Question

The required investment cost of a​ new, large shopping center is ​$48 million. The salvage value of the project is estimated to be $20 million​ (the value of the​ land). The​ project's life is 19 years and the annual operating expenses are estimated to be ​$16 million. The MARR for such projects is 20% per year. What must the minimum annual revenue be to make the shopping center a worthwhile​ venture?  

Click the icon to view the interest and annuity table for discrete compounding when the MARR is 20% per year.

To make the shopping center a worthwhile​ venture, the minimum annual revenue must be $______ million per year. ​(Round to three decimal​ places.)

Answer 1

ANSWER:

Initial investment cost = $48,000,000

Salvage value = $20,000,000

n = 19 years

annual expenses = $16,000,000

annual revenue = ?

i = 20%

In order to find the annual revenue we will equate the present worth of the project to 0 at 20%

pw = initial investment cost +annual expenses(p/a,i,n) + annual revenue(p/a,i,n) + salvage value(p/f,i,n)

0 = -48,000,000 -16,000,000(p/a,20%,19) + annual revenue(p/a,20%,19) + 20,000,000(p/f,20%,19)

0 = -48,000,000 - 16,000,000 * 4.843 + annual revenue * 4.843 + 20,000,000 * 0.0313

0 = -48,000,000 - 77,488,000 + 4.843 annual revenue + 626,000

0 = -124,862,000 + 4.843 annual revenue

124,862,000 = 4,843 annual revenue

annual revenue = 124,862,000 / 4.843

annual revenue = 25,781,953.335

so the annual revenue is $25,781,953.335