SOLUTION: Asset X generates a perpetual stream of cash flows of $100,000 every 3 months. The relevant interest rate is 12%, compounded quarterly. How much would you pay to buy Asset X today

Question 1200990: Asset X generates a perpetual stream of cash flows of $100,000 every 3 months. The relevant interest rate is 12%, compounded quarterly. How much would you pay to buy Asset X today if the first payment occurs right away? (5 marks)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the stream of payments is 100,000 evry 3 months, starting right away.
the interest rat is 12% compounded quarterly = 3% per quarter.

pv = c/r is the formula used.
pv is the present value
c is the perpetual cash flow every time period.
r is the interest rate per time period.

the pv in this problem is equal to 100,000 / 3% which is equal to 100,000 / .03 which is equal to 3,333,333.333333.........

this is equal to 3,333,333.33, when rounded to the nearest penny.

thisi assumes the payments are made at the end of each time period.

if the payment are made at the beginning of each time period, then the present value is 100,000 more to be equal to 3,433,333.33.

i used the texas instruments business analyst 2 to determine this.

it can also be done with the finanicial calculator at https://arachnoid.com/finance/, as shown below.

the present value of the first payment made right away is the the first payment.
that is added to the total present value from the formula.

note that i should have entered the payment as positive because that would be money coming in.
in that case, the present value would have been negative because what would be money going out (how much you would invest).

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