Question

A commercial development project requires annual outlays of $65,000 for 10 years. Net cash inflows beginning in year 11 are expected to be $170,000 per year for 20 years. If the developer requires a rate of return of 16% , compute the net present value of the project.

Answer 1

Net Present Value = - $99,360

Explanation:

As provided,

Cash outlay = $65,000 each year for 10 years

Since the first outlay will be immediately, the cumulative discounting factor for cash outlay will be @ 16% = 1 for year 0 + 4.606 for 9 years = 5.606

Therefore, cumulative present value of total cash outlay = $65,000
`*` 5.606 = $364,390

Cash inflows beginning in year 11 = $170,000 for another continuous 20 years.

these cash flow will occur in the beginning of year 11 and end of year 10

Discounting factor will be
`(1)/((1+0.16)^1^0)` = 0.2267

For, consecutive 20 years = 1.559

Therefore, value of inflows = $170,000
`*` 1.559 = $265,030

Net Present Value = Present Value of Cash Inflows - Present Value of Cash Outflows = $265,030 - $364,390 = - $99,360