$5\mathrm{.}3.$A company decided to develop low$-$cost photo$-$voltaic solar$-$energy cells. It decided on two development choices: a fully automatic line for $$800,000$ capable of producing $200,000$ cells$/$year for a profit of $$1/$cell$,$ or a semi$-$automatic line for $$500,000$ capable of producing $120,000$ cells$/$year for a profit $$1/$cell$.$ It is estimated that both lines will last for five years and will have a book value at the end of the five years of $10$ percent. Assume both lines will be working to $100$ percent capacity. You are the PM for development. Please make all calculations with or without taxes.

Show the ROI calculations for both machines, based on five$-$year life, $10$ percent book value, and $33$ percent taxes when applicable.

a$.$Fully automatic machine $=$ assume $33\%$ taxes, salvage value $10\%,$ and five$-$year life

b$.$Fully automatic machine $=$ assume no taxes, no salvage value, and five$-$year life

c$.$Semi$-$automatic machine $=$ assume $33$ percent taxes, salvage value $10\%,$ and five$-$year life

d$.$Semi$-$automatic machine $=$ assume no taxes, no salvage value, and five$-$year life

e$.$Conclusion: show which plan is better

$$With taxes and remaining book value: fully or semi$-$automatic?

$$Without taxes and remaining book value: fully or semi$-$automatic?

f$.$Show fixed and variable profit $($including operating costs$)$ breakeven point based on yearly volume for the first five years for both machines. Assuming i $=5\%,10$ cents$/$cell cost to operate the automatic and $40$ cents$/$cell to operate the semi$-$automatic machine. Selling price for both is $$1/$unit$.$ Please make a plot of the breakeven sales point.

g$.$Assuming an interest rate of $5\%$ and life of n $=5$ years with no tax consequences or book value remaining, show probability analysis for PV for $$500,000$ semi$-$automatic @ $120,000$ cells$/$year machine assuming two probabilities of profit per cell and useful number of years $($n$)$ for the machine. P $($profit $=$ $$0\mathrm{.}80)$ is $0\mathrm{.}8$ and P $($profit $=$ $$1)$ is $\mathrm{.}20$; and P $($n $=5)$ is $0\mathrm{.}4$ and P $($n $=4)$ is $0\mathrm{.}6$

h$.$Assuming an interest rate of $5\%$ and life of n $=5$ years with no tax consequences or book value remaining, show sensitivity analysis for PV for semi$-$automatic machine @ $120,000$ cells sold$/$year @ $$1$ profit per cell machine, assuming $\backslash$pm $20\%$ variations in the profit per cell and useful life. Plot the PV results versus the profit and useful life $\backslash$pm $20\%$ variations.

$5\mathrm{.}3.$

a$.$ Fully automatic machine, $33\%$ taxes, salvage value $=10\%,5-$year life

Depreciation$=($Asset Value$-$Book Value $)/$Lifecycle$=(800,000-80,000)/5=$$$144,000$

Year End Before Tax Cash Flow Depreciation Taxable Income Taxes After Tax Cash Flow

A B C D $=$ B $+$ C E $=-0\mathrm{.}33$ F $=$ B $+$ E

$0-800000$

$1200000-14400056000-18480181520$

$2200000-14400056000-18480181520$

$3200000-14400056000-18480181520$

$4200000-14400056000-18480181520$

$5200000-14400056000-18480181520$

$580000$

PV $=-800000+181520($P$/$A$,$ i$\%,5)+80000($P$/$F$,$ i$\%,5)$

Use i $=7\%$ PV $=-800000+181520($P$/$A$,7\%,5)+80000($P$/$F$,7\%,5)$

PV $=-800000+181520(4\mathrm{.}10)+80000(0\mathrm{.}7130)$ PV $=$ $$1272$

Use i $=8\%$ PV $=-800000+181520($P$/$A$,8\%,5)+80000($P$/$F$,8\%,5)$

PV $=-800000+181520(3\mathrm{.}99)+80000(0\mathrm{.}6806)$ PV $=$ $$-21,287\mathrm{.}2$

Since the PV goes from negative $(-)$ to positive $(+),$ the ROI is between $7$ and $8\%.$

Using a prorated average, closer to $7\%$ since PV $=$ $$1272$ at $7\%$

$1272/(1272+21287\mathrm{.}2)=0\mathrm{.}0567+0\mathrm{.}056$ ROI $=7\mathrm{.}056\%$

b$.$ Fully automatic machine, NO taxes, NO salvage value, $5-$year life

PV $=-800000+200000($P$/$A$,$ i$\%,5)$

Use i $=6\%$ PV $=-800000+200000($P$/$A$,6\%,5)$

PV $=-800000+200000(4\mathrm{.}21)$ PV $=$ $$42,000$

Use i $=7\%$ PV $=-800000+200000($P$/$A$,7\%,5)$

PV $=-800000+200000(4\mathrm{.}10)$ PV $=$ $$20,000$

Use i $=8\%$ PV $=-800000+200000($P$/$A$,8\%,5)$

PV $=-800000+200000(3\mathrm{.}99)$ PV $=-$$$2,000$

Since the PV goes from negative $(-)$ to positive $(+),$ the ROI is between $7$ and $8\%.$

Using a prorated average, closer to $8\%$ since PV $=-$ $$2,000$ at $7\%$

$20000/(20000+2000)=0\mathrm{.}9097+0\mathrm{.}909$ ROI $=7\mathrm{.}909\%$

c$.$ Semi$-$automatic machine, taxes $=33\%,$ salvage value $=10\%,5-$year life $($similar to a$)$

d$.$ Semi$-$automatic machine, NO taxes, NO salvage value, $5-$year life $($similar to b$)$

e$.$ Based on the ROI calculations performed in the parts above, the best option would be the highest ROI, Option $\_\_\_\_$

$5\mathrm{.}3$f$)$ Breakeven Analysis

Automatic machine $$ Cost $=$ $$800,000,10$ cents$/$cell cost

Semi$-$automatic machine $$ Cost $=$ $$500,000,40$ cents$/$cell cost

Selling cost $=$ $$1/$unit

Profit of automatic machine $=$ $$1-$ $$0\mathrm{.}1=$ $$0\mathrm{.}9/$part

Profit of semi$-$automatic machine $=$ $$1-$ $$0\mathrm{.}4=$ $$0\mathrm{.}6/$part

Assume NO salvage value, interest rate $=5\%,5-$year life

AV$1=-800000($A$/$P$,5\%,$ n $=5)+0\mathrm{.}9$N $=-800000(0\mathrm{.}231)+0\mathrm{.}9$N $=-184800+0\mathrm{.}9$N

AV$2=$

Breakeven is when AV$1=$ AV$2$ and solve for N pieces

N $=$ XXXXXX pieces

To demonstrate the breakeven analysis graphically, please generate a graph $($Figure $1)$ based on a range of x values $($N parts sold$)$ versus Y values from both machines $($AV$1$ and AV$2)$ <