Which of the following is true for calculating the present value of multiple cash flows?

• A. The present value is calculated by multiplying all cash flows by the discount rate.
• B. Only the final cash flow needs to be discounted to the present.
• C. All cash flows can be added together first and then discounted as a lump sum.
• D. Each cash flow should be discounted to the present separately and then summed.

Answer: (D)

Verified step by step guidance

1. Understand the concept of present value: Present value (PV) is the current worth of a future sum of money or stream of cash flows, given a specified rate of return (discount rate). It accounts for the time value of money, which states that money today is worth more than the same amount in the future due to its earning potential.
2. Recognize the principle for multiple cash flows: When calculating the present value of multiple cash flows, each individual cash flow must be discounted separately to account for the time value of money. This ensures that each cash flow is adjusted for its specific timing.
3. Apply the formula for present value: The formula for the present value of a single cash flow is PV = \( \frac{CF}{(1 + r)^t} \), where CF is the cash flow, r is the discount rate, and t is the time period. For multiple cash flows, this formula is applied to each cash flow individually.
4. Sum the discounted cash flows: After calculating the present value of each cash flow separately, add all the discounted values together to determine the total present value of the cash flows.
5. Avoid common misconceptions: Do not multiply all cash flows by the discount rate, as this does not account for the time value of money. Similarly, do not add all cash flows together first and discount them as a lump sum, as this approach ignores the timing of individual cash flows.