b.What is the probability that the outcome will be between $21,000 and $39,000? c.What is the probability that the outcome will be at least $18,000? d.What is the probability that the outcome will be less than $41,760? e.What is the probability that the outcome will be less than $27,000 or greater than $39,000? 13-2 2 . Solut ion: a.expected value = $ 3 0,000, σ = $6,000 $24,000 > $30,000 < $36,000 expected value ± 1 σ .6826 b.$21,000 > $30,000 < $39,000 expected value ± 1.5 σ .8664 13 - 22 . (Continued) c.at least $18,000 .4772
.9772 Distribution under the curve $18,000 Less than $41,760 .4750
.9750 Distribution under the curve $41,760 13 - 22 . (Continued) e.Less than $27,000 or greater than $39,000 $27,000 $39,000
Area Distribution under the curve is .3753 23. Increasing risk over time (LO1) The Oklahoma Pipeline Company projects the following pattern of inflows from an investment. The inflows are spread over time to reflect delayed benefits. Each year is independent of the others. Year 1 Year 5Year 10Cash InflowProbabilityCash InflowProbabilityCash Inflow Probability65.20 50.25 40.3080.60 80.50 80.4095.20110.25120.30The expected value for all three years is $80. a.Compute the standard deviation for each of the three years. b.Diagram the expected values and standard deviations for each of the three years in a manner similar to Figure 13–6. c.Assuming 6 percent and 12 percent discount rates, complete the table below for present value factors. YearPVIF6% PVIF12% Difference 1.943.893.050 5________________________10________________________d.Is the increasing risk over time, as diagrammed in part b, consistent with the larger differences in PVIFs over time as computed in part c? e.Assume the initial investment is $135. What is the net present value of the investment at a 12 percent discount rate? Should the investment be accepted? 13-23.Solution: Oklahoma Pipeline Company a.Standard deviation—year 1 DPP$6580–15225.20458080 0 0.60 09580+15225.204590Standard deviation—year 5 DPP 5080–30900.25225 8080 0 0.50 011080+30900.2522545013-23. (Continued) Standard deviation—year 10 DPP 4080–401,600.30480 8080 0 0.40 012080+401,600.30480960b.Risk over time c. Year(1)PVIF (2)PVIF (3)PVIF 6% 12%Difference 1.943.893.050 5.747.567.18010.558.322.23613-23. (Continued) d.Yes. The larger risk over time is consistent with the larger differences in the present value interest factors (IFPV) over time. In effect, future uncertainty is being penalized by a lower present value interest factor (IFPV). This is one of the consequences of using progressively higher discount rates to penalize for risk. |

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