Question

9-32 An investor is considering buying some land for $100,000 and constructing an office building on it. Three different buildings are being analyzed. Building Height 2 Stories 5 Stories 10 Stories $2,100,000 400,000 Cost of building (excluding $400,000 $800,000 cost of land) Resale value of land + 200,000 300,000 building after 20-year horizon Annual net rental income 70,000 105,000 256,000 *Resale value considered a reduction in cost-not a benefit. Using benefit-cost ratio analysis and an 8% MARR, determine which alternative, if any, should be selected.

Answer 1

ANSWER:

I = 8%

1) 2 stories:

aw of benefits = annual net rental income = $70,000

aw of costs = cost of building(a/p,i,n) - resale value(a/f,i,n) = 400,000(a/p,8%,20) - 200,000(a/f,8%,20) = 400,000 * 0.1019 - 200,000 * 0.0219 = 40,760 - 4,380 = 36,380

b/c ratio = aw of benefits / aw of costs = 70,000 / 36,380 = 1.92

2) 5 stories:

aw of benefits = annual net rental income = $105,000

aw of costs = cost of building(a/p,i,n) - resale value(a/f,i,n) = 800,000(a/p,8%,20) - 300,000(a/f,8%,20) = 800,000 * 0.1019 - 300,000 * 0.0219 = 81,520 - 6,570 = 74,950

b/c ratio = aw of benefits / aw of costs = 105,000 / 74,950 = 1.4

3) 10 stories:

aw of benefits = annual net rental income = $256,000

aw of costs = cost of building(a/p,i,n) - resale value(a/f,i,n) = 2,100,000(a/p,8%,20) - 400,000(a/f,8%,20) = 2,100,000 * 0.1019 - 400,000 * 0.0219 = 213,990 - 8,760 = 205,230

b/c ratio = aw of benefits / aw of costs = 256,000 / 205,230 = 1.247

so alternative 2 stories should be chosen as it has the highest b/c ratio.