Answer:
the company should not buy the machine.
Explanation:
Given that:
cost of the new machine = $38000
lifespan = 8 years
constant income = 5,000
Interest = 1.7%
no of days = 365
The value of earning at the time of buying can be calculated as follows:
[tex]= \dfrac{5000}{(1+ \dfrac{1.7}{100})^8}+ \dfrac{5000}{(1+ \dfrac{1.7}{100})^7}+\dfrac{5000}{(1+ \dfrac{1.7}{100})^6}+...+ \dfrac{5000}{(1+ \dfrac{1.7}{100})^0}[/tex]
[tex]= 5000 \begin {pmatrix} \dfrac{1}{(1.017)^8}+ \dfrac{1}{(1.017)^8}+\dfrac{1}{(1.017)^6}+...+ 1} \end {pmatrix}[/tex]
Sum of a Geometric progression [tex]S=a \dfrac{(r^n -1)}{(r-1)}[/tex]
[tex]S=(\dfrac{1}{1.017})^8 \dfrac{((1.017)^9 -1)}{(1.017-1)}[/tex]
[tex]S= \dfrac{((1.017)^9 -1)}{ (1.017)^8(0.017)}[/tex]
S = 8.4211
The value of earning at the time of buying = (5000 × 8.4211)-$5000
The value of earning at the time of buying = $42105.5 -$5000
The value of earning at the time of buying = $37105.5
The Machine price = $38000
If the value - Machine price > 0, then the company should buy the machine
∴
= $ 37105.5 - $38000
= -$ 894.5
Since the value is negative which is less than zero, then the company should not buy the machine.
The company should not buy the machine since it earns a negative NPV of $894.25.
Data and Calculations:
Cost of machine in present value = $38,000
Projected lifespan = 8 years
Additional annual income = $5,000
Compound interest rate = 1.7%
Present value annuity factor for 1.7% for 8 years = 0.13475
Present value of annual income = $37,105.75 ($5,000/0.13475)
Net present value = -$894.25 ($38,000 - $37,105.75)
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