Net Present Value (NPV) is calculated by discounting future cash flows at the cost of capital ($r$); mathematically, as $r$ increases, the present value of inflows decreases, causing NPV to decrease [1]. Discounted Payback relies on these same present values; as they shrink, it takes longer to recover the initial outlay, causing the period to increase [2]. MIRR assumes positive cash flows are reinvested at the cost of capital; a higher rate creates a larger terminal value, causing MIRR to increase [3].

In contrast, Payback Period (undiscounted), Internal Rate of Return (IRR), and Accounting Rate of Return (ARR) are intrinsic metrics derived solely from the project's cash flows or accounting profits. They do not use the external cost of capital in their calculation formulas and thus stay the same [1][2].

Ross, S. A., Westerfield, R. W., & Jaffe, J. (2013). Corporate Finance (10th ed.). McGraw-Hill Education.Chapter 5 (Net Present Value and Other Investment Rules): Section 5.1 covers NPV's inverse relationship with the discount rate. Section 5.5 covers IRR as a rate intrinsic to cash flows, independent of the market rate.Brealey, R. A., Myers, S. C., & Allen, F. (2019). Principles of Corporate Finance (13th ed.). McGraw-Hill Education.Chapter 5 (Net Present Value and Other Investment Criteria): Page 134 discusses the Payback rule (independent of discounting). Page 136 discusses the Discounted Payback rule.Brigham, E. F., & Ehrhardt, M. C. (2013). Financial Management: Theory & Practice (14th ed.). Cengage Learning.Chapter 10 (The Basics of Capital Budgeting): Page 404, Section 10-5 "Modified Internal Rate of Return (MIRR)". Explicitly defines MIRR using the cost of capital as the reinvestment rate, establishing the direct relationship (Rate $\uparrow$ $\rightarrow$ MIRR $\uparrow$).