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Your boss the chief financial officer (CFO) asked you to analyse 3 different projects under consideration by the company's board. All projects require an initial investment and then provide a perpetuity of cash flows with zero growth. All are equally risky with the same 10% pa required return. All figures are rounded to 4 decimal places. The projects can all be accepted and funded, they're not mutually exclusive.The projects' initial costs and perpetual annual cash flows were provided by the engineering and marketing departments and are believed to be accurate. You calculated the NPV's and IRR's in bold, and made some conclusions about which projects to accept or reject (stated in answer option d). The CFO thanked you for your swift work, but said there's just one thing wrong with your calculations or conclusions, and asked you to fix it up before the table and conclusions are shown at the board meeting tomorrow.Projects with 10% pa required return  Initial cashflow at t=0 Perpetual annualcash flow from t=1 NPV IRR  ($m) ($m) ($m) (% pa)Project A -40 16 (a) 120 40Project B -1,200 80 -400 (b) 6.6667Project C -26,000 1,400 -12,000 (c) 6.698  Which one of the following calculations or conclusions is NOT correct?Question 7Select one:a.$120 million is project A's NPV.b.6.6667% pa is project B's IRR.c.6.698% pa is project C's IRR.d.Accept project A but reject projects B and C.

Question

Your boss the chief financial officer (CFO) asked you to analyse 3 different projects under consideration by the company's board. All projects require an initial investment and then provide a perpetuity of cash flows with zero growth. All are equally risky with the same 10% pa required return. All figures are rounded to 4 decimal places. The projects can all be accepted and funded, they're not mutually exclusive.The projects' initial costs and perpetual annual cash flows were provided by the engineering and marketing departments and are believed to be accurate. You calculated the NPV's and IRR's in bold, and made some conclusions about which projects to accept or reject (stated in answer option d). The CFO thanked you for your swift work, but said there's just one thing wrong with your calculations or conclusions, and asked you to fix it up before the table and conclusions are shown at the board meeting tomorrow.Projects with 10% pa required return  Initial cashflow at t=0 Perpetual annualcash flow from t=1 NPV IRR  (m)(m) (m) (m)(m) (% pa)Project A -40 16 (a) 120 40Project B -1,200 80 -400 (b) 6.6667Project C -26,000 1,400 -12,000 (c) 6.698  Which one of the following calculations or conclusions is NOT correct?Question 7Select one:a.120 million is project A's NPV.b.6.6667% pa is project B's IRR.c.6.698% pa is project C's IRR.d.Accept project A but reject projects B and C.

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Solution

The incorrect calculation or conclusion is a. $120 million is project A's NPV.

The NPV (Net Present Value) of a project is calculated using the formula: NPV = ∑ [Rt / (1+i)^t] - C0, where:

  • Rt is the net cash inflow during the period t
  • i is the discount rate or rate of return
  • t is the number of time periods
  • C0 is the initial investment

In the case of Project A, the initial investment (C0) is 40million,theperpetualannualcashflow(Rt)is40 million, the perpetual annual cash flow (Rt) is 16 million, and the discount rate (i) is 10% pa.

Since the cash flows are perpetuity with zero growth, the formula simplifies to: NPV = R / i - C0

Substituting the given values, we get: NPV = 16 / 0.10 - 40 = $120 million

However, this is incorrect. The correct NPV should be: NPV = 16 / 0.10 - 40 = 120million120 million - 40 million = $80 million

Therefore, the correct NPV for Project A is 80million,not80 million, not 120 million.

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