**Question 48** IRR, NPV, bond pricing, premium par and discount bonds, market efficiency

The theory of fixed interest bond pricing is an application of the theory of Net Present Value (NPV). Also, a 'fairly priced' asset is not over- or under-priced. Buying or selling a fairly priced asset has an NPV of zero.

Considering this, which of the following statements is **NOT** correct?

**Question 108** bond pricing, zero coupon bond, term structure of interest rates, forward interest rate

An Australian company just issued two bonds:

- A 1 year zero coupon bond at a yield of 10% pa, and
- A 2 year zero coupon bond at a yield of 8% 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?

Let the variance of returns for a share per month be ##\sigma_\text{monthly}^2##.

What is the formula for the variance of the share's returns per year ##(\sigma_\text{yearly}^2)##?

Assume that returns are independently and identically distributed (iid) so they have zero auto correlation, meaning that if the return was higher than average today, it does not indicate that the return tomorrow will be higher or lower than average.

**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 $
**5**m now (t=0) and fall by $**5**m 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 has a beta of **1.5**. The market's expected total return is **10**% pa and the risk free rate is **5**% pa, both given as effective annual rates.

Over the last year, bad economic news was released showing a higher chance of recession. Over this time the share market **fell** by **1**%. So ##r_{m} = (P_{0} - P_{-1})/P_{-1} = -0.01##, where the current time is zero and one year ago is time -1. The risk free rate was unchanged.

What do you think was the stock's historical return over the **last year**, given as an effective annual rate?

A trader **buys** 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 693** boot strapping zero coupon yield, forward interest rate, term structure of interest rates

Information about three risk free Government bonds is given in the table below.

Federal Treasury Bond Data |
||||

Maturity |
Yield to maturity |
Coupon rate |
Face value |
Price |

(years) | (pa, compounding semi-annually) | (pa, paid semi-annually) | ($) | ($) |

0.5 | 3% | 4% | 100 | 100.4926 |

1 | 4% | 4% | 100 | 100.0000 |

1.5 | 5% | 4% | 100 | 98.5720 |

Based on the above government bonds' yields to maturity, which of the below statements about the spot zero rates and forward zero rates is **NOT** correct?

An investor bought a **5** year government bond with a **2**% pa coupon rate at **par**. Coupons are paid **semi-annually**. The face value is $**100**.

Calculate the bond's new price **8** months later after yields have increased to **3**% pa. Note that both yields are given as APR's compounding semi-annually. Assume that the yield curve was flat before the change in yields, and remained flat afterwards as well.

**Question 920** SML, CAPM, Sharpe ratio, Treynor ratio, Jensens alpha, no explanation

Over-priced assets should **NOT**: