Question 1165407: A company is considering a project which requires an investment of Rs. 1,200,000
now and Rs. 300,000 at the end of the 1st year. It will earn Rs. 200,000 at the end of
2nd year and thereafter it will earn a fixed annual amount up to the 7th year.
If interest rate is 11%, find the amount that the project should earn annually i.e.
from year 3 to year 7 if the company desires to earn a net present value of
Rs. 100,000
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! take the first 2 years.
the cash flow is:
end of year 0 = -1,200,000
end of year 1 = -300,000
end of year 2 = +200,000
find the present value of the cash flow at 11% per year.
you will get present value of cash flow (NPV) = -$1,307,945.78
you want a present value of cash flow of +100,000.
the difference is 1,407,945.78
that's in year 0.
multiply that by 1.11^3 to get a present value of cash flow (NPV) at the end of year 3 = 1,925,550.295.
your cash flow becomes:
end of year 0 = -1,200,000
end of year 1 = -300,000
end of year 2 = +200,000
end of year 3 = +1,925,550.295
find the present value of the cash flow at 11.5% per year.
you would get present value of cash flow (NPV) = +100,000.
this tells you the present value of cash flow at the end of year 3 is good.
now you want to change that to an annuity that has a present value of that at the end of year 3.
you would use a financial calculator to give you the annual payment at the end of year 3 to the end of year 7 that will give you a present value of 1,925,550.295 at the end of year 3.
in this calculation, the payments would be made at the beginning of each year.
the calculator will tell you that the annual payment would be 469,366.4318 at the end of year 3 going to the end of year 7.
you would plug that into your cash flow and find that the present value of that cash flow is equla to 100,000.
this is the figure you wanted so you're ok.
i used excel and the ti-ba-ii financial calculator.
the excel takes the annual cash flow and brings it back to the end of year 0 at 11% per year.
the financial calculator finds the annual payments from a present value for 5 years.
the inputs to the calculator are:
present value = -1925550.295 at the end of year 3.
future value = 0
interest rate per year = 11%
number of years = 5 (from end of year 3 to end of year 7 = 5 years of payments).
payments are made at the beginning of each year.
this means the first payment is made at the end of year 3.
the output of that calculator was annual payments of 469,366.43 starting at the end of the third year and going to the end of the 7th year.
the output of the online financial calculator agrees with the output of the ti-ba-ii.
here's a display of the excel spreadsheet used.
the left table is using the present value calculated for end of year 3.
the right table is using the annuity generated from that present value with payments from end of year 3 to end of year 7.
here's a display of an online calculator that does pretty much the same thing that the ti-ba-ii does, only it rounds the answer for you.
input
output
note that the annuity calculation could have been done 2 ways.
when the initial investment is at the end of year 3, the calculations shown above apply.
if you assume the initial investment was at the beginning of year 3 (same as the end of year 2), then the present value would be -1925550.295 divided by 1.11 = -1,734,729.996.
the annuity calculations would then be made assuming end of year payments.
the payment at the end of each year would be the same as the payments at the beginning of each year in the above calculations.
here is the display of the annuity calculations assuming end of year payments.
in both cases, the first payment is made at the end of year 3.
the online calculator that i used that performs the same functions as the ti-ba-ii can be found at https://arachnoid.com/finance/index.html
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