CapitalBudgeting Payback Net present value (NPV) Internal rate of return (IRR) Profitability index (PI) Modified internal rate of return (MIRR)

What Is capital budgeting? Analysis of potential additions to fixed assets. Long-term decisions; involve large expenditures. Very important to firm’s future.

Steps 1. Generate ideas. 2. Estimate CFs (inflows & outflows). 3. Assess riskiness of CFs. 4. Determine k = WACC (adj.). 5. Find NPV and/or IRR. 6. Accept if NPV > 0 and/or IRR > WACC.

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 1 2 3 4 5 N NN - + + + + + N - + + + + - NN - - - + + + N + + + - - - NN - + + - + - NN

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) 1 2 2.4 3 CFt -100 10 60 80 Cumul -100 -90 -30 50 PaybackL = 2 + 30/80 = 2.375 years.

Project S (Short: CFs come quickly) 1 1.6 2 3 CFt -100 70 50 20 Cumul -100 -30 20 40 PaybackS = 1 + 30/50 = 1.6 years. Payback is a type of breakeven analysis.

Strengths of Payback Provides an indication of a project’s risk and liquidity. Easy to calculate and understand. Weaknesses of Payback Ignores the TVM. Ignores CFs occurring after the payback period.

Discounted Payback: Uses discounted rather than raw CFs. Apply to Project L. 2.7 1 2 3 10% CFt -100 10 60 80 PVCFt -100 9.09 49.59 60.11 Cumul -100 -90.91 -41.32 18.79 Disc. payback = 2 + 41.32/60.11 = 2.7 years. Recover invest. + cap. costs in 2.7 years.

Net Present Value (NPV) Sum of the PVs of inflows and outflows. n t=0 CFt (1 + k)t NPV =  . If one expenditure at t = 0, then n t=1 CFt (1 + k)t NPV = - CF0.

What is Project L’s NPV? Project L: 18.78 = NPVL NPVS = $19.98. 1 2 3 1 2 3 10% -100.00 9.09 49.58 60.11 18.78 = NPVL NPVS = $19.98. 10 60 80

Calculator Solution Enter in CFLO for L: = 18.78 = NPVL. -100 10 60 80

Rationale for the NPV Method 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.

Using NPV method, which project(s) should be accepted? If Projects S and L are mutually exclusive, accept S because NPVS > NPVL . If S & L are independent, accept both; NPV > 0. Note that NPVs change as cost of capital changes.

Internal Rate of Return (IRR) 1 2 3 CF0 CF1 CF2 CF3 Cost Inflows IRR is the discount rate that forces PV inflows = cost. This is the same as forcing NPV = 0.

( ) NPV: Enter k, solve for NPV. CF k NPV ๅ + 1 . = ๅ + 1 . IRR: Enter NPV = 0, solve for IRR.

Enter CFs in CFLO, then press IRR: What is Project L’s IRR? 1 2 3 IRR = ? -100.00 10 60 80 PV1 PV2 PV3 Enter CFs in CFLO, then press IRR: 0 = NPV IRRL = 18.13%. IRRS = 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.

IRR Acceptance Criteria If IRR > k, accept project. If IRR < k, reject project.

Using IRR method, which project(s) should be accepted? If S and L are independent, accept both. IRRs > k = 10%. If S and L are mutually exclusive, accept S because IRRS > IRRL . Note that IRR is independent of the cost of capital, but project acceptability depends on k.

Define Profitability Index (PI) PV of inflows PV of outflows PI = .

Calculate each project’s PI. Project L: $9.09 + $49.59 + $60.11 $100 PIL = = 1.19. Project S: $63.64 + $41.32 + $15.03 $100 PIS = = 1.20.

PI Acceptance Criteria 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.

Managers prefer IRR to NPV. Can we give them a better IRR? 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.

MIRR for Project L (k = 10%): 1 2 3 10% 10.0 60.0 80.0 -100.0 10% 66.0 12.1 10% MIRR = 16.5% 158.1 -100.0 $158.1 (1+MIRRL)3 $100 = TV inflows PV outflows MIRRL = 16.5%

Why use MIRR rather than IRR? 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.

When there are nonnormal CFs, use MIRR: 1 2 -800,000 5,000,000 -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.