Question

ABC Corporation wants to purchase an old office building with an estimated remaining service life of 25 years. Recently, the tenants signed long-term leases, which leads you to believe that the current rental income of $250,000 per year will remain constant for the first 5 years. Then the rental income will increase by 10% for every 5-year interval over the remaining life of the asset. For example, the annual rental income would be $275,000 for years 6 through 10, $302,500 for years 11 through 15, $332,750 for years 16 through 20, and $366,025 for years 21 through 25. You estimate that operating expenses, including income taxes, will be $50,000 for the first year and that they will increase by $5000 each year thereafter. You also estimate 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 earn interest at the rate of 10% per annum, what would be the maximum amount you would be willing to pay for the building and lot now?

Answer 1

Rental Income

Rental income for year 1 to 5 =250000, Rental income for year 6 to 10 = 275000, Rental income for year 11 to 15 = 302500

Rental income for year 16 to 20 = 332750 and Rental income for year 21 to 25 = 366025

Expenses

Expense for year 1 = 50000

Since expenses increase by 5000 every year

Expense for year 2 = Expense of year 1 + 5000 = 50000 + 5000 = 55000

Expense for year 3 = Expenses for year 2 + 5000 = 55000 + 5000 = 60000

Similarly expenses can be calculated for other years

Net Cash Flow for a year = Rental income for a year - Expenses for a year

For year 1 Net Flow for year 1 = 250000 - 50000 = 200000

For year 2 Net Cash Flow year 2 = 250000 - 55000 = 195000

Similarly Net cash flow can be calculated for other years

Discounted Net Cash for a year = Net Cash x PV Factor

PV Factor = 1 / (1 + r)ⁿ

where r = rate of interest or opportunity cost = 10% and n=year of cash flow

For year 1 PV Factor for year 1 = 1/(1+10%)¹ = 0.909090909

Discounted Net cash flow for year 1 = 200000 x 0.909090909 = 181818.18

For year 2 PV factor for year 2 = 1/(1+10%)² = 0.8264462681

Discounted Net cash flow for year 2 = 195000 x 0.8264462681 = 161157.02

We get following discounted cash flows for year 1 to 25

Year	Rental Income	Expenses	Net Cash Flow	PV Factor at 10%	Discounted Net Cash Flow
1	250000	50000	200000	0.909090909	181818.18
2	250000	55000	195000	0.826446281	161157.02
3	250000	60000	190000	0.751314801	142749.81
4	250000	65000	185000	0.683013455	126357.49
5	250000	70000	180000	0.620921323	111765.84
6	275000	75000	200000	0.564473930	112894.79
7	275000	80000	195000	0.513158118	100065.83
8	275000	85000	190000	0.466507380	88636.40
9	275000	90000	185000	0.424097618	78458.06
10	275000	95000	180000	0.385543289	69397.79
11	302500	100000	202500	0.350493899	70975.01
12	302500	105000	197500	0.318630818	62929.59
13	302500	110000	192500	0.289664380	55760.39
14	302500	115000	187500	0.263331254	49374.61
15	302500	120000	182500	0.239392049	43689.05
16	332750	125000	207750	0.217629136	45212.45
17	332750	130000	202750	0.197844669	40113.01
18	332750	135000	197750	0.179858790	35567.08
19	332750	140000	192750	0.163507991	31516.17
20	332750	145000	187750	0.148643628	27907.84
21	366025	150000	216025	0.135130571	29191.58
22	366025	155000	211025	0.122845974	25923.57
23	366025	160000	206025	0.111678158	23008.49
24	366025	165000	201025	0.101525598	20409.18
25	366025	170000	196025	0.092295998	18092.32
			Sum of Discounted Cash Flows		1752971.57

Selling price of lot = 50000

Present value of selling price of lot = 50000 / (1 + 10%)²⁵ = 50000 / 10.83471 = 4614.79

Maximum Amount one would be willing to pay today for building and lot = Sum of Discounted Net Cash Flow + Present value of selling price of lot = 1752971.57 + 4614.79 = 1757586.36

Maximum Amount one would be willing to pay today for building and lot = 1757586.36