We have to calculate the EAC for both the conveyor belt system.
Solutions :
<u>Equivalent Annual Cost or (EAC) for the SYSTEM-A</u>
tax rate )
![$=-855,000(1-0.23)+\left[\left(\frac{280,000}{4}\right)\times 0.23\right]$](https://tex.z-dn.net/?f=%24%3D-855%2C000%281-0.23%29%2B%5Cleft%5B%5Cleft%28%5Cfrac%7B280%2C000%7D%7B4%7D%5Cright%29%5Ctimes%200.23%5Cright%5D%24)
![$= (-85,000 \times 0.77 ) + (70,000 \times 0.23)$](https://tex.z-dn.net/?f=%24%3D%20%28-85%2C000%20%5Ctimes%200.77%20%29%20%2B%20%2870%2C000%20%5Ctimes%200.23%29%24)
= $ 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 <u> 0.683013 </u> <u>-33,706.71 </u>
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 :
![$\text{EAC}= \text{Net present value / (PVIFA 10 percent, 4 years)}$](https://tex.z-dn.net/?f=%24%5Ctext%7BEAC%7D%3D%20%5Ctext%7BNet%20present%20value%20%2F%20%28PVIFA%2010%20percent%2C%204%20years%29%7D%24)
![$=\frac{436,432.86}{3.169865}$](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B436%2C432.86%7D%7B3.169865%7D%24)
dollar (negative)
tax rate)
![$=79,000(1-0.23)+\left[\left(\frac{360,000}{6}\right) \times 0.23\right]$](https://tex.z-dn.net/?f=%24%3D79%2C000%281-0.23%29%2B%5Cleft%5B%5Cleft%28%5Cfrac%7B360%2C000%7D%7B6%7D%5Cright%29%20%5Ctimes%200.23%5Cright%5D%24)
![$=(-78,000 \times 0.77)+(60,000 \times 0.23)$](https://tex.z-dn.net/?f=%24%3D%28-78%2C000%20%5Ctimes%200.77%29%2B%2860%2C000%20%5Ctimes%200.23%29%24)
= -$ 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 <u> 0.564474 </u> <u> -26,547.21 </u>
Total $ 4.355261 $ -204,827.91
Net Present Value = Present Value of annual cash inflows – Initial Investment
![$= 204,827.91 - 360,000$](https://tex.z-dn.net/?f=%24%3D%20204%2C827.91%20-%20360%2C000%24)
= -$ 564,827.91 (negative)
EAC for system B:
Equivalent Annual Cost for system B ![$=\frac{\text{net present value}}{\text{PVIFA 10 \text percent, 6 years}}$](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B%5Ctext%7Bnet%20present%20value%7D%7D%7B%5Ctext%7BPVIFA%2010%20%5Ctext%20percent%2C%206%20years%7D%7D%24)
![$=\frac{-564,827.91}{4.355261}$](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B-564%2C827.91%7D%7B4.355261%7D%24)
= -$129,688.66 (negative)