2019年4月英国精算师-精算数学真题

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  10 April 2019 (am)

  

  Subject CM1B – Actuarial Mathematics Core Principles

  

  1 A loan of £250,000 is taken out at an effective rate of interest of 3.5% per annum for the frst three years and an effective rate of interest of 7.5% per annum thereafter.


  For the frst 18 months, no loan repayments are made. After this time, level loan repayments are made monthly in arrears such that the loan will be fully repaid 25 years after it is taken out. If repayments are insuffcient to cover the interest due then the loan will be increased to cover the shortfall.


  Construct the loan schedule.


  2 A coffee company is opening a new store in a large town. The company purchased the premises for £500,000 on 1 January 2019. The total cost of refurbishing the premises will be £1,500,000 which will be incurred in six equal instalments payable monthly in advance with the frst payment made on 1 October 2019.


  The store is expected to open on 1 May 2020 and is expected to sell cups of coffee each month as shown in the base sheet of the CM1 Q2 workbook, with each cup of coffee assumed to sell for £3. All income from coffee sales can be assumed to be received continuously during the month.


  The costs of staffng and maintaining the new store will be £10,000 per month payable continuously from 1 May 2020 and it is assumed that these will increase on each 1 September by 2% per annum effective. It is also assumed that all costs and income will cease at the end of 2030.


  The risk discount rate is 12% per annum effective.


  (i) (a) Calculate the net present value of the proposed store and determine whether the store is proftable.


  (b) Calculate the discounted payback period to the nearest month.


  (c) Calculate the internal rate of return.


  The company now assumes that the price of cups of coffee increases by 5% at the start of each calendar year, with the frst increase on 1 January 2023.


  (ii) Calculate the revised net present value.


  (iii) Comment on your answers to part (i)(a) and part (ii) and the suitability of the


  underlying assumptions made.



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