An Example of Mutually Exclusive Projects BRIDGE VS. BOAT TO GET PRODUCTS ACROSS A RIVER.
Normal Project Cost (negative CF) followed by a series of positive cash inflows. Nonnormal Project One or more outflows occur after inflows have begun. Most common: Cost (negative CF), then string of positive CFs, then cost to close project. Nuclear power plant, strip mine.
Inflow (+) or Outflow (-) in Year 012345NNN -+++++N -++++- ---+++N +++--- -++-+-
What is the payback period? The number of years required to recover a project’s cost, or how long does it take to get our money back?
Payback for Project L (Long: Most CFs in out years) 108060 0123 -100 CF t Cumul -100-90-3050 Payback L = 2 + 30/80 = 2.375 years. 0 2.4
CF t Cumul -100-302040 Payback S = 1 + 30/50 = 1.6 years. 702050 0123 Project S (Short: CFs come quickly) -100 0 1.6 Payback is a type of breakeven analysis.
Ignores the TVM. Ignores CFs occurring after the payback period. Provides an indication of a project’s risk and liquidity. Easy to calculate and understand. Weaknesses of Payback Strengths of Payback
= 2 + 41.32/60.11 = 2.7 years. -41.32 60.11 108060 0123 CF t Cumul -100-90.9118.79 Disc. payback Discounted Payback: Uses discounted rather than raw CFs. Apply to Project L. PVCF t -100 10% 9.0949.59 Recover invest. + cap. costs in 2.7 years. 2.7
Sum of the PVs of inflows and outflows. Net Present Value (NPV) If one expenditure at t = 0, then NPV = n t=0 CF t (1 + k) t NPV = - CF 0. n t=1 CF t (1 + k) t
What is Project L’s NPV? 108060 0123 10% Project L: -100.00 9.09 49.58 60.11 18.78 = NPV L NPV S = $19.98.
= 18.78 = NPV L. Calculator Solution Enter in CFLO for L: -100 10 60 80 10 CF 0 CF 1 NPV CF 2 CF 3 I
NPV= PV inflows - Cost = Net gain in wealth. Accept project if NPV > 0. Choose between mutually exclusive projects on basis of higher NPV. Adds most value. Rationale for the NPV Method
Using NPV method, which project(s) should be accepted? If Projects S and L are mutually exclusive, accept S because NPV S > NPV L. If S & L are independent, accept both; NPV > 0. Note that NPVs change as cost of capital changes.
Internal Rate of Return (IRR) 0123 CF 0 CF 1 CF 2 CF 3 CostInflows IRR is the discount rate that forces PV inflows = cost. This is the same as forcing NPV = 0.
NPV:Enter k, solve for NPV. IRR:Enter NPV = 0, solve for IRR. t n t t CF k NPV 0 1.
What is Project L’s IRR? 108060 0123 IRR = ? -100.00 PV 3 PV 2 PV 1 0 = NPV Enter CFs in CFLO, then press IRR: IRR L = 18.13%.IRR S = 23.56%.
Rationale for the IRR Method If IRR > WACC, then the project’s rate of return is greater than its cost-- some return is left over to boost stockholders’ returns. Example:WACC = 10%, IRR = 15%. Profitable.
If IRR > k, accept project. If IRR < k, reject project. IRR Acceptance Criteria
If S and L are independent, accept both. IRRs > k = 10%. If S and L are mutually exclusive, accept S because IRR S > IRR L. Using IRR method, which project(s) should be accepted? Note that IRR is independent of the cost of capital, but project acceptability depends on k.
PI =. PV of inflows PV of outflows Define Profitability Index (PI)
Calculate each project’s PI. Project L: $9.09 + $49.59 + $60.11 $100 Project S: $63.64 + $41.32 + $15.03 $100 PI L = = 1.19. PI S = = 1.20.
If PI > 1, accept. If PI < 1, reject. The higher the PI, the better the project. For mutually exclusive projects, take the one with the highest PI. Therefore, accept L and S if independent; only accept S if mutually exclusive. PI Acceptance Criteria
Yes, modified IRR (MIRR) is the discount rate which causes the PV of a project’s terminal value (TV) to equal the PV of costs. TV is found by compounding inflows at WACC. Thus, MIRR forces cash inflows to be reinvested at WACC. Managers prefer IRR to NPV. Can we give them a better IRR?
$158.1 (1+MIRR L ) 3 10.080.060.0 0123 10% 66.0 12.1 158.1 MIRR for Project L (k = 10%): -100.0 10% TV inflows -100.0 PV outflows MIRR = 16.5% MIRR L = 16.5% $100 =
MIRR correctly assumes reinvestment at opportunity cost = k. MIRR also avoids problems with nonnormal projects. Managers like rate of return comparisons, and MIRR is better for this than IRR. Why use MIRR rather than IRR?
When there are nonnormal CFs, use MIRR: 012 -800,0005,000,000-5,000,000 PV outflows @ 10% = -4,932,231.40. TV inflows @ 10% = 5,500,000.00. MIRR = 5.6%
Accept Project P? NO. Reject because MIRR = 5.6% < k = 10%. Also, if MIRR < k, NPV will be negative: NPV = -$386,777.