**Question 1: Time Value of Money **

**a)**Ted Ltd is entitled to receive a cash inflow of $80,000 in 2 years’ time and a further cash inflow of $14,000 in 5 years’ time (in year 5). If the interest rate is 8.5% per annum, how much is this stream of cash inflows worth:

**i)**today

**ii)**in 5 years’ time

**b)**On your 18^{th} birthday your uncle states that he will give you $1,000 each year for 5 years commencing on your 21^{st} birthday. What is the value to you at the time of your 18^{th} birthday of this promised cash flow if the rate of interest is 10%?

**c)**What is the present value of a perpetual cash inflow of $1,000 received at the end of each year, the first inflow occurring 2 years from now, if the interest rate is 5% per annum? If the above cash inflows can be produced by investing $10,000 in a business this year (year 0) and $6,000 next year (year 1), what is the present value of the investment?

**d)**Your friend is celebrating her 35^{th} birthday today and wants to start saving for her anticipated retirement at age 65. She wants to be able to withdraw $10,000 from her savings account on each birthday for 10 years following her retirement; the first withdrawal will be on her 66^{th} birthday. Your friend intends to invest her money in the local savings bank, which offers 7% per annum. She wants to make equal, annual payments on each birthday in a new savings account she will establish for her retirement fund.

If she starting these deposits on her 36^{th} birthday and continues to make deposits until she is 65 (the last deposit will be on her 65^{th}birthday), what amount must she deposit annually to be able to make the desired withdrawals on retirement?

**Question 2: Interest Rates **

**a)**Ted Bank charges 7% per annum compounded daily (365 days in a year), on its personal loans. Pine Bank charges 7.1% per annum compounded semi-annually. As a potential borrower, which do you prefer?

**b)**You are considering the purchase of a new home for $700,000. You have a deposit of $100,000. The bank will lend you money at 7% per annum compounded monthly over a period of up to 20 years. If you borrow the required funds over 20 years, what are the monthly repayments? After 2 years, how much do you still owe the bank? What is the interest component of the 25^{th} repayment?

**c)**Mickey is planning to save $50,000 per quarter for 10 years. Savings will earn interest at an (nominal) interest rate of 12% per annum. Calculate the present value for this annuity if interest is compounded semi-annually.

**Question 3: Bonds and Stock Valuation**

**a)**Ted Ltd shares currently sell for $3 per share. The last dividend was $0.2 per share. The dividend is expected to grow at 5%.

**i)**What is the required return on Ted Ltd?

**ii)**The dividend yield?

**b)**Ted Ltd is contemplating selling some 10-year bonds to raise funds for a planned expansion. Ted currently has an issue outstanding with an $8 annual coupon, paid semi-annually. These bonds currently sell for $93.49, a discount relative to their $100 face value, and they have 10 years remaining to maturity. What coupon rate must the new issue have if it is to sell at par when it is issued?

**c)**Ted Investment Ltd has a portfolio of 3 bands (A, B and C). Their terms to maturity are 5, 10 and 25 years, respectively. Each of the bond has a coupon interest rate of 8% per annum and a yield of 6% per annum. All 3 bonds pay annual coupons.

**a)**Calculate the price of each bond

**b)**Re-calculate the price of each bond if the required yield on each bond increases to 7% per annum.

**c)**Comparing your answers to parts (a) and (b), what patterns are evident?

**d)**You have predicted the following dividends for the next three years on Ted Ltd’s shares:

Year | Projected Dividend |

1 | $0.20 |

2 | $0.30 |

3 | $0.40 |

Beginning in the 3^{rd} year, you project that the dividend will increase at 8% per annum indefinitely. The required return is 15% per annum.

**i)**Calculate the price today for the shares

**ii)**Calculate the price at year 3

**Question 4: Investment Decision Rules**

A firm with a 14% WACC is evaluating 2 projects for this year’s budget. After-tax cash flows are as follows:

Year 0 | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | |

Project A | -$8,000 | $2,200 | $2,200 | $2,200 | $2,200 | $2,200 |

Project B | -$20,000 | $5,700 | $5,800 | $5,600 | $6,200 | $6,500 |

**i)**Calculate NPV for each project.

**ii)**Calculate IRR for each project.

**iii)**Calculate MIRR for each project.

**iv)**Calculate payback for each project.

**v)**Calculate discounted payback for each project.

**Question 5: Risk and Return**

**a)**What are the portfolio weights for a portfolio that has 200 shares that sell for $10 per share and 100 shares that sell for $4 per share?

**b)**Calculate the expected return and standard deviation of the following share

State of the economy | Probability of state of economy | Rate of return if state occurs |

Recession | 0.30 | 14% |

Boom | 0.70 | 20% |

**c)**Ted has invested one-third of his funds in Share A and two-thirds of his funds in Share B. His assessment of each investment is as follows:

Share A | Share B | |

Expected return | 15% | 21% |

Standard deviation | 18% | 25% |

Correlation between the returns | 0.5 |

**i)**Calculate the expected return and the standard deviation of return of Ted’s portfolio?

**ii)**Re-calculate the expected return and the standard deviation where the correlation between the returns is 0 and 1, respectively.

**iii)**Is Ted better or worse off as a result of investing in the portfolio rather than in one share?** **

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