Question

question b

Valuation fundamentals Personal Finance Problem Imagine that you are trying to evaluate the economics of purchasing a condominium to live in during college rather than renting an appartment. If you buy the condo, during each of the next 4 years you will have to pay property taxes and maintenance expenditures of about $7,000 per year but you will avoid paying rent of $10,000 per year when you graduate 4 years from now, you expect to sell the condo for $125.000 after taxes If you buy the condo, you will use money you have saved that is currently invested and earning a 6% annual after-tax rate of return Assume for simplicity that all cash flows (rent, maintenance, etc) would occur at the end of each year a. Draw a timeline showing the cash flows, their timing, and the required return applicable to valuing the condo b. What is the maximum pnce you would be willing to pay to acquire the condo? Explain

Answer 1

(a) If the condominium is bought instead of renting, the buyer saves $ 10000 in annual rent and ends up paying $ 7000 for property taxes and maintenance costs. The buyer's net savings which can be considered equivalent to a net cash inflow is, therefore (10000 - 7000) = $ 3000 per annum for a period of 4 years. Further, the buyer earns $ 125000 at the end of year 4 when he/she sells the condominium.

Cash Flows would be as given below:

Year 1: $ 3000

Year 2: $ 3000

Year 3: $ 3000

Year 4: Net Savings + Sale Proceeds = 3000 + 125000 = $ 128000

All cash flows are assumed to occur at the end of the time periods mentioned. Further, the condominium will be purchased with proceeds from the buyer's savings which are currently earning 6 % per annum. The existing interest rate would serve as an appropriate discount rate as by purchasing the condominium, money which could have been invested is used up, thereby making the 6 % investment return rate, the condominium purchases' opportunity cost. An underlying assumption, however, is the fact that the risk level of net annual savings and the sale proceeds is similar to the risk of keeping the purchase price invested.

(b) The maximum purchase price of the condominium (condominium's intrinsic price) should be equal to the present value of its expected annual savings and sale proceeds discounted at the purchase decision's opportunity cost of 6 % per annum.

Therefore, maximum purchase price = 3000 x (1/0.06) x [1-{{1/(1.06)^(4)}] + 125000 / (1.06)^(4) = $ 109404.90099 approximately.