Cash flow analysis, NPV and IRR

2 free worked examples

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1. Exam FMCash flow analysis, NPV and IRRCore

   A project costs 50,000 now and returns 18,000, 22,000 and 25,000 at the ends of years 1 to 3. Find the NPV at 9%.

   1. A$-4,335.31$
   2. B$0.00$
   3. C$4,335.31$
   4. D$15,000.00$
   5. E$54,335.31$

   Solution

   1. Discount each inflow at 9% and subtract the outlay, which is NOT discounted because it occurs at time 0.
   2. $18,000(0.917431)=16,513.76$; $22,000(0.841680)=18,516.96$; $25,000(0.772183)=19,304.58$.
   3. Total inflows: $54,335.31$.
   4. $NPV=54,335.31-50,000=4,335.31$, so the project clears the 9% hurdle.

   Trap. Discounting the initial outlay by one period, which overstates the NPV by about 4,100.

2. Exam FMCash flow analysis, NPV and IRRCore

   Which return measure is designed to judge an investment MANAGER rather than the investor's own timing?

   1. ADollar-weighted return
   2. BTime-weighted return
   3. CInternal rate of return
   4. DCurrent yield
   5. ENominal yield

   Solution

   1. The time-weighted return chains sub-period growth factors, so the size and timing of deposits cancel out.
   2. That isolates the performance of the underlying investments, which is what a manager controls.
   3. The dollar-weighted return (an IRR on the fund's cash flows) does depend on timing, which is what the INVESTOR controls.
   4. A manager who performs well while investors add money at the wrong moments will show a good time-weighted and a poor dollar-weighted return.