ch7

• Investment in real assets is known as capital budgeting
• $1 today


  Worth more than $1 tomorrow
• Time value of money


  $1 today can be invested to earn interest immediately
• Opportunity cost


  Discount rate = rate of return = cost of capital
• Present value (PV)


  Discounted value

  
• Perpetuity (no growth)


  PV = C/r
• Net Present Value (NPV)


  • Co + C1/(1+r)1 + C2/(1+r)2 + ... + Cn/(1+r)n

  
• Additivity Principle: NPV(X + Y) = NPV(X) + NPV(Y)
• NPV rule


  Enables firms to maximize shareholder wealth
• Mutually exclusive projects means only one can be chosen
• Internal Rate of Return (IRR)


  Rate at which the PV of the cash inflows associated with a project equal the cash investment

  
• IRR = rate that makes the NPV = 0

  
• Growing perpetuity


  PV = C/(r-g)
• PV of a perpetuity


  No growth
• Net Present Value (NPV)


  Additivity Principle: NPV(X + Y) = NPV(X) + NPV(Y)

  
• Mutually exclusive


  Only one can be chosen
• Internal Rate of Return (IRR)


  Rate at which the PV of the cash inflows associated with a project equal the cash investment, makes the NPV = 0

  
• The cash flows that have to be discounted in the NPV method are the incremental cash flows, the additional cash flows from the project. Sunk costs have to be excluded because they are incurred whether or not the project is accepted.
• The implicit assumption about cash flows associated with the investment project is that they can be estimated without error. However, in the real world, the cash flows associated with investment projects represent forecasts, and not real values.

  
• The NPV decision rule is consistent with the objective of the firm to maximise shareholder wealth because the maximisation of the NPV increases the market value of the stockholder's share in the firm.
• The NPV possesses the additivity principle, which means that when there are mutually exclusive projects, the NPV method indicates that the project with the largest positive NPV should be adopted as it generates the largest NPV of the firm's aggregated cash flows.
• Additivity property


  The NPV of projects X and Y is equal to the NPV of project X plus the NPV of project Y
• The choice of project relies on the additivity property
• If project X is a positive NPV project and project Y is a negative NPV, the joint project (X+Y) will have a lower NPV than project X on its own
• The NPV enables managers to avoid choosing bad projects just because they are packaged with good ones
• NPV (Net Present Value)


  A method to evaluate the profitability of investment projects

  
• Mutually exclusive projects


  Projects where only one can be chosen
• If the opportunity cost of capital is 8%


  Calculate the NPV for each project
• Projects


  • Alpha
  • Omega
• Calculating NPV


  1. Cash flow

  2. Discount factor

  3. Present value

  
• Accept the project with the higher positive NPV
• If both projects have negative NPV, reject both
• If both projects have positive NPV, accept both
• If NPV and IRR give conflicting results, follow the NPV decision
• Internal rate of return (IRR)


  The rate at which the present values of the cash inflows associated with a project equal the cash investment. It is the rate that makes the NPV equal to zero.

  
• Steps to solve IRR

  1. Set any 2 rates (R%, r%)

  2. Find NPV(R%), NPV (r%) (must +NPV, -NPV)

  3. Use interpolation formula: IRR = r% + NPV______ (R%-r%) / (NPV + NPV)
• The choice of projects is made by comparing the IRR to a required rate of return termed hurdle rate (R*)
• If the IRR is higher than the hurdle rate, the project has to be accepted
• The hurdle rate is usually represented by the risk-free interest rate where cash flows are riskless
• If the hurdle rate is the opportunity cost of capital used in the NPV calculation


  The 2 methodologies (IRR & NPV) would give the same result, and thus the same investment recommendation