Question

The monthly income from a piece of commercial property is $1,200. Annual expenses are $3,000 for upkeep of the property and $1,000 for property taxes. The property is surrounded by a security fence that cost $4,000 to install four years ago

a. If i = 12% per year (the MARR) is an acceptable interest rate, how much could you afford to pay now for this property if it is estimated to have a resale value of $150,000 10 years from now?

b. Draw a cash-flow diagram for this situation. Use the viewpoint of the buyer.

c. Based on this situation, give an example of an opportunity cost.

d. Based on this situation, give an example of a fixed cost.

e. Based on this situation, give an example of a sunk cost.

f. If the 12% interest had been a nominal interest rate, what would the corresponding effective annual interest rate have been with bi-weekly (every two weeks) compounding?

Please solve showing Excel formulas if possible.

Answer 1

A. If your Minimum Acceptable rate of return (MARR) is 12% per year i.e. 0.12, then the amount you afford to pay now for this property = Present value of Annual Cash Inflow from Commercial property for 10 years + Present value of resale value at 10 th year

= $58762.32(note 1) + $48295.99(note 2)

=$107058.31

b. Cash flow Diagram for this situation from buyer's point of view

C. example of opportunity cost is MARR on Amount invested i.e. 12% of 107058.31 = $ 12846.99

D. example of fixed cost is Annual expenses for upkeeping of property = $ 3000, Property Taxes = $ 1000

E. example of Sunk Cost is Installation cost of Security Fencing = $ 4000(installed 4 years ago)

F. compounded annual interest rate = 12.7186% (excel formula = ((1+0.12/26)^26)-1

here 26 stands for no. of bi week in a year (52/2)

Note 1. Present value of Annual Cash inflow p.a. for 10 years

Annual Cash inflow = Annual Rent(monthly income *12) - (Annual Expenses + property taxes)

=14400-(3000+1000)

=$ 10400

Present Value = Annual Cash inflow * PVAF@12%,10years = 10400 * 5.6502 = $58762.32

Note 2. Present Value of Resale value at 10 th year

= Resale value * PVAF@12%,10th year = 150000 * 0.32197 = $48.295.99