Answer: $354,738.94
Explanation:
Okay so for the 3 years this machine took up about $11,000 per annum in costs.
And it had an original cost of $870,000.
And we need to find the equivalent total annual average cost.
Cool.
Here's what we'll do.
We'll present value all the costs add them up so that we find the total cost TODAY. Then we will divide by the present value annuity factor for the period since the payments are equal.
Calculating that therefore we have,
Present Value of Total Cost = 870,000 + (11,000/1.09) + (11,000/1.09^2) + (11,000/1.09^3)
= $897,844.24 is the Total Cost.
Now we divide that total cost by the Present Value Interest factor for an annuity of,
PVIFA = ( 1 - ( 1 + r) ^-n )/r
= (1 - (1 + 0.09) ^ -3) / 0.09
= 2.53129466599
= 2.531
Now we divide the total cost by the PVIFA to get,
= 897,844.24/2.531
= 354738.937179
= $354,738.94
$354,738.94 is the equivalent total average annual cost of the oven if the required rate of return is 9 percent.
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