Suppose you need a car, and you are considering the following two options: Optio

Question

Suppose you need a car, and you are considering the following two options:

Option A: Buy an old car for $1,000 now. However, old cars only last for 1 year each, so you’ll have to keep buying such cars every year. Fuel economy of an old car is 20 mpg; in other words, you’ll use 1 gallon of gasoline for each 20 miles you drive.

Option B: Buy a newer car for $8,000 now. You can drive this car for 4 years (it will fall apart after that), and fuel economy of this car is 40 mpg.

Assume that all other costs and benefits of having a car are the same for these two options. Also, assume that you drive 20,000 miles per year, the price of gasoline is $2 per gallon, and you buy gasoline for an entire year at the beginning of each year.

If the interest rate is 10% a year, which option will you choose?

How would your answer to the previous question change if the interest rate increases or decreases? Do not do any calculations, but explain the intuition behind your answer.

Explanation / Answer

683

Present value of option A = $ 12507

Present value of option B = $ 12169

Option B must be selected due to its low present value. We have selected low value because it is cost.

When interest rate will increase the present value of option B be high because initial cost of car is paid now and its value will not get diluted due to discounting. While option A will be having lower present value since it's cash flow is distributed uniformly due to which it's present value would be less.

Similarly when interest rate is less than 10% point the present value of option A would be greater than the present value of option B.

Year Plan A Plan B Discount factor 10% PV A PV B 0 3000 9000 1 3000 9000 1 3000 1000 0.909 2727 909 2 3000 1000 0.826 2678 826 3 3000 1000 0.751 2253 751 4 3000 1000 0.683 2049

683

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.