Question

A party shop owner wants to open a 2nd store in a nearby town, and she has found a building and land to purchase for $1.5 Million immediately. She believes that the additional store will increase her sales by $300,000 per year over the next 12 years. The new store will incur an additional $100,000 per year in operating and labor expenses. If the owner's MARR is 10%, use the net present worth criterion to determine if she should proceed with the new store.

Answer 1

Cost of building and land for new bpuilding = $1.5 million

It will raise sales by $300,000 per year and raise cost by $100,000. Therefore, net benefit per year is $300,000 - $100,000 = $200,000

Duration = 12 years

MARR = 10%

Present value of net benefit of 1st year is [200,000 / (1 + 0.12)^¹]

Present value of net benefit of 2nd st year is [200,000 / (1 + 0.12)^²]

Present value of net benefit of 3rd year is [200,000 / (1 + 0.12)^³]

and so on till year 12.

Sum of present value of net benefit = [200,000 / (1 + 0.12)^¹] + [200,000 / (1 + 0.12)^²] + [200,000 / (1 + 0.12)^³] + .............. + [200,000 / (1 + 0.12)^¹²]

This forms a G.P. of 12 terms whose sum can be calculated using this formula: [a * (1 - r^ⁿ) / (1 - r)]

a (first term) = [200,000 / (1 + 0.12)^¹]

n = 12

r (ratio of two consecutive terms) = (1 / 1.12) = 0.892

Sum of 12 terms = [200,000 / (1 + 0.12)^¹] * [(1 - 0.892^¹²) / (1 - 0.892)] = 1,238,875

As the initial cost is $1,500,000 which is higher than present value of net worth attained in next 12 years, this store should not be opened.