Question

1. Hadey's House of Hummus (HHH) is really taking off and he is considering expanding his business by selling franchises. He estimates that from the moment a franchise opens, it will earn approximately $60000 per year, but that the revenue will increase continuously at a rate of 8% per year. The prevailing interest will be 3.5% for the foreseeable future. a. What is the present value of a 4-year franchise? b. What would the present value of a 4-year franchise be if Hadey estimated that the value of the franchise would increase by $5000 per year instead? c. Which estimate do you think would be more attractive to potential franchise operators?

Answer 1

(a) Expected Revenue = $ 60000 per annum, Rate of Continuous Revenue Growth = 8%

Interest Rate = 3.5 % and Annuity Tenure = 4years

Therefore, PV of Annuity = 60000 x [1/e^(0.035 x 4)] x [{e^(0.035 x 4) - 1} / {e^(0.035) - 1}] = $220060.92

(b) Increment in Revenue = $ 5000 per annum

Year 1 Revenue = $ 60000, Year 2 Revenue = $ 65000, Year 3 Revenue = $ 70000 and Year 4 Revenue = $ 75000

PV of Annuity = 60000 / e^(0.035 x 1) + 65000 / e^(0.035 x 2) + 70000 / e^(0.035 x 3) + 75000 / e^(0.035 x 4) = $ 246766.51

(c) A franchise operator will select option (b) over option (a) because the former has a greter PV as compared to the latter.