Invest 500000 today and get 200000 at the end of each year for 4 years if cost of capital is 15%
To calculate the present value of an annuity, we can use the formula:
PV = PMT * (1 - (1 + r)^-n) / r
Where:
PV = Present Value (initial investment)
PMT = Payment (cash flow received each year)
r = Interest rate (cost of capital)
n = Number of periods (years)
Given:
Initial investment (PV) = $500,000
Payment per year (PMT) = $200,000
Interest rate (r) = 15% or 0.15
Number of periods (n) = 4 years
Using the formula, we can calculate the present value:
PV = $200,000 * (1 - (1 + 0.15)^-4) / 0.15
PV = $200,000 * (1 - (1.15)^-4) / 0.15
PV = $200,000 * (1 - 0.50840) / 0.15
PV = $200,000 * 0.49160 / 0.15
PV = $982,320
Therefore, to receive $200,000 at the end of each year for 4 years with a cost of capital of 15%, the present value of this investment would be approximately $982,320.
To calculate the present value of the future cash flows, we need to discount each cash flow back to the present using the cost of capital. The formula to calculate the present value is as follows:
PV = CF / (1 + r)^n
Where:
PV = Present value
CF = Cash flow
r = Cost of capital
n = Number of years
Let's calculate the present value of the cash flows:
Year 1:
PV1 = 200,000 / (1 + 0.15)^1 = 173,913.04
Year 2:
PV2 = 200,000 / (1 + 0.15)^2 = 150,390.63
Year 3:
PV3 = 200,000 / (1 + 0.15)^3 = 130,799.38
Year 4:
PV4 = 200,000 / (1 + 0.15)^4 = 114,347.07
Now, let's add up the present values of all the cash flows:
PV = PV1 + PV2 + PV3 + PV4
= 173,913.04 + 150,390.63 + 130,799.38 + 114,347.07
= 569,450.12
Therefore, the present value of receiving 200,000 at the end of each year for 4 years, with a cost of capital of 15%, is 569,450.12.
Note: If you are investing 500,000 initially, and receiving a total of 800,000 over the 4 years, then the net present value of this investment would be the difference between the total present value of the cash flows and the initial investment:
Net Present Value = PV - Initial Investment
= 569,450.12 - 500,000
= 69,450.12
To determine the value of the investment, we need to calculate the present value of each cash flow and then sum them up. The present value formula is:
PV = CF / (1 + r)^n
Where:
PV = Present value
CF = Cash flow
r = Discount rate (cost of capital)
n = Number of years
Let's calculate the present value for each cash flow and sum them up:
Year 1:
PV1 = 200000 / (1 + 0.15)^1 = 173913.04
Year 2:
PV2 = 200000 / (1 + 0.15)^2 = 151260.50
Year 3:
PV3 = 200000 / (1 + 0.15)^3 = 131478.87
Year 4:
PV4 = 200000 / (1 + 0.15)^4 = 114335.77
Now, we can sum up the present values to determine the total present value:
Total PV = PV1 + PV2 + PV3 + PV4 = 573988.18
Therefore, if you invest 500000 today and receive 200000 at the end of each year for 4 years, with a cost of capital of 15%, the total present value of the investment would be 573988.18.