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Quantitative Methods - Quantitative Methods Section 1

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1. The Chinese government wishes to invest in a project that requires an initial investment of $18 million.The project is expected to produce positive cash flows of $5 million for the first three years, and $3 million for the next two years. Given that the required rate of return is 10 percent, the approximate internal rate of return (IRR) of this project is closest to:

  • Option : B
  • Explanation : Enter the given cash flows in a financial calculator: CF0 = -18 million, CF1 = 5 million, CF2 = 5 million
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2. A company is planning to invest $25,000 in a new project. The project is expected to generate annual after-tax cash flows of $5000 for the next 3 years and $15,000 in its fourth year. Given that the appropriate discount rate for this project is 5.5 percent, the NPV of the project is closest to:

  • Option : A
  • Explanation : Enter the given cash flows and discount rate in a financial calculator to calculate NPV: C0= -25,000, CF1= 5000, CF2= 5000, CF3= 5,000, CF4= 15000, i = 5.5%, CPT NPV. NPV = $597.92.
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3. The expected cash flows of a project are given below:

TimeCash Flow ($)
0(180,000)
1100,000
2200,000
3250,000

  • Option : C
  • Explanation : Opportunity cost of capital for the investment = risk free rate + the market risk premium * beta Opportunity cost = 3% + (6% x 1.2) = 10.2%. The NPV equals the present value (at t = 0) of the future cash flows discounte at the opportunity cost of capital (10.2%) minus the initial investment, or $123,725. Using a financial calculator, solve for NPV. CF0= –180,000, CF1= 100,000, CF2= 200,000, CF3= 250,000, %i = 10.2, CPT NPV = 262,241.84 ≈ 262,000.
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4. Lee Kwan Group is about to invest in a 2-year project that requires an initial outlay of $5 million. The expected cash flows in years 1 and 2 are $3 million and $3.5 million respectively. The internal rate of return of this project is closest to:

  • Option : B
  • Explanation : Using a financial calculator, compute IRR:CF0 = -5,000,000, CF1 = 3,000,000, CF2 = 3,500,000; CPT IRR = 18.88% ≈ 19%.
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5. The table below shows the after-tax cash flows of a project:

Year  0123456
Cash flow (€)    -50,00035,00025,00010,0002,0002,0003,000

The IRR of the project is closest to:

  • Option : A
  • Explanation : Using a financial calculator, compute IRR: CF0 = –50,000, CF1 = 35,000, CF2 = 25,000, CF3 = 10,000, CF4 = 2,000, CF5 = 2,000, and CF6 = 3,000, CPT IRR. The IRR is 27.05%.
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Quantitative Methods Section 1