Final answer:
The present value of the expected cash flows ($1,082,375) from the investment is greater than the initial investment ($1 million) when using a 5% discount rate. Therefore, it would be a sound decision to invest in the business, assuming all other factors remain constant. The correct option is a.
Step-by-step explanation:
To determine whether it is a sound decision to invest $1 million in a business that is expected to generate cash flows of $250,000 per year over the next five years with a 5% discount rate, we can use the Present Value (PV) of an annuity formula:
PV = C * [(1 - (1 + r)⁻tⁿ) / r]
Where:
- C = Annual cash flow ($250,000)
- r = Discount rate (5% or 0.05)
- n = Number of periods (5 years)
Plugging the values into the formula gives us:
PV = $250,000 * [(1 - (1 + 0.05)⁻⁵) / 0.05]
PV = $250,000 * 4.3295
PV = $1,082,375
The total Present Value of the expected cash flows is $1,082,375. Since this value is greater than the initial investment of $1 million, it indicates that the investment would be worthwhile under the given conditions.
However, the real world involves uncertainties like future market conditions and potential capital gains or dividends. Nonetheless, from a purely mathematical perspective, the investment seems sound based on the presented cash flows and discount rate.
Hence, Option a is correct.