] Monica Geller, head chef at Allesandro's and is looking to update the commercial equipment in her kitchen and bar that will allow them to serve 15 more people per day increase average menu order by $5. Allesandro’s currently serves 230 people per day with an average menu order of $16 per person. Monica also estimated spending $56,000 in added utility and maintenance cost every year. The expected salvage value of the upgrade at the end of 4 years is about 10% of the initial purchase. To expect a 15% required rate of return on investment, what would be the maximum amount that should be spent on the upgrade.

The maximum amount that should be spent on the upgrade is $38,298,000.

Step-by-step explanation:

Let the initial purchase be x.

The ROI = 15% of x = 0.15x

At the end of 4 years, salvage value = 10% of x = 0.1x

Current income per day = $16 × 230 = $3680

Expected income per day = $21 × 245 = $5145

Increase in income per day = $5145 - $3680 = $1465

For 4 years (assuming a year is 365 days),

Increase in income = $1465 × 365 × 4 = $2138900

Maintenance and utility cost for 4 years = 4 × $56000 = $224000

At the end of 4 years,

ROI = $2138900 + salvage value = $2138900 + 0.1x - $224000

0.15x = $1914900 + 0.1x

0.05x = $1914900

x = $38298000

$ 1,449,682

Step-by-step explanation:

Current number of customers per day = 230 people per day

Current Average menu order = $ 16 per person

Current daily revenue = 230*16 = $ 3,680

Added utility and maintenance cost per year = $ 56,000

Expected salvage value of the upgrade at the end of 4 years = 10% of the initial purchase

Required rate of return on investment = 15%

Incremental customers = 15

Incremental average menu order = $ 5

New average menu order = 16+5 = $ 21

New number of customers per day = 230+15 = 245

New revenue per day = 245*21 = $ 5,145

Incremental revenue per day = 5145 - 3680 = $ 1,465

Incremental revenue per year = 1465*365 = $ 534,725 (considering 365 days per year)

After subtracting the added utility and maintenance cost, net incremental cash flow per year = 534725 - 56000

= $ 478,725

Present value factor for incremental cash flow over 4 years

= (1 - 1.15^-4)/0.15

= 2.855

Present value factor for salvage value after 4 years = 1.15^-4 = 0.5718

Present Value (PV) of net incremental cash flow over 4 years = 478725*2.855 = $ 1,366,760

Let x be the maximum amount that should be spent on the upgrade

Net Present Value = PV of net incremental cash flow over 4 years - initial purchase cost + Present Value of salvage value

= 1366760 - x + 0.1x*0.5718

= 1366760 - 0.9428x

To find the maximum amount to be spent on upgrade, NPV should be equated to 0

1366760 - 0.9428x = 0

x = 1366760/0.9428

= $ 1,449,682

Therefore, maximum amount to be spent on the upgrade = $ 1,449,682

Acronym to remember the 3 basic trigonomic functions: 

Soh - Cah - Toa 

             opposite
sin =
            hypotenuse

              adjacent 
cos =
             hypotenuse

             opposite 
tan =  
             adjacent 

In your case, you can set up a sine trigonomic function, like this: 

Sin 48 = 10      (adjacent)
                 
                 x       (hypotenuse)

                       10
 (x) Sin 48 = (x)
                         x

  (x) Sin 48 = 10 
     
  Sin 48         Sin 48 

Plug in 10(sin)(48) into a calculator.

x = 7.43

I just realized that you didn't ask me to find the answer, but now you will know even more than you need to :D