"You are told you will receive the following cash payments at the end of the next three years:
Year 1: $10,000
Year 2: $25,000
Year 3: $50,000
Assuming a discount rate of 12%, what is present value of all payments?"
To calculate the present value of future cash payments, you need to discount each payment to its present value using the given discount rate. The present value formula is:
PV = FV / (1 + r)^n
Where:
PV = Present Value
FV = Future Value
r = Discount Rate
n = Number of periods
Let's calculate the present value of each cash payment and then sum them up:
For Year 1: FV = $10,000, r = 12%, n = 1
PV1 = $10,000 / (1 + 0.12)^1 = $8,928.57
For Year 2: FV = $25,000, r = 12%, n = 2
PV2 = $25,000 / (1 + 0.12)^2 = $19,580.11
For Year 3: FV = $50,000, r = 12%, n = 3
PV3 = $50,000 / (1 + 0.12)^3 = $36,493.16
Now, add up all the present values:
PV = PV1 + PV2 + PV3
PV = $8,928.57 + $19,580.11 + $36,493.16
PV = $64,001.84
Therefore, the present value of all the cash payments is $64,001.84 when assuming a discount rate of 12%.