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I need help with question 7.18. I looked at the solution for this questions but it was a given a thumbs down and I don't know why

7.17 Barron Chemical uses a thermoplastic polymer to enhance the appearance of certain RV panels. The initial cost of one process was $130,000 with an- nual costs of $49,000 and revenues of $78,000 in year 1, increasing by $1000 per year. A salvage value of $23,000 was realized when the process was discontinued after 8 years. What rate of return did the company make on the process? Solve by trial and error and verify i* by spreadsheet. 7.18 Steel cable barriers in highway medians are a low- cost way to improve traffic safety without over- stressing department of transportation budgets. Cable barriers cost $44,000 per mile, compared with $72,000 per mile for guardrail and $419,000 per mile for concrete barriers. Furthermore, cable barriers tend to snag tractor-trailer rigs, keeping them from ricocheting back into same-direction traffic. The state of Ohio spent $4.97 million in- stalling 113 miles of cable barriers. Answer the

Answer 1

Please find the solution in given screen shots,

Amount in $ - million.

(a) Calculation of Rate of Return when Cable Barrier is used Using Tabulated Factors Rate of Return i.e. IRR under trial & error method is derived by extrapolating two NPVs that have been calculated using two random discount rates R1 NPV 1 R2 NPV 2 15% Random Rate 1 is based on Net Cash Value as explained in WN-1 1.55 WN-1 23% Random Rate 2 is based on Random 1 Rate as explained in WN-1 -0.03 WN-2 IRR = R1 + NPV1 X (R2-R1)/(NPV1 - NPV2) R2-R1 NPV1 - NPV2 NPV1 X (R2-R1) NPV1 X (R2-R1) / (NPV1 - NPV2) IRR (putting the numbers in Formula) 8% 1.59 0.12 0.078438 22.84%

WN-1 8.03 | Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Initial Outlay -4.97 Prevention of Accident 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.31 131 13 Net Cash flow -4.97 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 PV Factor @15% 1 0.87 0.76 0.66 0.57 0.50 0.43 0.38 0.33 0.28 0.25 NPV -4.97 1 .13 0.98 0.85 0.74 0 .65 0.56 0.49 0.42 0.37 0.32 1.55 Net Cash flow when not discounted gives a return of 8.03 million which is positive, we may assume that it may have a positive rate of return therefore we have considered a random positive rate of 15% At 15% we find NPV of 1.55 million which means the project will give return even more than of 15% because when discounted by higher rate the NPV will become zero or less than zero - Rate of return is the rate where NPV becomes zero, therefore next 23% is considered as Random Rate Year o Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 Year 10 Total -4.97 1.3 Initial Outlay Prevention of Accident Net Cash flow PV Factor @23% NPV 8.03 -4.97 11 -4.97 1.3 1.3 0.81 1.06 1.3 1.3 0.66 0.86 1.3 1.3 0.54 0.70 1.3 1.3 0.44 0.57 1.3 1.3 0.36 0.46 1.3 1.3 0.29 0.38 1.3 1.3 0.23 0.31 1.3 1.3 0.19 0.25 1.3 1.3 0.16 0.20 0.13 0.16 -0.03

Using Spreadsheet Function To arrive at rate of return for given seriese of cash flows given below function can be used - using the same function IRR also is arrived and shown. =IRR(values, (guess]) In place of values we need to select the array of net cash flows starting from year 0 to year 10 In place of [guess] we can put a guess which we believe could be the IRR - this is optional - we may just select the net cash flows and close the bracket If Year Onet cash flow is in spreadsheet cell B2 and Year 1 in B3 and so on then the function will look like, =IRR(B2:L2) Solving in Spread Sheet we find that IRR is 22.80% Calculation of Rate of Return when Guardrail is used Using Tabulated Factors Rate of Return i.e. IRR under trial & error method is derived by extrapolating two NPVs that have been calculated using two random discount rates R1 NPV 1 R2 NPV 2 -10% Random Rate 1 is based on Net Cash Value as explained in WN-2 -26.80 WN-1 -20% Random Rate 2 is based on Random 1 Rate as explained in WN-2 -1.62 WN-2 IRR = R1 + NPV1 X (R2-R1)/(NPV1 - NPV2)

-10% -25.18 R2-R1 NPV1 - NPV2 NPV1 X (R2-R1) NPV1 X (R2-R1)/(NPV1 - NPV2) IRR (putting the numbers in Formula) -0.10645 -20.65% WN-2 Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 | Year 7 Year 8 Year 9 Year 10 Total Initial Outlay -47.35 Prevention of Accident 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 Net Cash flow -47.35 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 -36.35 PV Factor @ -10% 1 1.11 1.23 1.37 1.52 1.69 1.88 2.09 2.32 2.87 NPV -47.35 1.22 1.36 1.51) 1.68 1.86 2.07 2.30 2.56 2.84 3.15 -26.80 Net Cash flow when not discounted gives return of negative 36.35 million which means if this project is discounted even with 0% rate the NPV is negative if discounted with higher rate we will get even more negative - we can conclude that rate of return will be negative hence -10% is used as first random rate. 2.58 At -10% we still find the NPV negative which means the project will give return even more than of -10% because when discounted by higher negative rate the NPV will become zero or more than zero - Rate of return is the rate where NPV becomes zero, therefore next -20% is considered as Random Rate Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 Year 10 Total Year -47.35 1.1 1.1 1.1 1.1 1.1 1.1 1.1 Initial Outlay Prevention of Accident Net Cash flow PV Factor @-20% NPV -47.347 1.1 1.1 1.1 1.1 1.1 -36.35 1.56 1.1 1.1 7.45 8.20 1.1 2.44 2.69 1.1 3.05 3.36 1.25 1.38 1.95 2.15 5.96 1.1 4.77 5.25 9.31 3.81 4.20 -47.35 1.72 6.56 10.24 -1.62

Calculation of Initial Outlay Per mile rate of Guardrail For 113, 0.419 X 113 0.419000 47.35 Using Spreadsheet Function To arrive at rate of return for given seriese of cash flows given below function can be used - using the same function IRR also is arrived and shown. =IRR(values, Iguess]) In place of values we need to select the array of net cash flows starting from year 0 to year 10 In place of (guess] we can put a guess which we believe could be the IRR - this is optional - we may just select the net cash flows and close the bracket If Year Onet cash flow is in spreadsheet cell B2 and Year 1 in B3 and so on then the function will look like, =IRR(B2:L2) Solving in Spread Sheet we find that IRR is -20.39%

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