Question

lo a participation if you aren't coming to class) Due September 30th Pretend you inherited $150,000 are trying to decide between buying a home outright (cash) with the money or investing it in the stock market earning an 8% return and renting a place for the next 20 years for $800 a month. Assume the house increase in value at 5% a year. Show your work and let me know which you would prefer. To start, keep this problem easier by assume there are no taxes, insurance, or other expenses. Next, look at what property taxes, insurance, and other expenses (HOA fee/maintenance) might be in an area you'd like to live after college and see how this effects your answer. Some concepts you should use are future value and future value of an annuity. Maybe other depending on how you solve the problem. I'm as much if not more interested in your approach as I am your final answer

Answer 1

For evaluating, which option is better is better we can use various methods such as Net Present Value Method, Future Value at Year end 20, MIRR. Net Present Value is normally considered to be best method when evaluating proposals of similar scale. Hence, Net Present Value method is used.

For Present Value Calculations, discounting rate is assumed to be 4%. (Other figure could also be assumed)

Option 1 :

Purchase house outright Cash.

In this case, there would be Cash Outfow upfront, i.e., at Year 0, of $1,50,000 & Value of house will keep appreciating @ 5% per annum for 20 years. ( as question has given time frame of 20 years).

Value at end of Year 20 = Future Value of $1,50,000 @ 5% = 1,50,000 * (1.05)^20 = 1,50,000 * 2.6533 = $ 3,97,995

Net Present Value = Present Value of Cash Inflows - Present Value of Cash Outflow = Present Value of $ 3,97,995 (Value of house at year end 20) - Value of house purchased now

= $3,97,995/(1.04)^20 - 1,50,000 = 1,81,640 - 1,50,000 = $ 31,640

Option 2 :

Invest $1,50,000 in Stock Market & Rent a house at $800 per month for 20 years

In this case, there would be 2 cash outflows & 1 cash inflow as follows:-

1. Cash Outflow upfront at year 0 of $1,50,000 for investing in stock market.

2. $800 per month, i.e., $9,600 per year for 20 years for House Rent. ( It is assumed house rent is paid at year end)

3. Cash Inflow from Stock Market at end of 20 years.

Present Value of Annuity = P ( 1 - (1+r)^(-n))/r); P = periodic payment, r = rate of interest, n= no. of periods

Present Value of Cash Outflows of Rent Payments = Present Value of Annuity Payment of $9,600 (based on above formula) = 9,600 * (1-(1+0.04)^(-20))/(0.04) = $1,30,467

Cash Inflow at Year end 20 out of Stock markets = Future Value of $1,50,000 @ 8% = 1,50,000 * (1.08)^20 = 1,50,000 * 4.6610 = $ 6,99,150

Present Value of Cash Inflows at years end 20 = $6,99,150 / (1.04)^20 = $ 3,19,083

Net Present Value = Present Value of Cash Inflows - Present Value of Cash Outflows = $ 3,19,083 - ( $1,30,467 + $ 1,50,000) = $ 38,596

As Net Present Value of Option 2, i.e., to invest in stock market & rent a house is better than NPV of Option 1,i.e., purchasing house upfront. Hence, It is better to Invest in Stock Market & Rent a house rather than purchasing house upfront.