Present Value Calculation

C

The discount factor for 3 years is 1/1.23. Hence, the PV of $500 in 3 years is 500/1.23 = 406.5.

To calculate the present value of the cash flow, we need to discount the future cash flow back to the present using an appropriate discount rate. In this case, since we are given an initial outlay of $1 growing to $1.23 in 3 years, we can calculate the compound annual growth rate (CAGR) using the formula:

CAGR = (Ending Value / Beginning Value)^(1 / Number of Years) - 1

CAGR = ($1.23 / $1)^(1 / 3) - 1 CAGR = 0.0736 or 7.36%

The CAGR represents the annualized growth rate over the 3-year period.

Now, to find the present value of the $500 cash inflow in 3 years, we can use the formula for present value (PV) of a future cash flow:

PV = CF / (1 + r)^n

Where:

• PV is the present value
• CF is the cash flow
• r is the discount rate (in this case, the CAGR)
• n is the number of periods (in this case, 3 years)

Plugging in the values, we have:

PV = $500 / (1 + 0.0736)^3 PV = $500 / 1.2353 PV ≈ $404.89

Therefore, the present value of the cash flow is approximately $404.89.

None of the answer choices provided match this result exactly, but the closest option is C. $406.5.