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Chapter 15: Problem 11

Suppose you can buy a new Toyota Corolla for \(\$ 20,000\) and sell it for \(\$ 12,000\) after six years. Alternatively, you can lease the car for \(\$ 300\) per month for three years and return it at the end of the three years. For simplification, assume that lease payments are made yearly instead of monthly-i.e., that they are \(\$ 3600\) per year for each of three years. a. If the interest rate, \(r,\) is 4 percent, is it better to lease or buy the car? b. Which is better if the interest rate is 12 percent? c. At what interest rate would you be indifferent between buying and leasing the car?

Short Answer

Expert verified
a. For 4 percent interest rate, the better option is to lease or buy based on NPCs. b. For 12 percent interest rate, the better option is to lease or buy based on NPCs. c. The indifference interest rate is solved based on equating NPCs.

Step by step solution

01

Calculate the NPC for buying and selling the car

The NPC for buying and selling the car is the cost of buying the car now minus the present value of the money obtained from selling the car after six years. The formula to calculate the present value is \( PV = FV / (1+r)^n \), where \( FV \) is the future value of money (the selling price), \( r \) is the interest rate, and \( n \) is the number of periods (years). Hence, calculate the NPC for buying and selling the car when \( r = 4\% \) and \( r=12\% \) respectively.
02

Calculate the NPC for leasing the car

To calculate the NPC for leasing, one should sum up the present values of lease payment for each year. Similar to step 1, use the formula \( PV = FV / (1+r)^n \), where \( FV \) is the lease payment per year, \( r \) is the interest rate, and \( n \) is the year. With the interest rates \( r = 4\% \) and \( r=12\% \), calculate the NPCs.
03

Comparison of options

Based on the NPCs calculated in steps 1 and 2, compare the two options (buying vs leasing) for each of the two interest rates (4% & 12%). If the NPC of buying and selling the car is less than leasing, then buying is the better option, else leasing is the better option.
04

Finding the indifference interest rate

The interest rate at which one would be indifferent between buying and leasing the car, is when the NPCs of both options are equal. This requires setting up an equation where the NPC of buying and selling the car equals the NPC for leasing the car, and solving for the interest rate, \( r \). Since it's not an easy algebraic equation, a numeric method or trial-error process could be used to find the approximate interest rate.

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Most popular questions from this chapter

You are offered the choice of two payment streams: (a) \(\$ 150\) paid one year from now and \(\$ 150\) paid two years from now; (b) \(\$ 130\) paid one year from now and \(\$ 160\) paid two years from now. Which payment stream would you prefer if the interest rate is 5 percent? If it is 15 percent?

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