Do all of the following
(i) Define the accumulation factor A(1,/ + h) and give a formula for the force of interest o() per unit time in terms of the accumulation factor. [2] (ii) The force of interest 6() at time / (measured in years) is given by 6(1) =0.01/ + 0.04. (a) Calculate the corresponding nominal rate of interest for the period / = 1 to / = 2. (b) If an investment of 1 is made at time / = - , calculate the value to which it will have accumulated by time / =6. [6] (iii) Calculate the accumulated value after 6 months of an investment of $100 at time 0 at the following rates of interest: (a) a force of interest of 0.05 pa (b) a rate of interest of 5% pa convertible monthly (c) an effective rate of interest of 5% pa. [3] [Total 1 1](i) The following data relates to the assets of an investment fund: Date Market value 1 January 2002 $4.2m 1 January 2003 $4.6m 1 January 2004 $5.1m 1 July 2004 $5. 1m 31 December 2004 $5.5m The only cashflow during the calendar years 2002, 2003 and 2004 that was not generated from the assets of the fund was a payment of $800,000, received by the fund on 30 June 2004. For the period from 1 January 2002 to 31 December 2004 calculate: (a) the money-weighted rate of return (b) the time-weighted rate of return (c) the linked annual rate of return (using equal year-long linking periods). Express your answers as annual rates rounded to the nearest 0. 1%. [8] (ii) A second fund was found to have a money-weighted rate of return of 3.5% pa and a time-weighted rate of return of 3.5% pa. Compare the relative performance of the two fund managers. [2] [Total 10]Partan is a quoted company. The directors have asked for a report on the company's cost of capital. The following information has been provided: . The market capitalisation of the company's equity is E600 million. . The company has debentures with a face value of E250 million. Their market value is E220 million. . The corporation tax rate is 23%. The risk-free rate of interest is 4% per annum . The ungeared beta on Partan's equity is 1.3. . The debentures have a coupon rate of 5% and are redeemable at par in five years' time. . The market rate of return is 9% p.a. The directors have already calculated Partan's weighted average cost of capital (WACC), but they wish you to prepare a calculation in order to confirm their figures. They are concerned that the WACC is higher than they think is justified and they wish to discuss some proposals for reducing the figure because the directors plan to raise further finance in order to fund expansion, but they are unwilling to do so if the cost of capital is overstated. (i) Determine Partani's cost of equity using the company's geared beta. [4] (ii) Determine Partan's approximate cost of debt. [4] (iii) Calculate Partan's WACC. [2] The marketing director has suggested that the company could dramatically reduce the cost of capital if the board promotes the company in the same way that it promotes its products. The directors should identify the market's needs and explain to those who provide finance just how well suited Partan is to meeting those needs. (iv) Discuss the logic of the marketing director's proposal for reducing the WACC. [10] [Total 20]
