Foodelicious Corp. is evaluating whether it should take over the lease of an ethnic restaurant in Manhattan. The current owner had originally signed a 25-year lease, of which 16 years still remain. The restaurant has been growing steadily at a 7 percent growth for the last several years. Foodelicious Corp. expects the restaurant to continue to grow at the same rate for the remaining lease term. Last year, the restaurant brought in net cash flows of $310,000. If the firm evaluates similar investments using a15 percent discount rate, what is the present value of this investment? (Round to the nearest dollar.)

Question

Quizplus · Accepted Answer

The present value of the investment can be calculated using the formula for the present value of a growing perpetuity: PV = C / (r - g), where C is the cash flow in the first period, r is the discount rate, and g is the growth rate. However, since this is not a perpetuity but a 16-year term, we use the formula for the present value of a growing annuity: PV = C * [(1 - (1 + g)^n / (1 + r)^n) / (r - g)], where n is the number of periods. Plugging in the values: C = $310,000, r = 0.15, g = 0.07, and n = 16, we get PV = $310,000 * [(1 - (1 + 0.07)^16 / (1 + 0.15)^16) / (0.15 - 0.07)], which approximates to $2,838,182 when rounded to the nearest dollar.