Question

Lalo Salamanca, a young entrepreneur, is evaluating the potential purchase of El Michoacáno, a small restaurant located in Albuquerque, New Mexico. The restaurant is currently generating $50,000 of after-tax cash flow (D0 = $50,000). Based on a review of similar-risk investment opportunities, Lalo must earn an 10% rate of return on the proposed purchase. Because Lalo is relatively uncertain about future cash flows, he decides to estimate the firm’s value using several possible assumptions about the growth rate of cash flows. a. What is El Michoacáno’s value if cash flows are expected to grow at an annual rate of 0% from now to infinity? b. What is El Michoacáno’s value if cash flows are expected to grow at a constant annual rate of 5% from now to infinity? c. What is the El Michoacáno’s value if cash flows are expected to grow at an annual rate of 15% for the first 3 years, followed by a constant annual rate of 8% from year 4 to infinity?

Answer 1

a]

present value of perpetuity = first payment / required return

first payment = next year cash flow =  $50,000

Value of El Michoacáno =  $50,000 / 10%

Value of El Michoacáno =  $500,000

b]

present value of growing perpetuity = first payment / (required return - growth rate)

first payment = next year cash flow =  $50,000 * (1 + 5%) = $52,500

Value of El Michoacáno =  $52,500 / (10% - 5%)

Value of El Michoacáno =  $1,050,000

c]

Value of El Michoacáno = present value of next 3 years cash flows + present value of terminal value at end of 3 years

Terminal value at end of 3 years = Year 3 cash flow * (1 + growth rate after 3 years) / (required return - growth rate after 3 years)

Present value = future value / (1 + required return)^{number of years}

The value of El Michoacáno = $3,249,225