Presentation on theme: "10 - 1 Chapter 10: The Basics of Capital Budgeting: Evaluating Cash Flows Overview and “vocabulary” Methods Payback, discounted payback NPV IRR, MIRR Profitability."— Presentation transcript:
Chapter 10: The Basics of Capital Budgeting: Evaluating Cash Flows Overview and “vocabulary” Methods Payback, discounted payback NPV IRR, MIRR Profitability Index Unequal lives Economic life
What is capital budgeting? Analysis of potential projects. Long-term decisions; involve large expenditures. Very important to firm’s future.
Steps in Capital Budgeting Estimate cash flows (inflows & outflows). Assess risk of cash flows. Determine r = WACC for project. Evaluate cash flows.
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. Digression:
An Example of Mutually Exclusive Projects BRIDGE VS. BOAT TO GET PRODUCTS ACROSS A RIVER.
Normal Project Nonnormal Project
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 NNN N N
c(1). What is the payback period?
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) CF t Cumul Payback L = /80 = years. n.b. Assumes CF’s occur evenly over the year
CF t Cumul Payback S = /50 = 1.6 years Project S (Short: CFs come quickly) Payback is a type of breakeven analysis.
Weaknesses of Payback Strengths of Payback
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 c(2). Strengths of Payback
= /60.11 = 2.7 years CF t Cumul Disc. payback c(3):Discounted Payback: Uses discounted rather than raw CFs. Apply to Project L. PVCF t % Recover invest. + cap. costs in 2.7 years. 2.7
d(1) Net Present Value (NPV)
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
NET PRESENT VALUE NPV = CF 0 + CF 1 /(1+k) + CF 2 /(1+k) CF n /(1+k) n
What is Project L’s NPV? % Project L: (Beware use of comp. fns)
What is Project L’s NPV? % Project L: = NPV L NPV S = $19.98.
= = NPV L. Calculator Solution Enter in CFLO for L: CF 0 CF 1 NPV CF 2 CF 3 I
d(2) Rationale for the NPV Method If NPV = 0, project breaks even; recovers cost of investment investors earn required rate of return (i.e. opportunity cost of capital) If NPV > 0; investors get above, plus additional $.
CONSIDER PROJECT L: SUM OF undiscounted CF’s = 150 Investors get $100 back Cover their 10% cost of capital; and have $18.79 left over. Who does this $18.79 belong to? Stockholders.
NPV= PV inflows - PV of 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, ? If S & L are independent, ?
Using NPV method, which project(s) should be accepted? If Projects S and L are mutually exclusive,….. If S & L are independent, accept….. What happens to the NPV as the cost of capital changes?
e(1) What is the Internal Rate of Return (IRR) 0123 CF 0 CF 1 CF 2 CF 3 CostInflows
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? IRR = ? PV 3 PV 2 PV 1 0 = NPV
What is Project L’s IRR? IRR = ? PV 3 PV 2 PV 1 0 = NPV Enter CFs in CFLO, then press IRR: IRR L = 18.13%.IRR S = 23.56%.
IRR = ? e(2) How is a project’s IRR related to a bond’s YTM?
IRR = ? How is a project’s IRR related to a bond’s YTM? They both measure percentage (rate of) return. A bond’s YTM is its IRR IRR = 7.08% (use TVM or CFLO).
e(3) Rationale for the IRR Method?
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
Using IRR method, which project(s) should be accepted?
If S and L are independent, ………. If S and L are mutually exclusive, accept…………. What effect does a change in the cost of capital have on the IRR? Using IRR method, which project(s) should be accepted?
f(1) Define Profitability Index (PI)
PI =. PV of inflows PV of outflows Define Profitability Index (PI) PI measures a project’s “bang for the buck”.
Calculate each project’s PI.
Calculate each project’s PI. Project L: $ $ $60.11 $100 Project S: $ $ $15.03 $100 PI L = = PI S = = 1.20.
PI Acceptance Criteria
If PI > 1, accept. If PI < 1, reject. The higher the PI, the better the project. For mutually exclusive projects, take the one with the highest PI. Therefore, accept L and S if independent; only accept S if mutually exclusive. Any problems with using PI? PI Acceptance Criteria
g(1) Construct NPV Profiles Enter CFs in CFLO and find NPV L and NPV S at different discount rates: k NPV L (4) NPV S
NPV ($) Discount Rate (%) IRR L = 18.1% IRR S = 23.6% Crossover Point = 8.7% k NPV L (4) NPV S S L Vertical intercept horizontal intercept crossover point
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.
g(2) 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
To Find the Crossover Rate 1.Find cash flow differences between the projects. 2.Enter these differences in CFLO 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.
How do you calculate the crossover point?
Which project do you choose?
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, NPV S > NPV L. h(1) Why do NPV profiles cross?
NPV assumes reinvestment at k (opportunity cost of capital). IRR assumes reinvestment at IRR. Reinvestment at opportunity cost, k, is more realistic, so NPV method is best. NPV should be used to choose between mutually exclusive projects. Reinvestment Rate Assumptions
i(1) 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. Managers prefer IRR to NPV. Can we give them a better IRR?
$158.1 (1+MIRR L ) % MIRR for Project L (k = 10%): % TV inflows PV outflows MIRR = 16.5% MIRR L = 16.5% $100 =
% MIRR for Project L (k = 10%): % TV inflows PV outflows 0 MIRR L = 16.5%
EXCEL HAS MIRR FUNCTION!
MIRR correctly assumes reinvestment at opportunity cost = k. MIRR also avoids problems with multiple IRR’s with nonnormal projects. Managers like rate of return comparisons, and MIRR is better for this than IRR. Why use MIRR rather than IRR?
J: Pavillion Project: NPV and IRR? 5,000-5, k = 10% -800 What is NPV?, IRR? What is MIRR?
Pavillion Project: NPV and IRR? 5,000-5, k = 10% -800 Enter CFs in CF j, enter I/YR = 10. NPV = -$ IRR = ERROR. Why?
How do we find the IRR on a 12c? Make a guess for i and key it in i. RCL g R/S.
We got IRR = ERROR because there are 2 IRRs. Nonnormal CFs with two sign changes. Here’s a picture: NPV Profile IRR 2 = 400% IRR 1 = 25% k NPV
At very low disc. rates, the PV of CF 2 is large & negative, so NPV < 0. At very high disc. rates, the PV of CF 1 and CF 2 are both low, so CF 0 dominates and again NPV < 0. In between, the disc. rate hits CF 2 harder than CF 1, so NPV > 0. Result: 2 IRRs. Logic of Multiple IRRs
When there are nonnormal CFs, use MIRR: ,0005,000,000-5,000,000 PV 10% = -4,932, TV 10% = 5,500, MIRR = 5.6%
j(2) Accept Project P?
Accept Project P? NO. Reject because MIRR = 5.6% < k = 10%. Also, if MIRR < k, NPV will be negative: NPV = -$386,777.
NEW QUESTION: Which of the following mutually exclusive project’s is better? (000s) Project S: (100) Project L: (100)
S L CF , ,000 CF 1 60,000 33,500 N j 2 4 I NPV 4,132 6,190 NPV L > NPV S. But is L better? Can’t say yet. Need to perform common life analysis.
Note that Project S could be repeated after 2 years to generate additional profits. Can use either replacement chain or equivalent annual annuity analysis to make decision.
Franchise S with Replication: NPV = $7,547. Replacement Chain Approach (000s) Franchise S: (100) (100) (100) (40) 60
Compare to Franchise L NPV = $6,190. Or, use NPVs: ,132 3,415 7,547 4,132 10%
Equivalent Annual Annuity (EAA) Approach Finds the constant annuity payment whose PV is equal to the project’s raw NPV over its original life.
EAA Calculator Solution Project S PV = Raw NPV = $4,132. n = Original project life = 2. k = 10%. Solve for PMT = EAA S = $2,381. Project L PV = $6,190; n = 4; k = 10%. Solve for PMT = EAA L = $1,953.
The project, in effect, provides an annuity of EAA. EAA S > EAA L so pick S. Replacement chains and EAA always lead to the same decision if cash flows are expected to stay the same.
If the cost to repeat S in two years rises to $105,000, which is best? (000s) NPV S = $3,415 < NPV L = $6,190. Now choose L. NPV S = $3,415 < NPV L = $6,190. Now choose L Franchise S: (100) 60 (105) (45) 60
Types of Abandonment Sale to another party who can obtain greater cash flows, e.g., IBM sold typewriter division. Abandon because losing money, e.g., smokeless cigarette.
Year CF ($5,000) 2,100 2,000 1,750 Salvage Value $5,000 3,100 2,000 0 Consider another project with a 3-year life. If terminated prior to Year 3, the machinery will have positive salvage value.
No termination 2. Terminate 2 years 3. Terminate 1 year (5) CFs Under Each Alternative (000s)
NPV (no) = -$123. NPV (2) = $215. NPV (1) = -$273. Assuming a 10% cost of capital, what is the project’s optimal, or economic life?
The project is acceptable only if operated for 2 years. A project’s engineering life does not always equal its economic life. Conclusions
The project is acceptable only if operated for 2 years. A project’s engineering life does not always equal its economic life. The ability to abandon a project may make an otherwise unattractive project acceptable. Abandonment possibilities will be very important when we get to risk. Conclusions
Choosing the Optimal Capital Budget Finance theory says to accept all positive NPV projects. Two problems can occur when there is not enough internally generated cash to fund all positive NPV projects: An increasing marginal cost of capital. Capital rationing
Increasing Marginal Cost of Capital Externally raised capital can have large flotation costs, which increase the cost of capital. Investors often perceive large capital budgets as being risky, which drives up the cost of capital. (More...)
If external funds will be raised, then the NPV of all projects should be estimated using this higher marginal cost of capital.
Capital Rationing Capital rationing occurs when a company chooses not to fund all positive NPV projects. The company typically sets an upper limit on the total amount of capital expenditures that it will make in the upcoming year. (More...)
Reason: Companies want to avoid the direct costs (i.e., flotation costs) and the indirect costs of issuing new capital. Solution: Increase the cost of capital by enough to reflect all of these costs, and then accept all projects that still have a positive NPV with the higher cost of capital. (More...)
Reason: Companies don’t have enough managerial, marketing, or engineering staff to implement all positive NPV projects. Solution: Use linear programming to maximize NPV subject to not exceeding the constraints on staffing. (More...)
Reason: Companies believe that the project’s managers forecast unreasonably high cash flow estimates, so companies “filter” out the worst projects by limiting the total amount of projects that can be accepted. Solution: Implement a post-audit process and tie the managers’ compensation to the subsequent performance of the project.