Finance: Time Value of Money and Investment Appraisal
Core concepts
A candidate must command compounding and discounting, present and future values of single sums and annuities, and net present value (NPV), internal rate of return (IRR), payback and the profitability index. Understand the cost of capital as the discount rate, and the weighted average cost of capital (WACC) as a blend of after-tax debt and equity costs. Know the relationship between risk and required return, and the difference between nominal and effective rates.
Traps in questions
- Timing of cash flows. An annuity due (cash at the start of each period) is worth more than an ordinary annuity; multiply by (1 + r).
- Tax and depreciation. Depreciation is not a cash flow, but the tax saving on it (depreciation × tax rate) is.
- Mutually exclusive projects. NPV and IRR can conflict; NPV is preferred because it measures value added in absolute terms.
- Sunk costs and financing costs. Exclude sunk costs; do not deduct interest if the WACC already reflects financing.
- Perpetuity growth. A growing perpetuity is valued as CF₁ / (r − g); the numerator must be the next period's cash flow.
Rule of thumb
Discount every cash flow to today at the opportunity cost of capital, then accept projects with positive NPV. If NPV is positive, value is created.
Worked example
A project costs KES 100,000 and returns KES 60,000 in each of years 1 and 2. At 10%, PV = 60,000/1.10 + 60,000/1.21 = 54,545 + 49,587 = KES 104,132. NPV = 104,132 − 100,000 = KES 4,132, so accept.