(Problem Set #1)
Before attempting these problems, you may want to listen to the guest lecture on factors of production and capital. For more background (optional), you can read Should you Buy a Timeshare? and Capital and Rental Cost.
Suppose that you can rent a condo for $12,000 a year ($1000 a month). Condos in that building sell for $150,000. The interest rate is 10 percent. The appreciation rate is 1 percent. Use the profitability formula to decide whether or not to buy the condo.
Calculate the rental rate, which is the rent as a percentage of the price.
Calculate profitability for owning the condo, using the formula
Should you buy or rent?
Recalculate profitability assuming that the appreciation rate is 3.5 percent per year. Should you buy or rent?
How high does the appreciation rate have to be to make the profitability rate just greater than zero? At this appreciation rate, what decision should you make on renting or buying?
Suppose that the appreciation rate is 1 percent per year and the interest rate is 10 percent. What should the rental rate be in order for profitability to equal 0? If the rent is $12,000 per year, what does the price have to be in order to have this rental rate?
Suppose that you can lease a lawnmower for $500 a year. The lawnmower sells for $2000. The interest rate is 8 percent. The lawnmower depreciates by 20 percent per year, which means that appreciation is negative: -20 percent per year.
Calculate the rental rate, which is the lease cost as a percentage of the price.
Calculate the profitability of buying the lawnmower rather than leasing it.
If the price of the lawnmower were $1500, what would be the rental rate? Would it be profitable to buy the lawnmower?
What would be the rental rate on the lawnmower that would make it a breakeven proposition whether to rent or buy? What would the price of the lawnmower have to be in order to get this rental rate?
Suppose that you can buy a car for $25,000 and sell it one year later for $20,000. Also, suppose that if you lease the car for one year, the lease costs $500 a month, or $6000 a year.
Is the appreciation rate positive or negative? Calculate the appreciation rate.
Calculate the rental rate, which is the lease cost as a percent of the purchase price.
If the interest rate is 5 percent, are you better off buying or leasing?
If the interest rate is 2 percent, are you better off buying or leasing?
What is the interest rate at which the profitability of buying is exactly zero, so that it makes no difference whether you buy or lease?
Suppose that you can buy a baseball franchise for $100 million, and its annual net revenues (revenues minus expenses) are $5 million. The interest rate is 10 percent per year.
What are net revenues as a percent of the purchase price? This is the "rental rate" for the baseball franchise.
If the appreciation rate of the franchise is 8 percent per year, use the profitability formula to calculate the profitability for the franchise. Should you buy the franchise?
If your cash flow is equal to net revenues minus interest expense, calculate the first year cash flow from owning the franchise.
Explain the difference between rent-buy analysis and cash flow analysis for this franchise.
A new fishing boat costs $130,000. The interest rate is 15 percent per year. At the end of one year, the boat can be sold for $117,000. Calculate the (negative) appreciation rate as a percent of the base price of the boat.
If the profitability formula is zero, meaning that the rental rate plus the appreciation rate minus the interest cost is zero, what should the rental rate be?
What does that mean it should cost to rent the boat for a year?
Re-calculate your answer using an interest rate of 20 percent.
You can buy a share of stock for $100. The stock pays a dividend of $1 per year. The ratio of the dividend to the price is the "rental income" from the stock. If the interest rate is 5 percent and the rate at which dividends and share prices appreciate is 3 percent, is the stock a good buy?