Question

Suppose you are considering a project that will generate quarterly cash flows of $17143 at the beginning of each quarter for the next 11 years. If the appropriate discount rate for this project is 13%, how much is this project worth today? Round to the nearest cent.

Answer 1

Here, the cash inflows will be same every quarter, so it is an annuity. And since the cash flows will start at the beginning of each quarter so it will be termed as an annuity due. For calculating the present value of annuity due, we will use the following formula:

PVAD = P * (1 - (1 / (1 + r)ⁿ / r) * (1 + r)

where, PVD is the present value of annuity due, P is the periodical amount = $17143, r is the rate of interest = 13%/ 4 = 3.25% quarterly rate and n is the time period = 11 * 4 = 44 quarter years.

Present worth of the project = Present value of annuity of $17143 at 3.25% for 44 quarter years

Now, putting these values in the above formula, we get,

PVAD = $17143 * (1 - (1 / (1 + 3.25%)⁴⁴ / 3.25%) * (1 + 3.25%)

PVAD = $17143 * (1 - (1 / (1 + 0.0325)⁴⁴ / 0.0325) * (1 + 0.0325)

PVAD = $17143 * (1 - (1 / (1.0325)⁴⁴ / 0.0325) * (1.0325)

PVAD = $17143 * (1 - (1 / 4.08472341084) / 0.0325) * (1.0325)

PVAD = $17143 * (1 - 0.244814617642) / 0.0325) * (1.0325)

PVAD = $17143 * (0.755185382358 / 0.0325) * (1.0325)

PVAD = $17143 * (23.2364733) * (1.0325)

PVAD = $411289

So, the project is worth $411289 today.