Question

13. NPV versus IRR Consider the following two mutually exclusive projects: Year Cash Flow (X) Cash Flow (Y) -$10,000 -$10,000 5,400 4,500 3,400 3,600 4,500 5,400 Sketch the NPV profiles for X and Y over a range of discount rates from zero to 25 percent. What is the crossover rate for these two projects?

Answer 1

In the following excel screenshots, Formula used for NPV is +NPV(Interest rate, B4:B6)+B3 for Project X and +NPV(Interest rate, C4:C6) + C3 or Project Y.

BC Year Cash Flow(x) -10000 5400 3400 4500 Cash Flow(Y) -10000 4500 3600 5400

ДА 3 4500 5400 Rate 9 1% 11 15 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 21% 22% 23% 24% 25% NPV(X) $3,047 $2,803 $2,566 $2,336 $2,114 $1,899 $1,690 $1,487 $1,291 $1,100 $915 $735 $560 $390 NPVIY) | $3,226 $2,961 $2,704 $2,456 $2,216 $1,983 $1,758 $1,540 $1,328 $1,123 $924 $731 $544 $362 $186 $14 -$152 -$314 -$472 $625 $774 $919 -$1,060 $1,197 $1,331 22 23 24 $225 27 $65 $91 -$243 $391 $535 -$675 $811 $944 $1,074 $1,200 32 33

At 12% the NPV's are almost equal. Thus, the crossover rate is 12%.

Chart Title $3,500 $3,000 $2,500 $2,000 $1,500 $1,000 $500 $731 So 09 2% 4% 6% 8% 10% 12% 14% 16% * 20% 22% -$500 $1,000 — NPV(X) — NPVM