Finance: Time Value, Risk and Return, and Capital Budgeting
Core concepts
Finance questions cover the time value of money (present and future value, annuities), risk and return (expected return, standard deviation, diversification), cost of capital, and capital budgeting tools such as net present value, internal rate of return, and payback period. Understand that money today is worth more than the same amount later because of opportunity cost and risk.
Traps to watch
Common errors include discounting at the wrong rate, mixing nominal and effective rates, and accepting a project on payback alone when it ignores cash flows after the cutoff. Remember that NPV and IRR can conflict when project sizes or timing differ; NPV is generally preferred because it measures value added. Higher risk raises the required return and lowers present value.
Worked example
A project costs 1,000 and returns 1,100 after one year. At a 12% required return, present value of the inflow is 1,100 / 1.12 = 982.14, so NPV = −17.86. Since NPV is negative, reject. Rule of thumb: accept a project when NPV is positive, meaning the return exceeds the required rate.
Strategy
Draw a simple timeline, place cash flows on it, and discount each to time zero. Compute NPV before IRR because it is less error-prone. Sanity-check results: a discount rate above the IRR must give a negative NPV.