Question

In: Economics

A city is considering buying a piece of land for $500.000 and construction an office complex...

A city is considering buying a piece of land for $500.000 and construction an office complex on it. Their planning horizon is 20 years. Two mutually exclusive building designs have been drawn up by an architectural firm. Use the modified benefit cost ratio method and a MARR of 10% per year to determine which alternative should be recommended to the city council.

Design A (x1000$) Design B (x1000$)
Cost of building including cost of the land 1,107 1,306
Resale value of land and building at end of 20 year planning horizon 655 893
Annual net rental income (after deducting all operating expenses) 128 208

Perform the incremental B/C Analysis. Write the incremental B/C ratio for these alternatives.

Solutions

Expert Solution

Modified BC ratio= PW of Annual Rental income/(Initial cost-PW of salvage value)

PW of Annual rental income= Annual Rental Income*(1-(1+MARR)^-n)/MARR

PW of Resale Value= Resale Value /(1+MARR)^n

MARR=10%

n=20 years

Design A Design B Incremental cash flow
Cost of Building including Land C 1107 1306 199
Resale Value at end of 20 years S 655 893 238
Annual Rental Income P 128 208 80
PW of Resale value  A 97.36 132.74 35.38
PW of Annual rental Income B 1089.74 1770.82 681.09
C-A 1009.64 1173.26 163.62
Modified B/C ratio 1.08 1.51 4.16

As the B/C ratio of Design  A is greater than 1.0, Design A now becomes the base alternative and is compared against the next higher equivalent cost alternative i.e. design  B. Now the incremental benefits and incremental costs between B and A are calculated and the incremental B/C ratio is obtained. Incremental cash flow is obtained by subtracting cash flow of design A from Design B.

So modified incremental BC Ratio=4.16

Rahul Sunny answered 2 years ago
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