Final answer:
To find the unknown value X for the given cash flows at a 6% interest rate, apply the present value formula for each cash flow and solve for X by setting the sum of all present values to zero.
Step-by-step explanation:
To evaluate the unknown cash flow value, X, for an interest rate of 6% compounded annually, we need to calculate the present value of cash flows and set it to zero to solve for X. In the given cash flow table, we have an initial cash flow at Year 0 (+$20,000), cash flows at Year 1 (-$5,000), Year 2 (-$10,000), and Year 6 (X). The present value (PV) formula for cash flows is PV = CF / (1 + i)^n, where CF is the cash flow, i is the interest rate, and n is the number of years t.
For Year 1, the present value of the cash flow would be $5,000 / (1 + 0.06)^1, for Year 2, it would be $10,000 / (1 + 0.06)^2, and for Year 6, the present value of X must be calculated as X / (1 + 0.06)^6. By adding all these present values, including the initial cash flow, and setting their sum to zero, we can solve for X.
Example: Think about a simple two-year bond. It was issued for $3,000 at an interest rate of 8%. At the end of the second year, the bond pays $240 in interest, plus the $3,000 in principle. The present value of this bond with a discount rate of 8% illustrates the application of the present value formula very similarly to our original problem with cash flows.