Consider the following cash flows (CF's)
(i) A single CF at t=5 of $15,000
(ii) A single CF at t=11 of of $10,000 and (111) A single cash flow CF at t=18 of $15,000 Calculate the present value of these CF's at time t=0 interest is 4 percent compounded each period.
To calculate the present value of cash flows, we need to discount them back to time t=0 using the interest rate and the number of periods.
For cash flow (i), we have a single cash flow of $15,000 at t=5. To calculate its present value at t=0, we need to discount it back by 5 periods using the given interest rate of 4 percent.
The formula to calculate the present value of a single future cash flow is:
PV = CF / (1 + r)^n
where PV is the present value, CF is the cash flow, r is the interest rate, and n is the number of periods.
Using this formula, we can calculate the present value of cash flow (i) as:
PV(i) = $15,000 / (1 + 0.04)^5
PV(i) = $15,000 / (1.04)^5
PV(i) = $15,000 / 1.2166529
PV(i) ≈ $12,338.52
For cash flows (ii) and (iii), we have similar calculations:
PV(ii) = $10,000 / (1 + 0.04)^11
PV(ii) ≈ $10,000 / 1.5834275
PV(ii) ≈ $6,312.32
PV(iii) = $15,000 / (1 + 0.04)^18
PV(iii) ≈ $15,000 / 2.1914671
PV(iii) ≈ $6,850.03
To find the total present value of these cash flows, we simply sum up the present values of each cash flow:
Total PV = PV(i) + PV(ii) + PV(iii)
Total PV ≈ $12,338.52 + $6,312.32 + $6,850.03
Total PV ≈ $25,500.87
Therefore, the present value of the cash flows at time t=0 is approximately $25,500.87