Question

A burger joint needs a $25,000 start up fee. the base demand for the burger buns is 40,000 patties per year with a decrease of 8,000 patties per year for every dollar the price increases past 0.The total cost for each patty is 1 dollar per patty. A pizza cafe needs a $18,000 start up fee the base demand for the slices is 60,000 per year with a decrease of 15,000 per year for every dollar the price increases past 0. The total cost for each slice is .50c per slice Demand for either food will increase 5 percent every year following year 1. What enterprise will be more profitable over 5 years not accounting for depreciations just cash flows. show work show percentage return.

Answer 1

Let Price of burger be P1

Quantity demanded would be 40000-8000P1

Revenue would be P1*(40000-8000P1)

Profit would be (P1-1)*(40000-8000P1)

Maximization of profit would occur at P1=3

Hence, demand in year 1=40000-8000*3=16000

profit in year 1=16000*2=32000

Let Price of patties be P2

Quantity demanded would be 60000-15000P2

Revenue would be P2*(60000-15000P2)

Profit would be (P2-0.5)*(60000-15000P2)

Maximization of profit would occur at P2=2.25

Hence, demand in year 1=60000-15000*2.25=26250

profit in year 1=26250*1.75=45937.5

Assuming price of burger/patties do not change despite demand changing

percentage return for burger:

-25000+32000/(1+IRR)+32000*1.05/(1+IRR)^2+32000*1.05^2/(1+IRR)^3+32000*1.05^3/(1+IRR)^4+32000*1.05^4/(1+IRR)^5=0

=>IRR=130.49%

percentage return for patties:

-18000+45937.5/(1+IRR)+45937.5*1.05/(1+IRR)^2+45937.5*1.05^2/(1+IRR)^3+45937.5*1.05^3/(1+IRR)^4+45937.5*1.05^4/(1+IRR)^5=0

=>IRR=259.67%