Suppose a third project will cost $20,000 today and yield a return of $2,500 a year indefinitely. What is the present value of the project? What is the present value if the interest rate increases to 20%?
Seeing $2500 a year is a perpetuity, as it continues indefinitely, assume the interest rate to be 8%.
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That is correct.
The PV of a perpetuity with interest rate of r is given as PV = C/r
where C is the yearly return.
a correction on scenario 2, the calculations are wrong.
Scenario 2: PV = -20,000 + 2500/(0.2) = -20,000 + 12500 = -$7,500
The outcome is still unfavorable due to high interest rate.
sorry about the error....
I think I'm still confused.
As I understood, the present value of receiving a sum each year forever equals the amount received each year divided by the interest rate?
When trying to figure this, I used the formula;
Present value of receiving M dollars
each year forever = M (dollars) / I (interest)
The present cost = $20,000
The PV of scenario 1 = - 20,000 + 2500/(0.08) = $11,250
For scenario 2, PV = -20,000 + 2500/(0.2) = -$15,000
(using the formula for PV of a perpetuity, PV = C/r, where C is the annual return and r is the rate of interest).
So, in this case, scenario 2, with a higher interest rate is not a favorable outcome, i.e. an increase in interest rate will reduce the PV of the perpetuity.
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