4. (a) A piece of with time until at 100 years 10,000. It year for the planning

Question

4. (a) A piece of with time until at 100 years 10,000. It year for the planning horizon per year by 100 Thnghorizon period. Costs start at 1000 per year and increase each equipment costs 100,000. The salvage value slowly decreases linearly of the system at the end of year rs it is 10,000. It generates a revenue stream of 20,000 per e interest rate for the situation is 6% per year, what is the future worth 80? Show all work (b) What is the annualized worth of the system? Show work. (Use back if needed)

Explanation / Answer

The ramaining years of life = 20 years salvage value at the end of year 100 = 10000

Cost starts as 1000 per year and it increases 100 per year that means cost for 81st year = 1000+80*100 = 9000 per year and it increases 100 per year up to 100 years

Annualised worth of system at year 80 = Total worth / (Pvf @ 6% for 20 years)

=

Year Cash inflow cash outflow Net PVF @ 6% DISCCf 81 20000 9100 10900 0.943396 10283.02 82 20000 9200 10800 0.889996 9611.962 83 20000 9300 10700 0.839619 8983.926 84 20000 9400 10600 0.792094 8396.193 85 20000 9500 10500 0.747258 7846.211 86 20000 9600 10400 0.704961 7331.59 87 20000 9700 10300 0.665057 6850.088 88 20000 9800 10200 0.627412 6399.606 89 20000 9900 10100 0.591898 5978.174 90 20000 10000 10000 0.558395 5583.948 91 20000 10100 9900 0.526788 5215.197 92 20000 10200 9800 0.496969 4870.3 93 20000 10300 9700 0.468839 4547.739 94 20000 10400 9600 0.442301 4246.089 95 20000 10500 9500 0.417265 3964.018 96 20000 10600 9400 0.393646 3700.275 97 20000 10700 9300 0.371364 3453.689 98 20000 10800 9200 0.350344 3223.163 99 20000 10900 9100 0.330513 3007.668 100 30000 11000 19000 0.311805 5924.29 (20000+10000) 11.46992 Future worth of system at year 80 119417.1

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