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

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

3 What is the difference between independent and mutually exclusive projects? Projects are: independent, if the cash flows of one are unaffected by the acceptance of the other. mutually exclusive, if the cash flows of one can be adversely impacted by the acceptance of the other.

4 An Example of Mutually Exclusive Projects Firm owns one corner lot, then it can build a gas station or an apartment building, but not both.

5 Normal(Conventional) Cash Flow Project: Cost (negative CF) followed by a series of positive cash inflows. One change of signs. Nonnormal Cash Flow Project: Two or more changes of signs. Most common: Cost (negative CF), then string of positive CFs, then cost to close project. e.g. Nuclear power plant

6 Inflow (+) or Outflow (-) in Year NNN N N N

7 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?

8 Payback for Project L (Long: Large CFs in later years) = CF t Cumulative Payback L 2+30/80 = years

9 Project S (Short: CFs come quickly) CF t Cumulative Payback S /50 = 1.6 years 1.6 =

10 Strengths of Payback: 1.Provides an indication of a project’s risk and liquidity. 2.Easy to calculate and understand. Weaknesses of Payback: 1.Ignores the TVM. 2.Ignores CFs occurring after the payback period.

11 Discounted Payback: Uses discounted rather than raw CFs CF t Cumulative Discounted payback /60.11 = 2.7 years PVCF t % = Recover investment in 2.7 years.

12 NPV:Sum of the PVs of inflows and outflows.

13 What’s Project L’s NPV? % Project L: = NPV L NPV S = $19.98.

14 Calculator Solution Enter CFs for L: CF 0 CF 1 NPV CF 2 CF 3 I = = NPV L

15 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.

16 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.

17 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.

18 NPV: Enter k, solve for NPV. IRR: Enter NPV = 0, solve for IRR.

19 What’s Project L’s IRR? IRR = ? PV 3 PV 2 PV 1 0 = NPV Enter CFs, then press IRR: IRR L = 18.13%.IRR S = 23.56%.

IRR = ? Find IRR if CFs are constant: -100 Or enter CFs and press IRR = 9.70% % INPUTS OUTPUT NI/YRPVPMTFV

IRR = ? Q.How is a project’s IRR related to a bond’s YTM? A.They are the same thing. A bond’s YTM is the IRR if you invest in the bond IRR = 7.08% (using Fin. Calc.)...

22 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.

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

24 Decisions on Projects S and L per IRR 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.

25 Construct NPV Profiles Fin. Calc.: Enter CFs and find NPV L and NPV S at different discount rates: k NPV L (4 NPV S (4)

NPV ($) Discount Rate (%) IRR L = 18.1% IRR S = 23.6% Crossover Point = 8.7% k NPV L (4) NPV S S L

27 NPV and IRR always lead to the same accept/reject decision for independent projects: k > IRR and NPV < 0. Reject. NPV ($) k (%) IRR IRR > k and NPV > 0 Accept.

28 Mutually Exclusive Projects k 8.7 k NPV % IRR S IRR L L S k NPV S, IRR S > IRR L CONFLICT k > 8.7: NPV S > NPV L, IRR S > IRR L NO CONFLICT

29 To Find the Crossover Rate 1.Find cash flow differences between the projects. See data at beginning of the case. 2.Enter these differences in CF register, then press IRR. Crossover rate = 8.68%, rounded to 8.7%. 3.Can subtract S from L or vice versa, but better to have first CF negative. 4.If profiles don’t cross, one project dominates the other.

30 Reasons for conflict Difference in project characteristics 1.Timing differences. Project with faster payback provides more CF in early years for reinvestment. If k is high, early CF especially good, NPV S > NPV L. k NPV L (4) NPV S

31 Difference in assumption of NPV and IRR Reinvestment Rate Assumptions NPV assumes reinvest at k (opportunity cost of capital). IRR assumes reinvest at IRR. Reinvest at opportunity cost, k, is more realistic, so NPV method is best. NPV should be used to choose between mutually exclusive projects.

32 To see the reinvestment rate assumptions Calculate average holding period return per year for projects S and L using WACC and IRR as reinvestment rates.

33 Managers like rates--prefer IRR to NPV comparisons. Can we give them a better IRR? Yes, MIRR is the discount rate that 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 assumes cash inflows are reinvested at WACC.

34 MIRR = 16.5% % MIRR for Project L (k = 10%) % TV inflows PV outflows MIRR L = 16.5% $100 = $158.1 (1 + MIRR L ) 3

35 Why use MIRR versus IRR? MIRR correctly assumes reinvestment at opportunity cost = WACC. MIRR also avoids the problem of multiple IRRs. Managers like rate of return comparisons, and MIRR is better for this than IRR.

36 Consider projects S and L Calculate MIRR and NPV of Projects S and L at different rates of cost of capital Thus, the use of MIRR accounts for timing differences.

37 Project P: NPV and IRR? 5,000-5, k = 10% -800 Enter CFs in CF register, enter I = 10. NPV = IRR = ERROR. Why?

38 We got IRR = ERROR because there are 2 IRRs. Nonnormal CFs--two sign changes. Here’s a picture: NPV Profile IRR 2 = 400% IRR 1 = 25% k NPV

39 Logic of Multiple IRRs 1.At very low discount rates, the PV of CF 2 is large & negative, so NPV < 0. 2.At very high discount rates, the PV of both CF 1 and CF 2 are low, so CF 0 dominates and again NPV < 0. 3.In between, the discount rate hits CF 2 harder than CF 1, so NPV > 0. 4.Result: 2 IRRs.

40 When there are nonnormal CFs and more than one IRR, use MIRR: ,0005,000,000-5,000,000 PV 10% = -4,932, TV 10% = 5,500, MIRR = 5.6%

41 Accept Project P? NO. Reject because MIRR = 5.6% < k = 10%. Also, if MIRR < k, NPV will be negative: NPV = -$386,777.

42 Reasons for conflict: Difference in project characteristics 2.Size (scale) differences.

43 Reasons for conflict Difference in project characteristics If Big and Little are mutually exclusive projects, which project should a firm prefer? If the firm goes strictly by the PI, IRR, or MIRR criteria, it would choose Project Little. But is this the better project? Project Big provides more value -- $89,299 versus $0.18. The techniques that ignore the scale of the investment such as IRR may lead to an incorrect decision.