In discounted cash flow (DCF) analysis for chemical engineering projects, how does increasing the assumed DCF rate of return (i.e., the discount rate) affect the ratio of total present value (PV of all future net cash flows) to the initial investment? Provide the qualitative trend clearly.

Introduction / Context:
Discounted cash flow (DCF) analysis converts future cash flows into their present worth using a discount rate. This question checks your understanding of how the chosen discount rate influences the attractiveness of a project, specifically the ratio: total present value (sum of discounted net cash inflows) divided by the initial investment amount.

Given Data / Assumptions:

• Initial investment occurs at time zero.
• Future net cash inflows occur at positive times (t > 0).
• Discount rate r is used to compute present value: PV = Σ (Cash_t / (1 + r)^t).
• Project risk and timing remain the same while r varies.

Concept / Approach:
Present value decreases as the discount rate increases because each future cash flow is divided by a larger compounding factor. Therefore, the sum of discounted cash flows falls. Since the initial investment is a fixed denominator, the ratio PV / Initial Investment declines as r rises. This is the same monotonic behavior seen in net present value (NPV) vs. discount rate graphs and is consistent with the definition of the internal rate of return where NPV crosses zero.

Step-by-Step Solution:
Write PV(r) = Σ Cash_t / (1 + r)^t for t = 1 to n.Increase r to r + Δr with Δr > 0.Each term Cash_t / (1 + r + Δr)^t becomes smaller than Cash_t / (1 + r)^t.Hence PV(r + Δr) < PV(r) and PV(r + Δr) / Initial Investment also decreases.

Verification / Alternative check:
Plot NPV(r). The curve slopes downward with r. Since PV/Initial Investment = (NPV + Initial Investment)/Initial Investment, it also trends downward with r, confirming the conclusion.

Why Other Options Are Wrong:
Increases / Increases linearly: Contradicts discounting; higher r reduces present value.Remains constant: Impossible unless all future cash flows are zero.

Common Pitfalls:

• Confusing nominal and real rates; the monotonic decrease holds for either as long as the rate increases.
• Assuming proportional (linear) behavior; the relationship is nonlinear due to compounding.

Final Answer:
decreases