Question 1168821
Let's break down this Net Present Value (NPV) calculation step-by-step.

**1. Calculate the Present Value (PV) of the Costs**

* **Equipment Cost:**
    * This is an upfront cost, so its present value is simply $14,000.
* **Space Rental Costs:**
    * These are annual costs of $7,400, forming an annuity. We need to find the present value of this annuity.
    * PV of annuity = Annual payment * [1 - (1 + r)^-n] / r
        * Where:
            * Annual payment = $7,400
            * r = discount rate = 6% or 0.06
            * n = number of years = 25
    * PV of space rental = $7,400 * [1 - (1 + 0.06)^-25] / 0.06
    * PV of space rental = $7,400 * [1 - (1.06)^-25] / 0.06
    * PV of space rental = $7,400 * [1 - 0.23299] / 0.06
    * PV of space rental = $7,400 * 0.76701 / 0.06
    * PV of space rental = $7,400 * 12.7835
    * PV of space rental = $94,597.9

* **Total PV of Costs:**
    * Total PV of costs = Equipment cost + PV of space rental
    * Total PV of costs = $14,000 + $94,597.9 = $108,597.9

**2. Calculate the Present Value (PV) of the Income**

* **Annual Income:**
    * The ice cream cakes will provide an extra income of $13,000 per year, forming an annuity.
* **PV of Income:**
    * PV of income = Annual income * [1 - (1 + r)^-n] / r
        * Where:
            * Annual income = $13,000
            * r = discount rate = 6% or 0.06
            * n = number of years = 25
    * PV of Income = $13,000 * [1 - (1 + 0.06)^-25] / 0.06
    * PV of Income = $13,000 * [1 - (1.06)^-25] / 0.06
    * PV of Income = $13,000 * [1 - 0.23299] / 0.06
    * PV of Income = $13,000 * 0.76701 / 0.06
    * PV of Income = $13,000 * 12.7835
    * PV of Income = $166,185.5

**3. Calculate the Net Present Value (NPV)**

* NPV = PV of income - PV of costs
* NPV = $166,185.5 - $108,597.9
* NPV = $57,587.6

**Therefore, the Net Present Value of the ice cream cake project is approximately $57,587.60.**