You currently pay $10,000 per year in rent to a landlord for a $100,000 house, w

Question

You currently pay $10,000 per year in rent to a landlord for a $100,000 house, which you are considering purchasing. You can qualify for a loan of $80,000 at 9% if you put $20,000 down on the house. To raise money for the down payment, you would have to liquidate stock earning you a 15% return. We neglect other concerns, like closing costs, capital gains, and tax consequences of owning. 1. Explain the concept of opportunity cost. 2. Explain the fixed cost and the the hidden cost fallacy. 3. Given the described situation, determine whether it is better to rent or own. Show all your calculations and logical arguments.

Explanation / Answer

1) Opportunity cost is the cost of the forgone alternative: the amount of a good that has been sacrificed in order to achieve something else. Forgone alternative is the next best option one has and which is sacrificed by choosing the other one.

It is thus the sum of explicit cost and implicit cost. One of the most significant determinant of housing demand and hence residential investment is the real interest rate. Most of the households acquire loans, in the form of mortgage, to buy home. Since they need to pay interest on the amount of mortgage, it becomes an opportunity cost of holding wealth in the form of loan.

2) Fixed cost of production is the unrelated to the level of production. Whether the firm is operating at full capacity or the production is ceased, fixed cost remains the same. A firm bears a fixed cost which remains constant for any number of units of output produced. Fixed Cost is the cost that accrues to a firm for paying off its fixed factors. This cost does not change with the level of output since it has to be paid whether the firm operates or not.

Hidden cost fallacy is the fallacy of ignoring the hidden cost, more generally, the implicit costs , like the value of the interest rate on saving accumulated, for which no direct transaction or payment occured.

3) Note that the time period for repayment of housing loan is not given so it is assumed to be at least one year. Consider this. The amount of rent is $10,000 per year so after one year the future value of this rent, at an interest rate of 9% will be $10900. The house is worth $100,000 now which is an asset and its value will rise at the market return of other asset, at 15%. So after one year, its value become $115,000

To purchase it, you take a loan of $80,000 at 9% which becomes $87,200 after one year, an interest rate of $7,200. You also put $20,000 down on the house by liquidating the stock earning you a 15% return. So the return of $3000 is forgone.

Now simply this. Your house has a current worth of $100,000. You take a loan of $80,000 and pay $20,000 down payment so that things are perfectly balanced. But taking the opportunities cost in picture will change the situation. The house value will increase by $15,000. The hidden cost of buying the house is $7,200 + $3,000 or $10,200. The hidden cost of not buying the house is the extra rent, which is $10,900. Clearly, buying the house now is worthy enough as it will fetch $4,800 next year while not buying it will empty your pocket by $10,900.

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