Final answer:
The student's business-related question involves calculating the present value of two investment alternatives considering a 16% discount rate, to evaluate which investment is preferable. It uses the formula PV = FV / (1 + r)^n for each cash flow from the investments. The investment with the higher total present value is the preferred one.
Step-by-step explanation:
The student's question involves computing the present value of two different investment alternatives, considering a discount rate, to determine which investment option is preferred. To calculate the present value of each alternative, we will use the formula for the present value of a future amount:
PV = FV / (1 + r)^n
where PV is the present value, FV is the future value, r is the rate of return (in decimal form), and n is the number of years until the payment is received.
To solve the student's question, we will apply this formula to both Alternative 1 and Alternative 2, considering a 16% rate of return, which is 0.16 in decimal form.
For Alternative 1, we have two future payments:
- $35,000 in five years: PV = $35,000 / (1 + 0.16)^5
- $70,000 in six years: PV = $70,000 / (1 + 0.16)^6
For Alternative 2, we have six annual payments of $12,000:
- PV (years 1-6) = $12,000 / (1 + 0.16)^1 + $12,000 / (1 + 0.16)^2 +...+ $12,000 / (1 + 0.16)^6
After calculating the present values using the formulas above, we sum them to get the total present value for each alternative. The alternative with the higher present value is the preferred choice, as it represents a greater value in today's dollars.