## Assignment 3

**Instructions**

Assignment 3 should be submitted after you have completed Unit 5. This assignment is worth

15 percent of your final grade.

Assignment 3 contains eight problems. The maximum mark for each problem is noted at the beginning of the problem. This assignment has a total of 100 marks.

Read the requirements for each problem and plan your responses carefully. Although your responses should be concise, ensure that you answer each of the required components as completely as possible. If supporting calculations are required, present them in good form.

When you receive your graded assignment, carefully review the comments the marker has made. This review component is an important step in your learning process. If you have any questions or concerns about the evaluation, please contact the Student Support Centre.

**Problem 1 (10 marks)**

Three years ago, you purchased a bond for $974.69. The bond had three years to maturity, a coupon rate of 8% paid annually, and a face value of $1,000. Each year you reinvested all coupon interest at the prevailing reinvestment rate shown in the table below. Today is the bond’s maturity date. What is your realized compound yield on the bond?

Time | Prevailing reinvestment rate |

0 (purchase date) | 6.0% |

1 | 7.2% |

2 | 9.4% |

3 (maturity date) |

**Problem 2 (15 marks)**

You will be paying $10,000 a year in education expenses at the end of the next two years. Currently the yield curve is flat at 8%.

- If you want to fully fund and immunize your obligation with a single issue of a zero-coupon bond, what maturity bond must you purchase?
- What must be the market value and the face value of the zero-coupon bond?
- Instead of using a single zero-coupon bond, you prefer to use a one-year T-Bill and a five-year zero-coupon bond to fund and immunize your obligation. How much of each security will you buy?

** Problem 3 (15 marks)**

A newly issued bond has the following characteristics:

Par value = $1000

Coupon rate = 8%

Yield to Maturity = 8%

Time to maturity = 15 years

Duration = 10 years

- Calculate modified duration using the information above.
- If the yield to maturity increases to 8.5%, what will be the change (in dollar amount) in bond price?
- Identify the direction of change in modified duration if:

i. the coupon of the bond is 4%, not 8%.

ii. the maturity of the bond is 7 years, not 15 years.

- How can you construct a portfolio with a duration of 8 years using this bond and a 5 year zero coupon bond?

**Problem 4 (10 marks)**

You have been provided with the following information zero coupon bonds with $1000 face value.

Maturity – semi -annual periods | semi-annual spot rates |

1 | 4.25 |

2 | 4.15 |

3 | 3.95 |

4 | 3.70 |

5 | 3.50 |

6 | 3.25 |

7 | 3.05 |

8 | 2.90 |

- Compute the forward interest rates.
- Graph the yield curve.
- Explain the factors that account for the shape of the curve.

**Problem 5 (10 marks)**

Company HTA had a free cash flow for the firm (FCFF) of $1,500,000 last year. It is expected the FCFF will keep a sustainable growth rate of 5%. The company has 2 million common shares outstanding. In addition, the following information has been gathered:

Capital structure: D/E=0.2:0.8?

Market value of Debt: V_{D} =$5,000,000;

Required return on equity: k_{E} =15%

Cost of debt before tax =6%

Tax rate: t_{c} =25%;

Determine the fair value of HTA stock.

**Problem 6 (15 marks)**

Company JUK has a ROE of 25% and the company will not pay any dividend for the next 3 years. It is estimated that the company will pay $2 dividend per share after three years and then to level off to 5% per year forever.

The company has a beta of 2. Assume the risk-free interest rate is 4%, and the market risk premium is 8%.

- What is your estimate of the fair price of a share of the stock?
- If the market price of a share is equal to this intrinsic value, what is the P/E ratio?
- What do you expect its price to be 1 year from now? Is the implied capital gain consistent with your estimate of the dividend yield and the market capitalization rate?

**Problem 7 (10 marks)**

MicroSense, Inc., paid $2 dividends per share last year. It is estimated that the company’s ROEs will be 12% and 10%, respectively, next two years. The plowback rate in next two years will be 0.6. It is expected that the dividends will grow at a sustainable rate of 3% per year after two years. Assume that the expected return on the market is 8%, the risk-free rate is 4%, and the beta of the stock is 1.4. What is the fair price of the stock?

**Problem 8 (15 marks):**

An analyst uses the constant growth model to evaluate a company with the following data for a company:

Leverage ratio (asset/equity): 1.8

Total asset turnover: 1.5

Current ratio: 1.8

Net profit margin: 8%

Dividend payout ratio: 40%

Earnings per share in the past year: $0.85

The required rate on equity: 15%

Based on an analysis, the growth rate of the company will drop by 25 percent per year in the next two years and then keep it afterward. Assume that the company will keep its dividend policy unchanged.

- Determine the growth rate of the company for each of next three years.
- Use the multi-period DDM to estimate the intrinsic value of the company’s stock.
- Suppose after one year, everything else will be unchanged but the required rate on equity will decrease to 14%. What would be your holding period return for the year?