East Coast Television is considering a project with an initial outlay of $X ( you will have to determine this amount) It is expected that the project will produce a positive cash flow of $60,000 a year at the end of each year for the next 16 years. The appropriate discount rate for this project is 11%. If the project has an internal rate of return of 16 percent, what is the present value?
To find the initial outlay (X) and the present value of the project, we can use the net present value (NPV) formula. NPV calculates the present value of cash inflows and outflows, taking into account the discount rate.
The formula for NPV is:
NPV = Cash Inflows - Cash Outflows / (1 + Discount Rate)^n
In this case, we have positive cash inflows of $60,000 a year for 16 years. The discount rate is 11%, and the internal rate of return (IRR) is 16%.
To find the initial outlay, we need to calculate the present value at the IRR. If the present value at the IRR is zero, it means the project's cash inflows equal the initial outlay.
Let's calculate the initial outlay using the NPV formula:
0 = X - [$60,000 / (1 + 0.16)^1] - [$60,000 / (1 + 0.16)^2] - ... - [$60,000 / (1 + 0.16)^16]
Note that the cash inflows occur at the end of each year, so we use the discount rate to calculate the present value.
We can solve this equation for X by rearranging it as follows:
X = [$60,000 / (1 + 0.16)^1] + [$60,000 / (1 + 0.16)^2] + ... + [$60,000 / (1 + 0.16)^16]
Now we can calculate the present value by using the formula:
PV = [$60,000 / (1 + 0.11)^1] + [$60,000 / (1 + 0.11)^2] + ... + [$60,000 / (1 + 0.11)^16]
By substituting the values into the equation, you can calculate the present value.