Calculating the Initial Cash Outlay for BackInSoon, Inc. Project

B

To calculate the initial cash outlay (ICO) required for a project, we need to find the present value (PV) of all cash inflows, including the terminal benefit, using the required rate of return (RRR) as the discount rate. Then, we subtract this present value from the initial investment to get the ICO.

The formula for the present value of a cash inflow is:

PV = CF / (1 + RRR)^n

Where: CF = Cash flow in year n RRR = Required rate of return n = Number of years from the present (i.e., year 0)

For the proposed project, we have:

• 10-year annual net cash benefit of $2,500
• Terminal benefit of $5,000 at the end of the tenth year
• Required rate of return of 8%

To calculate the present value of the annual cash inflows, we can use the formula:

PV_annuity = CF * [1 - (1 + RRR)^(-n)] / RRR

Where: CF = Cash flow per period (i.e., $2,500) RRR = Required rate of return n = Number of periods (i.e., 10 years)

Using this formula, we get: PV_annuity = $2,500 * [1 - (1 + 0.08)^(-10)] / 0.08 PV_annuity = $2,500 * [1 - 0.4632] / 0.08 PV_annuity = $2,500 * 6.0649 PV_annuity = $15,162.25

To calculate the present value of the terminal benefit, we can simply discount it back to year 0 using the required rate of return: PV_terminal = $5,000 / (1 + 0.08)^10 PV_terminal = $2,336.96

Now, we can find the total present value of all cash inflows: PV_total = PV_annuity + PV_terminal PV_total = $15,162.25 + $2,336.96 PV_total = $17,499.21

Finally, we can calculate the initial cash outlay using the formula: ICO = PV_total - Terminal Benefit ICO = $17,499.21 - $5,000 ICO = $12,499.21

Therefore, the answer is not one of the given options. None of the answer options match the calculated ICO of $12,499.21.