Question

Sigma Ltd. wants to invest in a project that has an initial investment of $40,000. The project is expected to yield $25,000 every year for the next three years. If the expected rate of return is 15%, what is the Net Present Value (NPV) of this project?
The NPV of the project is $

Answer 1

Answer: The NPV of the project is $17,080.63.

We follow these steps to arrive at the NPV

We first need to calculate the Present value of the cash flows of each of the years.

Since the project yields $25,000 in each of the three years we can treat the $25,000 as an annuity for 3 years and discount it at 15% to find the Present Value.

We use the following formula for this:

$PV_{Annuity} = C * \left ( \frac{1 -(1+r)^{-n}}{r} \right )$

Substituting the values we get,

$PV_{Annuity} = 25000 * \left ( \frac{1 -(1+0.15)^{-3}}{0.15} \right )$

$PV_{Annuity} = 25000 * \left ( \frac{1 -(1+0.15)^{-3}}{0.15} \right )$

$PV_{Annuity} = 25000 * \left ( 0.342483768}{0.15} \right )$

$PV_{Annuity} = 25000 * 2.283225117$

$PV_{Annuity} = 57080.62793$

Next, we calculate NPV as follows:

$\mathbf{NPV = PV of cash flows - investment}$

$\mathbf{NPV = 57080.63 - 40000 = USD 17,080.63}$