Solve the following problems at the annual interest rate 5%. Initial Cost Annual
ID: 2780375 • Letter: S
Question
Solve the following problems at the annual interest rate 5%. Initial Cost Annual costs Annual benefit $70,000 5,000 Salvage 30,000 Useful lives 5 years 18,000 1) Calculate the Net Present Worth (present worth of all benefits minus present worth of all costs) when the analysis period is 6 years. Consider the salvage at the end of points) 2) Calculate the Net Equivalent Uniform Annual Benefit (equivalent uniform annual benefit minus equivalent uniform annual cost) when the analysis period is 9 years. Consider the salvage at the end of useful life a benefit. (15 points) useful life a benefit. (15Explanation / Answer
Initial cost = $70,000
Annual cost = $5,000
Annual benefit = $18,000
Salvage value = $30,000
Net annual benefit = Annual benefit - Annual cost = 18,000 – 5000 = $13,000
Useful life = 3 years
R = 5%
Net Present value of benefits for 3 year life = present value of all benefits - initial cost
Net Present value of benefits for 3 year life = 13,000*(1-1/(1+R)3)/R + 30,000/(1+R)3 - 70,000
Net Present value of benefits for 3 year life = 13,000*(1-1/1.053)/0.05 + 30,000/1.053 – 70,000 = -8682.75
If analysis period is 6 years and repeatability of the data is possible.
Then,
Net Present value of benefits for 6 year = (-8682.75) + (-8682.75)/(1+0.05)3 = (-8682.75)+ (-7500.49) = -16183.24
(Because, the investment, benefits, cost and salvage value will again occur at the end of 3 years)
Net Present value of benefits for 6 year = -$16183.24
B.If the study period is 9 years
Net Present value of benefits for 9 year = (-8682.75) + (-8682.75)/(1+0.05)3 + (-8682.75)/(1+0.05)6
(As repeatability will take place at the end of 3 years and 6 years)
Net Present value of benefits for 9 year = -$22662.9
Let, net annual uniform benefit = AUB
Then,
-22,662.9 = AUB*(1 – 1/(1+R)9)/R = AUB*(1-1/(1+5%)9)/0.05 = AUB* 7.107
AUB = -22662.9 / 7.107
AUB = - $3188.81
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