EMAR expects to receive $2,000 per year for 10 years and $3,500 per year for the next 10 years. What is the present value of this 20-year cash flow? Use an 7% discount rate.
What did you get so far ?
To calculate the present value of the cash flow, we need to find the present value of each individual cash flow and then sum them together.
Let's calculate the present value of the $2,000 per year cash flow for 10 years. We can use the formula for the present value of an annuity:
PV = Pmt * [1 - (1+r)^(-n)] / r
Where:
PV = Present Value
Pmt = Payment per year
r = Discount rate
n = Number of years
Plugging in the values:
Pmt = $2,000
r = 7% (0.07)
n = 10
PV1 = $2,000 * [1 - (1+0.07)^(-10)] / 0.07
PV1 ≈ $2,000 * (1 - 0.5084) / 0.07
PV1 ≈ $2,000 * 0.4916 / 0.07
PV1 ≈ $2,000 * 7.0228/0.07
PV1 ≈ $140,456
Now, let's calculate the present value of the $3,500 per year cash flow for the next 10 years using the same formula:
Pmt = $3,500
r = 7% (0.07)
n = 10
PV2 = $3,500 * [1 - (1+0.07)^(-10)] / 0.07
PV2 ≈ $3,500 * (1 - 0.5084) / 0.07
PV2 ≈ $3,500 * 0.4916 / 0.07
PV2 ≈ $3,500 * 7.0228/0.07
PV2 ≈ $245,080
Finally, to find the present value of the entire 20-year cash flow, we sum the present values of each cash flow:
Present Value = PV1 + PV2
Present Value ≈ $140,456 + $245,080
Present Value ≈ $385,536
Therefore, the present value of this 20-year cash flow is approximately $385,536.