Question 1085994: You have an annuity at a fianacial instiution. the installments is yearly and the first installment of R 10 000 is payable at the end of the first year. the contract period is 20 years. the payment escalates yearly with 10%. the capitalization rate is 12%, compounded yearly, what is the present value of the contract?
Found 2 solutions by Theo, JuanKoss:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! first installment is 10,000
each additional installment is multiplied by 1.10
that means your inflation rate is 10% per year.
your discount rate is 12% per year.
your effective discount rate is equal to (1 + dr) / (1 + ir) = 1.12 / 1.10 = 1.01818181818........ - 1 = .0181818181818 * 100% = 1.818181818.....%
one more adjustment needs to be made.
the first payment is 10,000 at the end of the first year.
when you use the composite discount rate, the payments need to be effective at the start of the analysis, which is at the beginning of year 1, also known at time point 0.
because of this, you need the annual payment to be equal to 10,000 / 1.10 = 9090.909091.
the calculator will tell you that the present value of annual payments of 9091.909091 for 20 years at the composite discount rate of 1.8181818...% per year is $151,290.92
the result of the calculation is shown below:
if you treat this as a cash flow problem, you will find that you get the same present value.
i used excel and this is what i got:
i also used excel to show you the difference between inflating the annual charges each year by 10% starting in time point 2 and then dividing by the discount rate of 12% to get the present value cash flows.
this is compared to finding the composite discount rate of (1.12/1.10 - 1) * 1005 = 1.8181818%, adjusting the 10,000 in time point 1 so that it will be equal to 10,000 in time point 1 after inflating by 10%, and then solving for the present value of cash flows using the composite discount rate.
the present value of cash flows is the same as it should be.
hopefully this makes sense to you.
if not, come back with questions and i'll try to answer as best i can.
Answer by JuanKoss(3)  (Show Source):
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