Question

For the cash flows shown table below, evaluate the unknown value, X for an interest rate of

6% compounded annually.
Year 0 1 2 6
Cash Flow in $ 20,000 -5,000 -10,000 X
a. $5,000
b. -$9,054
c. $6,377
d. $8,252
-Please help me find the values in the formula (P/F, i, n) i am confused on what goes in p and f. NEED THIS ASAP BEFORE 2:20 pm July 8th 2022

Answer 1

To find the value of X, the unknown cash flow at year 6, we must use the present value formula and balance the net present value equation using the cash flows provided and an interest rate of 6%. The value of X can be determined by equating cash inflows and outflows to zero.

Step-by-step explanation:

The question is asking to determine the unknown cash flow (X) at year 6 for a given set of cash flows, using an interest rate of 6% compounded annually. In the formula (P/F, i, n), 'P' stands for the present value of a single future sum, 'F' is the future sum of money that is being valued, 'i' is the interest rate, and 'n' is the number of periods until payment or receipt of the sum occurs. To solve for X, we need to calculate the present value of all cash flows and set their sum equal to zero, as they should balance out at an interest rate of 6%.

Let's start by calculating the present value of the cash flow received at year 6. We'll denote it as PV(X). Since no specific formula or set of formulas was specified in the question, we'll use the fundamental present value formula:

PV(X) = X / (1 + 0.06)6

We want the net present value of all cash flows to be zero, so:

20,000 - 5,000 / (1 + 0.06) - 10,000 / (1 + 0.06)2 + PV(X) = 0

Plugging PV(X) into the equation and solving for X will give us the value of the unknown cash flow at year 6, which can then be compared with the answer options to identify the correct answer.

Answer 2

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.