Answer:
a) NPV = $43,874.65
b) IRR = 24.37%
c) payback period = 5.33 years
d) equivalent annual cost = $6,024.55
e) equivalent annual savings = $13,298.61
f) since the NPV is positive, the equivalent annual savings must be higher than the equivalent annual costs
Explanation:
initial outlay year 0 = -$45,000
net savings year 1 = -$1,400 + (4,200 x $2) = $7,000
net savings year 2 = -$1,400 + (4,200 x $2.50) = $9,100
net savings year 3 = -$1,400 + (4,200 x $3) = $11,200
net savings years 4 - 20 = -$1,400 + (4,200 x $3.50) = $13,300
discount rate = 12%
using a financial calculator:
NPV = $43,874.65
IRR = 24.37%
payback period = 5.33 years
equivalent annual cost = (present value of costs x 12%) / / [1 - (1 + 12%)⁻ⁿ] =[($45,000 + $10,457.22) x 12%] / [1 - (1 + 12%)⁻ⁿ] = $6,654.87 / 0.89633 = $7,424.57
equivalent annual savings = (present value of savings x 12%) / / [1 - (1 + 12%)⁻ⁿ] = ($99,332.87 x 12%) / / [1 - (1 + 12%)⁻ⁿ] = $11,919.94 / 0.89633 = $13,298.61
