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 ( (1 -(1+r)^(-n))/(r) \right )`

Substituting the values we get,

`PV_(Annuity) = 25000 * \left ( (1 -(1+0.15)^(-3))/(0.15) \right )`

`PV_(Annuity) = 25000 * \left ( (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}`