To determine the maximum amount you would pay for an asset that generates an income of $250,000 at the end of each of five years, we need to calculate the present value of these cash flows using the opportunity cost of funds, which is 8 percent.
The present value (PV) of each cash flow can be calculated using the formula:
PV = CF / (1 + r)^n
Where:
CF = Cash flow
r = Interest rate (opportunity cost of funds)
n = Number of periods
In this case:
CF = $250,000
r = 8% or 0.08
n = 5
Calculating the present value of each cash flow:
PV1 = $250,000 / (1 + 0.08)^1 = $231,481.48
PV2 = $250,000 / (1 + 0.08)^2 = $214,466.02
PV3 = $250,000 / (1 + 0.08)^3 = $198,675.50
PV4 = $250,000 / (1 + 0.08)^4 = $184,015.50
PV5 = $250,000 / (1 + 0.08)^5 = $170,408.04
To find the maximum amount you would pay for the asset, we sum up all the present values:
PV_total = PV1 + PV2 + PV3 + PV4 + PV5
= $231,481.48 + $214,466.02 + $198,675.50 + $184,015.50 + $170,408.04
= $999,046.54
Therefore, the maximum amount you would pay for the asset is approximately $999,046.54.
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