CHAPTER 6 ANSWER KEY
6.1 NPV and Stand-Alone Projects
1.
2.
3.
4.
5.
NPV = 909.09. Take it. IRR = 20%. Cost of capital can increase to 20% w/o changing decision.
NPV = -6,193. Do not take it. IRR = 19.58%. Close call.
NPV = 275M. Invest. IRR = 30%. Invest as long as cost of capital does not exceed 30%.
The project should be accepted as long as the discount rate is below 15.24%.
a. NPV = -9.895M.
b. NPV = -503,381.
6. a. NPV = 169,482. Invest.
b. IRR = 12.66%.
c. NPV = -64,816.
7. IRR = 12.72%. NPV will be positive at a discount rate of 12%.
6.2 The Internal Rate of Return Rule
8. IRR = 20%. Break-even investment.
9. IRR = 12.2%. NPV = -986.71. Both rules agree --- do not undertake investment.
13. a. r = 6%, NPV = 693,420.38. r = 2%, NPV = -1,017,414.99. r = 12%, NPV = -183,110.30.
b. There are two IRR’s: 2.745784% and 10.879183%.
c. IRR rule cannot be used to evaluate this investment.
14. IRR’s = 2.924% and 8.723%. Cannot apply IRR rule. NPV = 2,621,791, so invest. If cost of
capital is between 2.93% and 8.72%, then the investment should be undertaken.
16. NPV is always negative, so no IRR exists!
6.3 The Payback Rule
19. 10 months.
20. 5 years. NPV = -628,322, so movie should not be made with either investment rule.
6.4 Choosing Between Projects
21. a. IRR for A = 20%, IRR for B = 17%. Based on IRR ranking, A would always be selected.
b. NPV for A = 18.5714M and NPV for B = 20M. Based on NPV ranking, select B.
c. NPV’s coincide when r = 8%. (You can solve for this directly.) IRR will give the correct decision
when the discount rate exceeds 8%.
22. a. NPV for A = 119.83. NPV for B = 130.37. (Initial cash flow = -11.25.) NPV for C = 124.65. (Final
cash flow = 254.25.) Choose B. Ranking projects by their IRR is not valid here because the
projects have different scale and different patterns of cash flow over time.
23. Incremental IRR is the discount rate at which the NPV’s coincide. This is 8%. For the incremental
project is A →B, then the incremental project will have negative outflows initially followed by
positive outflows. Therefore, since the cost of capital is 7%, the incremental project is worth it.
That is, B is preferred.
24. The IRR for the incremental project Playhouse → Fort has cash flows = (-50, 24, 32).
Let d = 1/(1+IRR). d is a root of the quadratic equation 32d2 + 24d – 50 = 0. Here, there is only one
positive value for d = 0.93004, which implies IRR = 7.522%. This value is less than the cost of capital,
and so the incremental project is not worth it. That is, the Playhouse project is preferred.
25. The IRR’s for X and Y are 21.53% and 15.14%, respectively. The cash flows for the incremental
project X →Y are (-50, 20, 40). Let d = 1/(1+IRR). d is a root of the quadratic equation 40d2 + 20d –
50 = 0. Here, there is only one positive value for d = 0.89564, which implies IRR = 11.652%. Because
all 3 projects have a negative cash flow followed by positive cash flows, the IRR rule can be used to
decide whether to invest. Here, if the discount rate is less than 11.652% < 15.14%, the incremental
project is preferred, i.e., choose Y. If the discount rate is higher than 11.652% but less than 21.53%,
then X is preferred. At rates higher than 21.53%, no project is worthwhile.
28. a. IRR for Huawei is 83.9%, IRR for Cisco is 36.3%.
b. NPV for Huaweii is 28M, NPV fofr Cisco is 44.1M.
c. Lease cash flows are (-20, 25, 25, 25). IRR is 111.9%.
d. The incremental project moving from the old bid to the new bid has cash flows =
(80, -35, -35, -35). IRR = 14.9%. In effect, this incremental project represents a loan with a
borrowing cost of 14.9%. Since this exceeds AOL’s cost of capital at 12%, the incremental
project is not worth it. Notice how high the lease cash flow IRR is!
6.5 Project Selection with Resource Constraints
29. Buy 300 of lilies, 400 of orchids and 300 of roses for an NPV of 225.
30. Take the MC237, MF302, MY4456 and MB345 for 890 sq ft. Use remaining 1,110 sq ft for office
space. NPV = 31,540.
31. Profitability indexes (NPV/Cost) = 1.98, 1.50, 1.76, 3.03, 1.27 and 2.52, respectively. According to
the PI’s, KP should invest in Seabreeze, West Ranch and Mountain Ridge. (This is optimal.) The IRR’s
are 43.1%, 38.2%, 40.9%, 42.7%, 27.2% and 38.9%, respectively. According to the IRR’s, KP should
invest in Mountain Ridge, Seabreeze and Lakeview, which is clearly inferior.
32. a. PI rule says take V, III and II, which is optimal.
b. Take I – IV instead of V.
c. Take V and IV.