CFA CFA Level 1 Question to be solved from CFA Level 1 mock – Perpetuity

Question to be solved from CFA Level 1 mock – Perpetuity

  • This topic has 1 reply, 2 voices, and was last updated Jan-18 by krishTa.
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    • cool_khanarohan
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      Kindly help me in answering the following question:

      Reena, a
      successful inventor has decided to set up a scholarship fund for deserving at
      her Alma matter. Her plan is for fund to the capable of awarding $25000
      annually in perpetuity the first scholarship is to be awarded and paid out
      exactly four years from today. The fund will be deposited into an account
      immediately and will grow at a rate of 4%, compounded semiannually for the
      foreseeable future. How much money must the inventor donate today to fund the scholarship?

      a.      
      $545,789

      b.     
      $549,487.

      c.      
      $543,254 

    • krishTa
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      This can be solved in 2 steps.
      Time line 1 -> What is the amount that Reena need to deposit to award $25,000 annually @ 4% semi annually, starting from next year
      Step 1 -> calculate Effective Annual rate which is ((1 + r/m)^m) -1. Hence EAR = ((1+0.04/2)^2) -1 = 4.04%
      Step 2 -> PV of a perpetuity where annual return is $25,000 and rate of return is 4.04% is A/r = 25,000/0.0404 = 618,811.88
      Time line 2 -> What is the amount that Reena needs to deposit now so that the deposit is 618,811.88 by the end of 3 years @4% semi annually
      This is simple TVM problem where FV = 61,8811.88, r = 4.04, N = 3. I got the answer $549,487.24
      Option b.

      Hope I am correct
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