Henry needs a car for going to law school. He needs the car for three years. He
ID: 1251896 • Letter: H
Question
Henry needs a car for going to law school. He needs the car for three years. He can buy or lease a new Honda Civic.A lease requires $3,000 at the signing and $160 per month each of the following 36 months. (The first $160 payment is due one month after signing.) At the end of the lease the car goes back to the dealer.
Alternatively, Henry can buy the car for $14,000 in cash; at the end of 36 months he is sure to sell it for $6000.
a. Suppose Henry discounts future costs and benefits at 9% per year. Calculate the present discounted value (cost) of each of Henry's options.
b. Find the monthly discount rate (i.e., personal interest rate) at which Henry would be indifferent between the two options. What is this as an annual interest rate? (a graphical calculator will be required)
Explanation / Answer
Henry needs a car for going to law school. He needs the car for three years. He can buy or lease a new Honda Civic.
A lease requires $3,000 at the signing and $160 per month each of the following 36 months. (The first $160 payment is due one month after signing.) At the end of the lease the car goes back to the dealer.
Alternatively, Henry can buy the car for $14,000 in cash; at the end of 36 months he is sure to sell it for $6000.
a. Suppose Henry discounts future costs and benefits at 9% per year. Calculate the present discounted value (cost) of each of Henry's options.
Option #1: Lease
3,000 + (160 x 36 x 0.91) = $8,241.60
Option #2: Cash
$14,000 - $6,000 = $8,000
b. Find the monthly discount rate (i.e., personal interest rate) at which Henry would be indifferent between the two options. What is this as an annual interest rate? (a graphical calculator will be required)
3,000 + (160 x 36 x 0.91 x (1 - I)) = 8,000
5, 241.60(1 - I) = 5,000
1 - I = 0.953907204
PERSONAL INTEREST = DISCOUNT = 4.71% (TOTAL)
OR (0.0471) = (MONTHLY RATE)160
LOGx0.0471 = 160
ln(0.0471)/ln(x) = 160
(1/160)(ln(0.0471)) = ln(x)
ln(x) = - 0. 01
x = 0.981
MONTHLY RATE = 1 - 0.981 = 1.9%
ANNUAL = (12/160)(ln(0.0471)) = ln(x)
x = 1 - 0.7952
ANNUAL = 20.48%
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