Respuesta :
We have to calculate the EAC for both the conveyor belt system.
Solutions :
Equivalent Annual Cost or (EAC) for the SYSTEM-A
[tex]$\text{Operating cash flow } = \text{Pre-tax annual operating cost (1-tax rate )} + (\text{depreciation expense} \times $[/tex]tax rate )
[tex]$=-855,000(1-0.23)+\left[\left(\frac{280,000}{4}\right)\times 0.23\right]$[/tex]
[tex]$= (-85,000 \times 0.77 ) + (70,000 \times 0.23)$[/tex]
= $ 49,350
Year Annual Cost flow Present value factor Present Value of Annual
at 10% cash flow
1 -49,350 0.909091 -44,863.64
2 -49,350 0.826446 -40,785.12
3 -49,350 0.751315 -37,077.39
4 -49,350 0.683013 -33,706.71
Total $ 3.169865 $ -156,432.86
Therefore, Net Present value = present value of the annual cash flow - initial investment.
= 156,432.86 - 280,000
= $ 436,432.86 (negative)
Now the EAC or the Equivalent Annual Cost for System A :
[tex]$\text{EAC}= \text{Net present value / (PVIFA 10 percent, 4 years)}$[/tex]
[tex]$=\frac{436,432.86}{3.169865}$[/tex]
[tex]$= 137,681.86 $[/tex] dollar (negative)
[tex]$\text{Operating cash flow } = \text{Pre-tax annual operating cost (1-tax rate )} + (\text{depreciation expense} \times $[/tex]tax rate)
[tex]$=79,000(1-0.23)+\left[\left(\frac{360,000}{6}\right) \times 0.23\right]$[/tex]
[tex]$=(-78,000 \times 0.77)+(60,000 \times 0.23)$[/tex]
= -$ 47,030
Year Annual Cost flow Present value factor Present Value of Annual
at 10% cash flow
1 -47,030 0.909091 -42,754.55
2 -47,030 0.826446 -38,867.77
3 -47,030 0.751315 -35,334.34
4 -47,030 0.683013 -32,122.12
5 -47,030 0.620921 -29,201.93
6 -47,030 0.564474 -26,547.21
Total $ 4.355261 $ -204,827.91
Net Present Value = Present Value of annual cash inflows – Initial Investment
[tex]$= 204,827.91 - 360,000$[/tex]
= -$ 564,827.91 (negative)
EAC for system B:
Equivalent Annual Cost for system B [tex]$=\frac{\text{net present value}}{\text{PVIFA 10 \text percent, 6 years}}$[/tex]
[tex]$=\frac{-564,827.91}{4.355261}$[/tex]
= -$129,688.66 (negative)
