Question 1168821: 1. Wen Seng operates an ice cream shop. He is trying to decide whether to expand his business to include ice cream cakes. He will need some additional space that will cost him $7,400 per year at the end of each year and some additional equipment that will cost $14,000 up front. The ice cream cakes will provide an extra income of $13,000 per year at the end of each year. The business is expected to last 25 years. The discount rate (or interest rate) for Wen Seng's new business is 6%. What is the Net Present Value of the ice cream cake project? (Assume there are no taxes.)
Thank you so much.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! 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.**
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