Question

You are contemplating the purchase of an office building. Next year net rental income will be $400,000, which will grow at 4% per year. You believe that in 10 years the office building could be sold for $7.4 million. The discount rate is 12%. What is the most you should be willing to pay for the office building today?

Solve this problem using formulas and showing your work. DO NOT USE EXCEL or take shortcuts. Every step must be shown and formulas written ahead of the step. No calculator use.

I believe the answer is $4,999,607 but I'm not sure.

Answer 1

Present Value = Future value/ ((1+r)^t)
where r is the interest rate that is 12% and t is the time period.
The cash flows will increase by 4% every year.
The most you should be willing to pay for the office building today = sum of present values of future cash flows.
t	1	2	3	4	5	6	7	8	9	10
future cash flow	400000	416000	432640	449945.6	467943.4	486661.2	506127.6	526372.7	547427.6	7400000
present value	357142.9	331632.7	307944.6	285948.6	265523.7	246557.7	228946.4	212593.1	197407.9	2382602
sum of present values	4816299
The most you should be willing to pay for the office building today is equal to $4816299.