7) (35 points) EmKay LLC purchases a new office building for S500,000 and plans

Question

7) (35 points) EmKay LLC purchases a new office building for S500,000 and plans to keep it for 10 years. At the end of the 10-year period it is estimated that the market value of the office building will be S600,000 Building operation and maintenance (O&M;) costs are estimated to be $50,000 for the first year. Thereafter these O&M; costs are expected to increase by 10% over the previous year's costs. If Emkay LLC's TVOM is 10% per year compounded annually, what is the equivalent uniform annual rent that must be generated by this real-estate investment, in order to break-even?

Explanation / Answer

7.

Initial investment = $500000

O&M cost for the first year = $50000

Time = 10 years

market value after 10 years= $600000

R = 10%

Annual increase in O&M cost (g) = 10%

Present value of the total cost = initial investment + present value of O&M cost – present value of the market value of building

Present value of the total cost = 500000 + (50000/1.1 + 50000*1.1/1.1^2 + 50000*1.1^2/1.1^3 + 50000*1.1^3/1.1^4 + 50000*1.1^4/1.1^5 +50000*1.1^5/1.1^6 + 50000*1.1^6/1.1^7 + 50000*1.1^7/1.1^8 + 50000*1.1^8/1.1^9 + 50000*1.1^9/1.1^10) - 600000/1.1^10

Present value of the total cost = $723219.5

Let, equivalent uniform annual rent = EUAC

Then,

EUAC = 723219.5/((1-1/(1+10%)^10)/10%)

EUAC = $117700.6

So, the uniform annual rent should be $117700.6 to achieve the break even.

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