Question

Suppose you are considering a project that will generate quarterly cash flows of $16429 at the beginning of each quarter for the next 12 years. If the appropriate discount rate for this project is 12%, how much is this project worth today? Round to the nearest cent.

Answer 1

Here, the cash inflow will be same every year, so it is an annuity. And since the cash flows will start at the beginning of each year 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 = $16429, r is the rate of interest = 12% /4 = 3% quarterly rate and n is the time period = 12 * 4 = 48

Present value of cash flows = Present value of annuity of $16429 at 3% for 48 quarter years

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

PVAD = $16429 * (1 - (1 / (1 + 3%)⁴⁸ / 3%) * (1 + 3%)

PVAD = $16429 * (1 - (1 / (1 + 0.03)⁴⁸ / 0.03) * (1 + 0.03)

PVAD = $16429 * (1 - (1 / (1.03)⁴⁸ / 0.03) * (1.03)

PVAD = $16429 * (1 - (1 / 4.13225187926 / 0.03) * (1.03)

PVAD = $16429 * (1 - 0.2419988 / 0.03) * (1.03)

PVAD = $16429 * (0.7580012 / 0.03) * (1.03)

PVAD = $16429 * (25.26670667) * (1.03)

PVAD = $427559.93

So, the project is worth $427559.93