By installing some elaborate inspection equipment
on its assembly line, the Robot Corp. can avoid hir-
ing an extra worker who would have earned $36,000
a year in wages and an additional $9500 a year in
employee benefits. The inspection equipment has a
6-year useful life and no salvage value. Use a nom-
inal 18% interest rate in your calculations. How
much can Robot afford to pay for the equipment if
the wages and worker benefits were to have been
paid
(a) At the end of each year
(b) Monthly
Explain why the answer in (b) is larger.
This is the formula im using
npw=p(p/a)+p(p/a)
To calculate the affordability of the inspection equipment, we need to determine the present worth of the savings from not hiring the extra worker.
(a) If the wages and employee benefits were paid at the end of each year, we can use the Present Worth (PW) formula:
PW = (P/A) + (P/A) * i
Where:
P = annual savings from not hiring the worker (wages + benefits)
A = annual uniform series factor for the interest rate and useful life
i = interest rate
First, let's calculate the annual savings:
Annual savings = wages + benefits
Annual savings = $36,000 + $9,500
Annual savings = $45,500
Now, we need to calculate the annual uniform series factor, A:
A = (1 - (1+i)^(-n))/i
Where:
i = interest rate (18% = 0.18)
n = useful life (6 years)
A = (1 - (1+0.18)^(-6))/0.18
A = (1 -(1.18)^(-6))/0.18
A = (1 - 0.3623)/0.18
A = 5.217
Now, substituting the values into the PW formula, we can find the affordability:
PW = (45,500/5.217) + (45,500/5.217) * 0.18
PW ≈ 8,735 + 1,493.44
PW ≈ $10,228.44
Therefore, if the wages and worker benefits were paid at the end of each year, Robot Corp. can afford to pay approximately $10,228.44 for the inspection equipment.
(b) Now, let's consider if the wages and benefits were paid monthly. To calculate this, we need to adjust the formula to reflect the monthly payments.
The adjusted formula becomes:
PW = (P/A) + (P/A) * (i/12)
Using the same calculations as before, we have:
Annual savings = $45,500
A = (1 - (1+0.18/12)^(-6*12))/(0.18/12)
A = (1 - (1.015)^(-72))/(0.015)
A = 37.007
Substituting the values into the adjusted PW formula, we can find the affordability:
PW = (45,500/37.007) + (45,500/37.007) * (0.18/12)
PW ≈ 1,231.87 + 224.71
PW ≈ $1,456.58
Therefore, if the wages and benefits were paid monthly, Robot Corp. can afford to pay approximately $1,456.58 for the inspection equipment.
The answer in (b) is larger because when the payments are made monthly, the interest is applied more frequently, resulting in an increased present worth of the savings.