22.2.4: Sensitivity Analysis

Sensitivity Analysis

To present the basics of the NPV and IRR methods, we have assumed that the expected values of cash flows will occur for certain. In reality, there is much uncertainty associated with predicting future cash flows. To examine how a result will change if the predicted financial outcomes are not achieved or if an underlying assumption changes, managers use sensitivity analysis, also called “what if” technique, introduced in Chapter 3.

A common way to apply sensitivity analysis to capital budgeting decisions is to vary each of the inputs to the NPV calculation by a certain percentage and assess the effect on the project’s NPV. Sensitivity analysis can take on other forms as well. Suppose a manager at Vector believes the firm’s forecasted cash flows are difficult to predict. She asks, “What are the minimum annual cash inflows that make the investment in a new hybrid bus acceptable—that is, what inflows lead to an $inline style begin inline style NPV equals straight $ 0 end style$ ?” For the data in Exhibit 22-2, let $A = annual$ cash flow and let the $inline style begin inline style NPV equals straight $ 0 end style$ . The net initial investment is $648,900, and the present value factor at the 8% required annual rate of return for a 5-year annuity of $1 is 3.993. Then

$\begin{array}{rcl} NPV & = & $ 0 \\ 3.993 A - $ 648,900 & = & $ 0 \\ 3.993 A & = & $ 648,900 \\ A & = & $ 162,509 \end{array}$

At the discount rate of 8% per year, the annual (after-tax) cash inflows can decrease to $162,509 (a decline of $$ 180,000 - $ 162,509 = $ 17,491$ ) before the NPV falls to $0. If the manager believes she can attain annual cash inflows of at least $162,509, she can justify investing in the hybrid bus on financial grounds.

Exhibit 22-4 shows that variations in the annual cash inflows or the RRR significantly affect the NPV of the hybrid bus project. NPVs can also vary with different useful lives of a project. Sensitivity analysis helps managers to focus on decisions that are most sensitive to different assumptions and to worry less about decisions that are not as sensitive. It is also an important risk-management tool because it provides information to managers about the downside risks of projects as well as their potential impact on the health of the overall firm.

Spreadsheet screenshot shows net present value calculations for Vector’s Hybrid Bus under different assumptions of annual cash flows and required rates of return. All calculated amounts assume the project’s useful life is 5 years.

Details are as follows:

Annual cash inﬂow: $140,000
Required Rate of Return 8%: $(89,880) in parentheses
Required Rate of Return 10%: $(118,160) in parentheses
Required Rate of Return 12%: $(144,200) in parentheses
Annual cash inﬂow: $160,000
Required Rate of Return 8%: $(10,020) in parentheses
Required Rate of Return 10%: $(42,340) in parentheses
Required Rate of Return 12%: $(72,100) in parentheses
Annual cash inﬂow: $180,000
Required Rate of Return 8%: $69,840
Required Rate of Return 10%: $33,480
Required Rate of Return 12%: $0
Annual cash inﬂow: $200,000
Required Rate of Return 8%: $149,700
Required Rate of Return 10%: $109,300
Required Rate of Return 12%: $72,100
Annual cash inﬂow: $220,000
Required Rate of Return 8%: $229,560
Required Rate of Return 10%: $185,120
Required Rate of Return 12%: $144,200.