Ambrin Corp. 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 a 11% discount rate.
To calculate the present value of the cash flow, you need to discount each cash flow back to its present value using the given discount rate. Here's how you can calculate it step by step:
1. Calculate the present value of the first 10-year cash flow of $2,000 per year. Since these cash flows are received annually, you can use the formula for the present value of an annuity:
PV1 = CF * (1 - (1 + r)^(-n)) / r
Where:
PV1 = Present value of the first 10-year cash flow
CF = Cash flow per period ($2,000)
r = Discount rate (11% or 0.11)
n = Number of periods (10 years)
Plugging in the values, the calculation becomes:
PV1 = $2,000 * (1 - (1 + 0.11)^(-10)) / 0.11
2. Calculate the present value of the second 10-year cash flow of $3,500 per year. Again, use the annuity formula:
PV2 = CF * (1 - (1 + r)^(-n)) / r
Where:
PV2 = Present value of the second 10-year cash flow
CF = Cash flow per period ($3,500)
r = Discount rate (11% or 0.11)
n = Number of periods (10 years)
Plugging in the values, the calculation becomes:
PV2 = $3,500 * (1 - (1 + 0.11)^(-10)) / 0.11
3. Finally, the total present value of the 20-year cash flow can be calculated by summing up the present values of the two cash flow streams:
Total PV = PV1 + PV2
Plugging in the calculated values, the final calculation will give you the present value of the 20-year cash flow.
Note: The discount rate represents the opportunity cost of investing money elsewhere, so it's important to consider if using an 11% discount rate is suitable for this analysis.