

What is an expression for the payoff at maturity ##(f_T)## in dollars from owning (being long) the put option?

The standard deviation and variance of a stock's annual returns are calculated over a number of years. The units of the returns are percent per annum ##(\% pa)##.

What are the units of the standard deviation ##(\sigma)## and variance ##(\sigma^2)## of returns respectively?

**Hint**: Visit Wikipedia to understand the difference between percentage points ##(\text{pp})## and percent ##(\%)##.

**Question 626** cross currency interest rate parity, foreign exchange rate, forward foreign exchange rate

The Australian cash rate is expected to be **2**% pa over the next one year, while the Japanese cash rate is expected to be **0**% pa, both given as nominal effective annual rates. The current exchange rate is **100** JPY per AUD.

What is the implied **1** year forward foreign exchange rate?

**Question 787** fixed for floating interest rate swap, intermediated swap

The below table summarises the borrowing costs confronting two companies A and B.

Bond Market Yields |
||||

Fixed Yield to Maturity (%pa) | Floating Yield (%pa) | |||

Firm A | 2 | L - 0.1 | ||

Firm B | 2.5 | L | ||

Firm A wishes to borrow at a floating rate and Firm B wishes to borrow at a fixed rate. Design an **intermediated** swap (which means there will actually be two swaps) that nets a bank **0.15**% and grants the remaining swap benefits to Firm A only. Which of the following statements about the swap is **NOT** correct?

**Question 906** effective rate, return types, net discrete return, return distribution, price gains and returns over time

For an asset's price to double from say $1 to $2 in one year, what must its effective annual return be? Note that an effective annual return is also called a net discrete return per annum. If the price now is ##P_0## and the price in one year is ##P_1## then the effective annul return over the next year is:

###r_\text{effective annual} = \dfrac{P_1 - P_0}{P_0} = \text{NDR}_\text{annual}###**Question 907** continuously compounding rate, return types, return distribution, price gains and returns over time

For an asset's price to double from say $1 to $2 in one year, what must its continuously compounded return ##(r_{CC})## be? If the price now is ##P_0## and the price in one year is ##P_1## then the continuously compounded return over the next year is:

###r_\text{CC annual} = \ln{\left[ \dfrac{P_1}{P_0} \right]} = \text{LGDR}_\text{annual}###