Question

Your firm is considering purchasing an old office bailding with an estimnted remaining service life of 25 years. Recently, the tenants signed a longterm lease, which leads you to believe that the current rental income of $250,000 per year will remain constant for the first five years. Then the rental income will increase by 10% for every five-year interval over the remaining life of the asset. That is, the annual rental ineome would be $275,000 for yeans 6 through 10,$302,500 for years 11 through 15, $332,750 for years 16 through 20 , and $366,025 for yeans 21 through 25. You eatimate that operating expenses, including income taxes, will be $85,000 for the first year and that they will increase by $5,000 each year thereafter. You also cstimate that razing the building and selling the lot on which it stands will realize a net amount of $50,000 at the end of the 25 -year period. If you had the opportunity to invest your money elsewhere and thereby cam interest at the rate of 12% per annum, what would be the maximum amount you would be willing to pay for the building and lot at the present time?

Answer 1

To determine the maximum amount you would be willing to pay for the building and lot at the present time, we need to calculate the present value of the future cash flows generated by the property.

First, let's calculate the net operating income (NOI) for each year, which is the rental income minus operating expenses:

Year 1:

Net Operating Income (NOI) = Rental Income - Operating Expenses

NOI = $250,000 - $85,000 = $165,000

Years 2-5:

Operating Expenses increase by $5,000 per year

NOI = $250,000 - ($85,000 + $5,000 + $5,000 + $5,000) = $150,000

Years 6-10:

Rental Income increases by 10% every five years

NOI = $275,000 - ($85,000 + $5,000 + $5,000 + $5,000) = $175,000

Years 11-15:

NOI = $302,500 - ($85,000 + $5,000 + $5,000 + $5,000) = $202,500

Years 16-20:

NOI = $332,750 - ($85,000 + $5,000 + $5,000 + $5,000) = $232,750

Years 21-25:

NOI = $366,025 - ($85,000 + $5,000 + $5,000 + $5,000) = $276,025

Next, we'll calculate the present value of each year's NOI. We'll discount the cash flows to the present time at a rate of 12% per annum:

Year 1:

Present Value (PV) = NOI / (1 + r)^n

PV1 = $165,000 / (1 + 0.12)^1 = $147,321.43

Years 2-5:

PV2 = $150,000 / (1 + 0.12)^2 = $114,034.61

PV3 = $150,000 / (1 + 0.12)^3 = $101,805.36

PV4 = $150,000 / (1 + 0.12)^4 = $91,014.20

PV5 = $150,000 / (1 + 0.12)^5 = $81,335.23

Years 6-10:

PV6 = $175,000 / (1 + 0.12)^6 = $105,873.05

PV7 = $175,000 / (1 + 0.12)^7 = $94,643.11

PV8 = $175,000 / (1 + 0.12)^8 = $84,413.71

PV9 = $175,000 / (1 + 0.12)^9 = $75,162.85

PV10 = $175,000 / (1 + 0.12)^10 = $66,775.94

Years 11-15:

PV11 = $202,500 / (1 + 0.12)^11 = $97,085.26

PV12 = $202,500 / (1 + 0.12)^12 = $86,530.40

PV13 = $202,500 / (1 + 0.12)^13 = $77,092.29

PV14 = $202,500 / (1 + 0.12)^14 = $68,665.90

PV15 = $202,500 / (1 + 0.12)^15 = $61,152.

Step-by-step explanation:

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