*This preview shows
page 1. Sign up
to
view the full content.*

**Unformatted text preview: **Chapter 11: THE BASICS OF CAPITAL BUDGETING Should we build this plant? Topic Overview Topic
Project Types Capital Budgeting Decision Criteria
◦ Net Present Value (NPV) ◦ Internal Rate of Return (IRR) ◦ Modified Internal Rate of Return (MIRR) ◦ Payback Period ◦ Discounted Payback Period Learning Objectives Learning
Understand how to calculate and use the 5 capital budgeting decision techniques:, NPV, IRR, MIRR, Payback, & Discounted Payback. Understand the advantages and disadvantages of each technique. Understand which project to select when there is a ranking conflict between NPV and IRR. Think about this as we cover Chapter 11 Capital Budgeting Decision Methods. Capital
Which of the following investment opportunities would you prefer? #1) Give me $1 now and I’ll give you $2 at the end of class. #2) Give me $100 now and I’ll give you $150 at the end of class. WHAT IS CAPITAL BUDGETING? BUDGETING?
Analysis of potential additions to fixed assets. Long-term decisions; involve large expenditures. Very important to firm’s future. Capital Budgeting Steps: Capital 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. Types of Projects Types
Brand new line of business Expansion of existing line of business Replacement of existing asset
Independent vs. Mutually Exclusive Normal vs. Non-normal An Example of Mutually Exclusive Projects: Exclusive BRIDGE VS. BOAT TO GET PRODUCTS ACROSS A RIVER. Normal vs. Nonnormal Projects Projects
Normal Project: ◦ Cost (negative CF) followed by a series of positive cash inflows. One change of signs.
Non-normal Project: ◦ Two or more changes of signs. ◦ 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 0 + 1 + + + + 2 + + + + 3 + + + 4 + + + + 5 + + N N NN N N NN NN Our Case Study Our We want to help Marge Simpson analyze the following business opportunities by using the following cash flow information. Assume Marge's cost of capital is 12%.
Time Falafel-Full How 'Bout A Pretzel? 0 1 2 3 4 (20,000) 15,000 15,000 13,000 3,000 (20,000) 2,000 2,500 3,000 50,000 Net Present Value (NPV) Net
NPV = PV of inflows minus Cost = Net gain in wealth. Acceptance of a project with a NPV > 0 will add value to the firm. Decision Rule:
◦ Accept if NPV >0, ◦ Reject if NPV < 0 NPV: Sum of the PVs of inflows and outflows. CFt NPV = ∑ . t t= 0 ( 1 + k)
n Cost often is CF0 and is negative. CFt NPV = ∑ − CF0 . t t =1 (1 + k ) n Marge’s NPVs: k = 12% Marge’s
Time Falafel-Full PV(CF) How 'Bout A Pretzel? PV(CF) 0 1 2 3 4 NPV (20,000) (20,000) 15,000 13,393 15,000 11,958 13,000 9,253 3,000 1,907 16,510 (20,000) (20,000) 2,000 1,786 2,500 1,993 3,000 2,135 50,000 31,776 17,690 Calculator Steps. Falafel-Full: CF0 = -20,000, C01 = 15,000, F01 = 2, C02 = 13,000, F02 = 1, C03 = 3,000. NPV: I = 12, CPT NPV = 16,510 Pretzel: CF0 = -20,000, C01 = 2,000, C02 = 2,500, C03 = 3,000, C04 = 50,000. NPV: I = 12, CPT NPV = 17,690 Excel and NPV: Excel Excel’s NPV function is goofed up. =NPV(k, range of cash flows) Assumes first cash flow in range occurs at t = 1. See spreadsheet. Solution to this spreadsheet problem: exclude CF0 (t = 0 cash flow) from NPV cell range and add CF0 (if CF0 is already negative) or subtract CF0 (if CF0 is positive) from NPV function. Marge’s NPV Decision Marge’s
If projects are independent, Marge should select both.
◦ Both have positive NPV. If the projects are mutually exclusive, select How ‘Bout A Pretzel?
◦ Pretzel NPV > Falafel NPV. Internal Rate of Return: IRR Internal
0 1 2 3 CF0 Cost CF1 CF2 Inflows CF3 IRR is the discount rate that forces PV inflows = cost. This is the same as forcing NPV = 0. NPV: Enter k, solve for NPV. CFt = NPV. ∑ t t = 0 ( 1 + k)
n IRR: Enter NPV = 0, solve for IRR. CFt = 0. ∑ t t = 0 ( 1 + IRR)
n Internal Rate of Return (IRR) Internal
Internal Rate of Return is a project’s expected rate of return on its investment. IRR is the interest rate where the PV of the inflows equals the PV of the outflows. In other words, the IRR is the rate where a project’s NPV = 0. Decision Rule: Accept if IRR > k (cost of capital). Non-normal projects have multiple IRRs. Don’t use IRR to decide on non-normal projects. Marge’s IRRs Marge’s
Best to use calculator. Calculator Steps. Falafel-Full: CF0 = -20,000, C01 = 15,000, F01 = 2, C02 = 13,000, F02 = 1, C03 = 3,000. Press IRR, then CPT: IRR = 54.7% Pretzel: CF0 = -20,000, C01 = 2,000, C02 = 2,500, C03 = 3,000, C04 = 50,000. Press IRR, then CPT: IRR = 33.3% k = 12%. If independent projects: Comparison of NPV & IRR Comparison
For normal independent projects, both methods give same accept/reject decision.
NPV ◦ NPV > 0 yields IRR > k in order to lower NPV to 0. NPV However, the methods can rank mutually exclusive projects differently. What to do, then? Today’s Agenda Today’s
NPV/IRR Ranking conflict Modified Internal Rate of Return Payback Period Discounted Payback Period NPV Profiles NPV
A graph which shows a project’s NPV at different interest rates (cost of capital). Can illustrate ranking conflicts between NPV and IRR. Below is a table of NPVs for Marge’s projects.
k 0% 5% 10% 12% 15% 25% 35% 55% Falafel-Full 26,000 21,589 17,849 16,510 14,649 9,485 5,529 (68) How 'Bout A Pretzel? 37,500 27,899 20,289 17,690 14,190 5,216 (874) (8,201) Determining NPV/IRR Conflict Range Range
For each year, subtract one project’s cash flows from the other. If there is a change of signs of these cash flow differences, a ranking conflict exists. Find IRR of these cash flow differences to find rate where the two projects have the same NPV = crossover rate. At a cost of capital less than this crossover rate, a ranking conflict Marge’s crossover rate Marge’s
Marge's NPV Profiles
Time 0 1 2 3 4 Falafel-Full 'Bout A Pretzel? Fal - Pret How (20,000) (20,000) 0 CF0 15,000 2,000 13,000 C01 15,000 2,500 12,500 C02 13,000 3,000 10,000 C03 3,000 50,000 (47,000) C04 IRR = Crossover Rate = 14.1%
40,000 30,000 20,000 10,000 0 -10,000 0% -20,000 IRR(P) IRR(F) Falafel-Full How 'Bout A Pretzel? NPV 10% 20% 30% 40% 50% 60% Cost of Capital (k) At a cost of capital less than 14.1%, Pretzel has higher NPV but lower IRR = Ranking Conflict. At cost of capital greater than 14.1%, Falafel has the higher NPV and IRR. Two reasons NPV profiles cross: cross:
1) Size (scale) differences. Smaller project frees up funds at t = 0 for investment. The higher the opp. cost, the more valuable these funds, so high k favors small projects. Timing differences. Project with faster payback provides more CF in early years for reinvestment. If k is high, early CF especially good, NPVS > NPVL. 2) Which project is best for Marge? Marge?
Think back to my indecent proposal. Which of the following investment opportunities would you prefer? #1) Give me $1 now and I’ll give you $2 at the end of class.
#2) Give me $100 now and I’ll give you $150 at the end of class. Reconciling Ranking Conflicts absent capital rationing. absent
Shareholder Wealth Maximization: Rate Assumption: ◦ Want to add more value to the firm than less.
Reinvestment ◦ NPV assumes cash flows are reinvested at company’s cost of capital (i.e.: the investors’ required rate of return). ◦ IRR assumes cash flows are reinvested at IRR. ◦ The NPV reinvestment rate assumption is more realistic.
Result: Choose project with highest NPV when NPV/IRR ranking conflict exists for mutually exclusive projects. Acme, Inc. Rocket-Powered Roller Blade Project Roller Acme is considering the following project which would market these roller blades to coyotes trying to catch road runners. Acme expects a cash inflow in the year 1, but an outflow in the 2nd (last) year of the project due to liability claims from injured cartoon coyotes. Acme’s opportunity cost of capital is 13%. Year 0 Cash Flow (5) NPV = -1.95 IRR = 26.8% 1 30 2 (30) Rocket-Powered Roller Blade NPV Profile Profile
4 NPV 1 0% 6 50% 100% 150% 200% 250% 300% 350% 400% 450% 500% 550% At Acme’s 13% opportunity cost of capital, the project has a negative NPV even though the IRRs (~27% & 374%) are greater than 13%. Because of this conflict, don’t use IRR to make decisions for nonnormal projects! Why even mess with IRR? Why Since we like NPV, why mess with something like IRR? A rate of return or interest rate is more intuitive for outsiders and easier to understand. But IRR assumes an unrealistic reinvestment rate an leads to multiple IRRs for non-normal projects. Solution: Modified Internal Rate of Return (MIRR). Modified Internal Rate of Return, MIRR MIRR The interest rate where the FV of a project’s inflows (TV) are discounted to equal the PV of a project’s outflows. Assumes cash inflows are reinvested at the project’s cost of capital (k). PV(outflows) = TV/(1+MIRR)n, where TV = Σ CIFt(1+k)n-t, and PV(outflows) = Σ COFt/(1+k)t
◦ Where CIF = annual cash inflow, and COF = annual cash outflow. Steps to finding MIRR. Steps Find TV of inflows by finding FV of each annual inflow to the end of the project’s life at the cost of capital. Find PV of outflows at the cost of capital today. Then find interest rate over the n years of the project that equates the TV (=FV) to the PV of the outflows(=PV). Decision rule same as IRR: Compare MIRR to cost of capital. The MIRR for Marge’s projects. The
Tim e Fa la fe l- Fu ll FV a t y r 4 a t 1 2 % H ow 'Bou t A Pr e tze l? FV a t y r 4 a t 1 2 % 0 1 2 3 4 (20,000) 15,000 15,000 13,000 3,000 TV = 2 1,074 1 8,816 1 4,560 3 ,000 57,450 (20,000) 2 ,000 2 ,500 3 ,000 5 0,000 TV = 2 ,810 3 ,136 3 ,360 5 0,000 59,306 Falafel-Full: -20,000 = PV, 57,450 = FV, 4 = N, 0 = PMT, CPT I/Y = 30.2% = MIRR How ‘Bout A Pretzel: -20,000 = PV, 59,306 = FV, 4 = N, 0 = PMT, CPT I/Y = 31.2% = MIRR Accept both projects if independent since MIRRs are greater than the 12% cost of capital. Prefer pretzel if mutually exclusive. CF Worksheet solution to MIRR MIRR Find NPV of inflows only first, then find FV of this single PV. YR FALAFEL ACIF CF WORK 0 0 CF0 = 0 1 15,000 C01 = 15,000 2 15,000 F01 = 2 3 13,000 C02 = 13,000 F02 =1 4 3,000 C03 = 3,000 F03 = 1 NPV: I = 12, CPT NPV = 36,510 -36,510 =PV, 12 = I/Y, 4 = N, 0 = PMT, CPT FV = 57,450. Now –20,000 = PV, MIRR: CPT I/Y = 30.2% Today’s Agenda Today’s
Calculating MIRR for multiple outflow projects Payback Period Discounted Payback Marge’s Projects Marge’s
Marge's NPV Profiles
40,000 30,000 20,000 10,000 0 -10,000 0% -20,000 IRR(P) IRR(F) Falafel-Full How 'Bout A Pretzel? NPV 10% 20% 30% 40% 50% 60% Cost of Capital (k) MIRR if more than one outflow outflow ACME Rocket Roller Blades YR CF 0 -5 1 +30 2 -30 Cost of capital = 13% FV of inflows at yr 2 = 30(1.13) = 33.9 PV of outflows today (yr 0) = -5 – 30/(1.13)2 = -28.49 -28.49 = PV, 33.9 = FV, 0 = PMT, 2 = N, CPT I/Y = 9.1% MIRR less than 13% consistent with negative NPV Disc TV project MIRR, WACC = 11% 11%
Year 0 1 2 3 4 5 Cash Flow -300 -200 -50 400 500 600 Find FV of inflows first ◦ CF0 = 0, C01 = 0, F01 = 2, C02 = 400, F02 = 1, C03 = 500, F03 = 1, C04 = 600 ◦ NPV: I = 11, CPT NPV = 977.91 ◦ PV = -977.91, N = 5, I/Y = 11, PMT = 0, CPT FV = 1647.84 Disc TV project MIRR, WACC = 11% (continued) 11%
Step 1: Find FV of the inflows at 11% = 1647.84 Step 2: find PV of the outflows: CF 2nd C/CE
◦ CF0 = -300, C01 = -200, F01 = 1, C02 = 50 ◦ NPV: I=11, CPT NPV = -520.76 = PV of outflows
Step 3: find MIRR. ◦ PV = -520.76, N = 5, PMT = 0, FV = 1647.84 ◦ CPT I/Y = 25.9% = MIRR Payback Period (PB) Payback
Measures how long it takes to recovers a project’s cost (CF0 = initial outlay). Easy to calculate and a good measure of a project’s risk and liquidity. Decision Rule: Accept if PB < some maximum period of time. If cash inflows are equal each year (in the form of an annuity), PB = CF0/Annual CF Marge’s Payback (Assume Marge’s max is 2 years) max
Time Falafel-Full Cumulative CF How 'Bout A Pretzel? Cumulative CF 0 1 2 3 4 PB (20,000) 15,000 15,000 13,000 3,000 (20,000) (5,000) 10,000 23,000 26,000 (20,000) 2,000 2,500 3,000 50,000 (20,000) (18,000) (15,500) (12,500) 37,500 = Years Before Full Recovery of Initial Cost + (Unrecovered CF0)/(Cash inflow during year) Falafel PB = 1 + 5,000/15,000 = 1.33 Pretzel PB = 3 + 12,500/50,000 = 3.25 Marge should choose Falafel using Payback Period. Problems with Payback Problems
Ignores time value of money! Ignores cash flows beyond payback period.
The Discounted Payback Period addresses the first problem. Disc. PB tells how long it takes to recover capital and financing costs for a project. Discount rate = cost of capital. Marge’s Discounted Payback Marge’s
Time Falafel-Full PV(CF) Cumulative PV(CF) How 'Bout A Pretzel? PV(CF) Cumulative PV(CF) 0 1 2 3 4 (20,000) (20,000) 15,000 13,393 15,000 11,958 13,000 9,253 3,000 1,907 (20,000) (6,607) 5,351 14,604 16,510 (20,000) 2,000 2,500 3,000 50,000 (20,000) 1,786 1,993 2,135 31,776 (20,000) (18,214) (16,221) (14,086) 17,690 PB = Years Before Full Discounted Recovery of Initial Cost + (Unrecovered Initial Cost)/(Disc. CF during year) Falafel DPB = 1 + 6,607/11,958 = 1.55 Pretzel DPB = 3 + 14,086/31,776 = 3.44 Discounted Payback stills ignores cash flows beyond the discounted payback period. Summary of Capital Budgeting Methods Methods
Want a method the uses the time value of money with all project cash flows: NPV, IRR & MIRR. IRR can give erroneous decision for non-normal projects. Overall, NPV is the best and preferred method. ...

View
Full
Document