Behavioral approaches can be used to get a “feel” for the level of project risk, whereas other approaches try to quantify and measure project risk. Here we pres- ent a few behavioral approaches for dealing with risk in capital budgeting:
breakeven analysis, scenario analysis, and simulation.
BREAKEVEN ANALYSIS
In the context of capital budgeting, the term risk refers to the uncertainty sur- rounding the cash flows that a project will generate. More formally, risk in capi- tal budgeting is the degree of variability of cash flows. Projects with a broad range of possible cash flows are more risky than projects that have a narrow range of possible cash flows.
In many projects, risk stems almost entirely from the cash flows that a proj- ect will generate several years in the future because the initial investment is gener- ally known with relative certainty. The subsequent cash flows, of course, derive from a number of variables related to revenues, expenditures, and taxes. Exam- ples include the level of sales, the cost of raw materials, labor rates, utility costs, and tax rates. We will concentrate on the risk in the cash flows, but remember that this risk actually results from the interaction of these underlying variables.
Therefore, to assess the risk of a proposed capital expenditure, the analyst needs to evaluate the probability that the cash inflows will be large enough to produce a positive NPV.
Treadwell Tire Company, a tire retailer with a 10% cost of capital, is considering investing in either of two mutually exclusive projects, A and B. Each requires a
$10,000 initial investment, and both are expected to provide constant annual cash inflows over their 15-year lives. For either project to be acceptable, its NPV must be greater than zero. In other words, the present value of the annuity (that is, the project’s cash inflows) must be greater than the initial cash outflow. If we let CF equal the annual cash inflow and CF0 equal the initial investment, the fol- lowing condition must be met for projects with annuity cash inflows, such as A and B, to be acceptable:1
Example 12.1 ▶
LG2
risk (in capital budgeting) The uncertainty surrounding the cash flows that a project will generate or, more formally, the degree of variability of cash flows.
1. This equation makes use of the algebraic shortcut for the present value of an annuity, introduced in Personal Finance Example 5.7 on page 175.
breakeven cash inflow The minimum level of cash inflow necessary for a project to be acceptable, that is, NPV . $0.
NPV = aCF
r b * c1 - 1
(1 + r)nd - CF0 7 $0 (12.1)
By substituting r = 10,, n = 15 years, and CF0 = $10,000, we can find the breakeven cash inflow, the minimum level of cash inflow necessary for Treadwell’s projects to be acceptable.
Calculator use Recognizing that the initial investment (CF0) is the present value (PV), we can use the calculator inputs shown at the left to find the breakeven cash inflow (CF), which is an ordinary annuity (PMT).
1,314.74 210000 PV
N
CPT PMT I 15 10
Solution Input Function
MyFinancelab financial calculator
Spreadsheet use The breakeven cash inflow also can be calculated as shown on the following Excel spreadsheet.
BREAKEVEN CASH INFLOW Cost of capital
Number of years Initial investment Breakeven cash inflow 1
2 3 4 5
10%
15 –$10,000
$1,314.74 Entry in Cell B5 is =PMT(B2,B3,B4,0,0).
The minus sign appears before the initial investment in B4 because it is a cash outflow.
A B
The calculator and spreadsheet values indicate that, for the projects to be ac- ceptable, they must have annual cash inflows of at least $1,315. Given this break- even level of cash inflows, the risk of each project can be assessed by determining the probability that the project’s cash inflows will equal or exceed this breakeven level. The various statistical techniques that would determine that probability are covered in more advanced courses.2 For now, we can simply assume that such a statistical analysis results in the following:
Probability of CFA 7 $1,315S100, Probability of CFB 7 $1,315S65,
Because project A is certain (100% probability) to have a positive net present value, whereas there is only a 65% chance that project B will have a positive NPV, project A seems less risky than project B. Of course, the expected level of annual cash inflow and NPV associated with each project must be evaluated in view of the firm’s risk preference before the preferred project is selected.
The example clearly identifies risk as it is related to the chance that a project is acceptable, but it does not address the issue of cash flow variability. Even though project B has a greater chance of loss than project A, it might result in higher potential NPVs. Recall that it is the combination of risk and return that determines value. Similarly, the benefit of a capital expenditure and its impact on the firm’s value must be viewed in light of both risk and return. The analyst must therefore consider the variability of cash inflows and NPVs to assess project risk and return fully.
SCENARIO ANALYSIS
Scenario analysis can be used to deal with project risk to capture the variability of cash inflows and NPVs. Scenario analysis is a behavioral approach that uses sev- eral possible alternative outcomes (scenarios) to obtain a sense of the variability of returns, measured here by NPV. This technique is often useful in getting a feel for the variability of return in response to changes in a key outcome. In capital
2. Normal distributions are commonly used to develop the concept of the probability of success, that is, of a project having a positive NPV. The reader interested in learning more about this technique should see any second- or MBA- level managerial finance text.
Scenario Analysis of Treadwell’s Projects A and B
budgeting, one of the most common scenario approaches is to estimate the NPVs associated with pessimistic (worst), most likely (expected), and optimistic (best) estimates of cash inflow. The range can be determined by subtracting the pessi- mistic-outcome NPV from the optimistic-outcome NPV.
Continuing with Treadwell Tire Company, assume that the financial manager created three scenarios for each project: pessimistic, most likely, and optimistic.
The cash inflows and resulting NPVs in each case are summarized in Table 12.2.
Comparing the ranges of cash inflows ($1,000 for project A and $4,000 for B) and, more important, the ranges of NPVs ($7,606 for project A and $30,424 for B) makes it clear that project A is less risky than project B. Given that both proj- ects have the same most likely NPV of $5,212, the assumed risk-averse decision maker will take project A because it has less risk (smaller NPV range) and no possibility of loss (all NPVs . $0).
The widespread availability of computers and spreadsheets has greatly en- hanced the use of scenario analysis because technology allows analysts to create a wide range of different scenarios quickly.
SIMuLATION
Simulation is a statistics-based behavioral approach that applies predetermined probability distributions and random numbers to estimate risky outcomes. By tying the various cash flow components together in a mathematical model and Example 12.2 ▶
simulation
A statistics-based behavioral approach that applies predetermined probability distributions and random numbers to estimate risky outcomes.
T A B L E 1 2 . 2
Project A Project B
Initial investment 2$10,000 2$10,000
Annual cash inflows
Outcome
Pessimistic $1,500 $ 0
Most likely 2,000 2,000
Optimistic 2,500 4,000
Range 1,000 4,000
Net present valuesa
Outcome
Pessimistic $1,409 2$10,000
Most likely 5,212 5,212
Optimistic 9,015 20,424
Range 7,606 30,424
aThese values were calculated by using the corresponding annual cash inflows. A 10% cost of capital and a 15-year life for the annual cash inflows were used.
repeating the process numerous times, the financial manager can develop a prob- ability distribution of project returns.
Figure 12.1 presents a flowchart of the simulation of the net present value of a project. The process of generating random numbers and using the probability distributions for cash inflows and cash outflows enables the financial manager to determine values for each of these variables. Substituting these values into the mathematical model results in an NPV. By repeating this process perhaps a thou- sand times, managers can create a probability distribution of net present values.
Although Figure 12.1 simulates only gross cash inflows and cash outflows, more sophisticated simulations using individual inflow and outflow components, such as sales volume, sale price, raw material cost, labor cost, and maintenance expense, are quite common. From the distribution of returns, the decision maker can determine not only the expected value of the return but also the probability of achieving or surpassing a given return. The use of computers has made the simulation approach feasible. Monte Carlo simulation programs, made popular by widespread use of personal computers, are described in the Focus on Practice box.
The output of simulation provides an excellent basis for decision making because it enables the decision maker to view a continuum of risk–return trade- offs rather than a single-point estimate.
F I G u R E 1 2 . 1 NPV Simulation
Flowchart of a net present value simulation
Mathematical Model
NPV = Present Value of Cash Inflows – Present Value of Cash Outflows
Probability
Cash Inflows Repeat
Generate Random Number
Probability
Cash Outflows
Probability
Net Present Value (NPV)
Generate Random Number
➔REVIEW QuESTIONS
12–2 Define risk in terms of the cash flows from a capital budgeting project.
How can determination of the breakeven cash inflow be used to gauge project risk?
12–3 Describe how each of the following behavioral approaches can be used to deal with project risk: (a) scenario analysis and (b) simulation.
➔ExCEL REVIEW QuESTION MyFinancelab
12–4 To judge the sensitivity of a project’s NPV, financial managers will of- ten compare a project’s forecasted cash inflows to the breakeven cash flows. Based on the information provided at MFL, develop a spread- sheet to compare forecasted and breakeven cash inflows.