Sensitivity analysis is used in capital budgeting to
Answer(s): B
After a problem has been formulated into any mathematical model, it may be subjected to sensitivity analysis, which is a trial-and-error method used to determine the sensitivity of the estimates used. For example, forecasts of many calculated NPVs under various assumptions may be compared to determine how sensitive the NPV is to changing conditions. Changing the assumptions about a certain variable or group of variables may drastically alter the NPV, suggesting that the risk of the investment may be excessive.
When determining net present value in an inflationary environment, adjustments should be made to
In an inflationary environment, nominal future cash flows should increase to reflect the decrease in the value of the unit of measure. Also, the investor should increase the discount rate to reflect the increased inflation premium arising from the additional uncertainty. Lenders will require a higher interest rate in an inflationary environment.
When evaluating a capital budgeting project, a company's treasurer wants to know how changes in operating income and the number of years in the project's useful life will affect its breakeven internal rate of return. The treasurer is most likely to use
Forecasts of many calculated NPVs under various assumptions are compared to see how sensitive NPV is to changing conditions. Changing or relaxing the assumptions about a certain variable or group of variables may drastically alter the NPV). Thus, the asset may appear to be much riskier than was originally predicted. In summary, sensitivity analysis is simply an iterative process of recalculated returns based on changing assumptions.
A company is evaluating the possible introduction of a new version of an existing product that will have a 2-year life cycle. At the end of 2 years, this version will be obsolete, with no additional cash flows or salvage value. The initial and sole outlay for the modified product is $6 million, and the company's desired rate of return is 10%. Following are the potential cash flows (assumed to occur at the end of each year) and their probabilities if the product is marketed:The following interest factors for the present value of $1 at 10% are relevant:Period 1 .9092 .826The project's net present value is
Answer(s): A
The expected value of the cash flows at the end of Year 1 is $4 million [(.3 x $2 million)+ (.4x $4 million) + (.3 x $6 million)], and the present value of this amount is $3,636,000 (.909 x $4 million). The expected I value of the cash flows at the end of Year 2 is $3,925,000 [(.3 x .5 x $0) + (.3 x .5 x $4 million) + (.4x .25 x $6.4 million) + (.4x .75 x $3.2 million) + (.3 x Ax $6.875 million) + (.3 x .6 x $5 million)], and the present value of this amount is $3,242,050 (.826 x $3,925,000). Hence, the NPV is $878,050 [($3,636,000 + $3,242,050) -- $6 million initial outlay].
A company is evaluating the possible introduction of a new version of an existing product that will have a 2-year life cycle. At the end of 2 years, this version will be obsolete, with no additional cash flows or salvage value. The initial and sole outlay for the modified product is $6 million, and the company's desired rate of return is 10%. Following are the potential cash flows (assumed to occur at the end of each year) and their probabilities if the product is marketed:The following interest factors for the present value of $1 at 10% are relevant:Period 1 .9092 .826Assume the company has the real option to abandon the project at the end of Year 1. If the salvage value at that time is $3 million and the desired rate of return remains at 10%, what is the project's net present value?
If the cash flows at the end of Year I equal $2 million, the expected value of the Year 2 cash flows is only $2 million [(.5 x $0) + (.5 x $4 million)]. If the cash flows at the end of year 1 equal $4 million or$6 million, the expected value of the Year 2 cash flows equals $4 million [(.25 x $6.4 million) + (.75 x $3.2 million)] or $5.75 million [(.4 x $6875 million) + (.6 x $5 million)], respectively. After discounting these expected values to the j end of Year 1,the present values are $1,818,000 (.909 x $2 million) given a $2 million Year I cash flow, $3,636,000 (.909 x $4 million) given a $4 million Year 1 cash flow, and $5,226,750 (.909 x $5.75 million) given a $6 million Year 1 cash flow. Accordingly, the real option of abandonment is preferable if the Year 1 cash flow is $2 million. The $3 million salvage value exceeds the expected value of the Year 2 cash flows discounted to the end of Year 1 in this case only. If the real option of abandonment is exercised only when Year I cash flows equal $2 million, the expected value of the cash flows at the end of Year 1 is $4.9 million{[.3 x ($2 million + $3 million salvage)] + (.4x $4 million) + (.3 x $6 million)}, and the present value of this amount is $4,454,100 (.909 x $4.9 million). The expected value of the cash flows at the end of Year 2 if the real option is exercised only when Year I cash flows equal $2 million is $3,325,000 (.3 x 1.0 x $0) + (.4 x .25 x $4 million) + (.4 x .75 x $3.2 million) + (.3 x .4 x $6.875 million) + (.3 x .6 x $5 million), and the present value of this amount is $2,746,450 (.826 x $3,325,000). Consequently, the NPV with an abandonment option is $1,200,550 ($4,454,100 + $2,746,450 --$6 million initial outlay). This amount is substantially greater than the NPV with no abandonment option.
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