Question

In: Finance

You are looking to buy a 2018 Ford Focus Titanium Hatchback with sunroof and leather seats...

You are looking to buy a 2018 Ford Focus Titanium Hatchback with sunroof and leather seats at a price of $26,000. Being a college student, you have cash to pay taxes, title, license and fees but your parents offer to give you 10% of the price, $2,600, as a down payment and you need to finance the remainder of $23,400. You smartly researched your finance options and got preapproval at a 3.6% APR with monthly compounding for 5 years on your own so you are not at the mercy of depending on financing from the car dealership. Ford is offering 0% APR financing or $3,250 cash back which would be used as an additional down payment that reduces the amount that you would need to finance. You would use your 3.6% APR pre-approved financing if you elect the $3,250 cash back option. Answer the following questions.

1. What would be your monthly car loan payment under the Ford’s 0% APR financing offer (assume a 60-month loan term)?

2. What would be your monthly car loan payment under the Ford’s $3,250 cash back offer and your 3.6% APR pre-approved financing?

3. At what APR would you be indifferent between the two offers? In other words, at what APR would you have the same monthly payment (assuming a 60-month loan term) for the $3,250 cash back offer as you would with the 0% APR financing offer?

4. Assume you go with the offer in question #2. Construct an amortization schedule for the loan for all 60 monthly payments. What is your loan balance after 36 months?

5. Now assume you were willing to make a monthly car loan payment of $450. Re-do your amortization schedule from question #4 with this monthly payment. How long will it take to pay off the loan with the $450 monthly payment?

Expert Solution

Price of car = $26000

Down payment = $2600

Remainder to be financed or arranged = $23400

Option 1. Monthly car loan payment under 0% APR

Total repayment to be made in 60 months at 0% rate assuming 10% paid as down payment = $23400

Formula to calculate = Total amount/No. of months

Monthly loan installment = $23400/60

Monthly loan payment amount = $ 390

Option 2 : Monthly car payment if cashback availed

Total repayment to be made in 60 months post cashback and down payment = $26000-$2600-$3250

Final car loan amount = $20150

Annual Percentage Rate = 3.6% (compounded monthly)

Formula to calculate monthly car loan payment = [P*R*(1+R)^N]/[(1+R)^N-1]

Where P=Principal : R=Rate/12 (monthly compounding) : N= Number of months

There fore putting values in formula = [20150*(3.6%/12)*(1+(3.6%/12))^60]/[(1+(3.6%)/12)^60-1]

Hence Monthly car loan payment amount = $367.4667

Option 3 :Calculate APR to make both offers indifferent

Monthly car payment at 0% APR = $390.....refer Option 1

Monthly car payment at 3.6% APR post cashback = $367.47......refer Option 2

Keeping APR as "R" and putting values in formula with same monthly payment as of option 1

390 =(20150*R*(1+R)^60)/((1+R)^60-1)

Solving for R

APR comes out to be 6.05%, Hence at APR of 6.05% both the options would be at indifferent point

Option 4 :Amortization schedule with 3.6% APR

Monthly loan payment as calculated in option 2 = 367.4667

First month interest = P*R = $20150*(3.6%/12) : P= Outstanding Principal

First month interest = $60.45

First month principal = Installment-Interest = $367.4667-$60.45 = $ 307.02

Second month outstanding principal = $20150-$307.02 = $19842.98

Second month interest = P*R = $19842*(3.6%/12) : P= Outstanding Principal

Second month interest = $59.53

Second month principal = Installment-Interest = $367.4667-$59.53 = $ 307.94

Calculate so on for 60 months to build complete repayment schedule.

Year/Month Wise Opening Outstanding Interest Principal Closing Outstanding

$20,150.00 $60.45 $307.02 $19,842.98

$19,842.98 $59.53 $307.94 $19,535.05

$19,535.05 $58.61 $308.86 $19,226.18

$19,226.18 $57.68 $309.79 $18,916.40

$18,916.40 $56.75 $310.72 $18,605.68

$18,605.68 $55.82 $311.65 $18,294.03

$18,294.03 $54.88 $312.58 $17,981.44

$17,981.44 $53.94 $313.52 $17,667.92

$17,667.92 $53.00 $314.46 $17,353.46

$17,353.46 $52.06 $315.41 $17,038.05

$17,038.05 $51.11 $316.35 $16,721.70

$16,721.70 $50.17 $317.30 $16,404.40

Year #1 End

$16,404.40 $49.21 $318.25 $16,086.14

$16,086.14 $48.26 $319.21 $15,766.94

$15,766.94 $47.30 $320.17 $15,446.77

$15,446.77 $46.34 $321.13 $15,125.64

$15,125.64 $45.38 $322.09 $14,803.55

$14,803.55 $44.41 $323.06 $14,480.50

$14,480.50 $43.44 $324.03 $14,156.47

$14,156.47 $42.47 $325.00 $13,831.48

$13,831.48 $41.49 $325.97 $13,505.50

$13,505.50 $40.52 $326.95 $13,178.55

$13,178.55 $39.54 $327.93 $12,850.62

$12,850.62 $38.55 $328.91 $12,521.71

Year #2 End

$12,521.71 $37.57 $329.90 $12,191.81

$12,191.81 $36.58 $330.89 $11,860.91

$11,860.91 $35.58 $331.88 $11,529.03

$11,529.03 $34.59 $332.88 $11,196.15

$11,196.15 $33.59 $333.88 $10,862.27

$10,862.27 $32.59 $334.88 $10,527.39

$10,527.39 $31.58 $335.88 $10,191.51

$10,191.51 $30.57 $336.89 $9,854.62

$9,854.62 $29.56 $337.90 $9,516.71

$9,516.71 $28.55 $338.92 $9,177.80

$9,177.80 $27.53 $339.93 $8,837.86

$8,837.86 $26.51 $340.95 $8,496.91

Year #3 End

$8,496.91 $25.49 $341.98 $8,154.93

$8,154.93 $24.46 $343.00 $7,811.93

$7,811.93 $23.44 $344.03 $7,467.90

$7,467.90 $22.40 $345.06 $7,122.84

$7,122.84 $21.37 $346.10 $6,776.74

$6,776.74 $20.33 $347.14 $6,429.60

$6,429.60 $19.29 $348.18 $6,081.42

$6,081.42 $18.24 $349.22 $5,732.20

$5,732.20 $17.20 $350.27 $5,381.93

$5,381.93 $16.15 $351.32 $5,030.61

$5,030.61 $15.09 $352.37 $4,678.24

$4,678.24 $14.03 $353.43 $4,324.80

Year #4 End

$4,324.80 $12.97 $354.49 $3,970.31

$3,970.31 $11.91 $355.56 $3,614.76

$3,614.76 $10.84 $356.62 $3,258.13

$3,258.13 $9.77 $357.69 $2,900.44

$2,900.44 $8.70 $358.77 $2,541.68

$2,541.68 $7.63 $359.84 $2,181.83

$2,181.83 $6.55 $360.92 $1,820.91

$1,820.91 $5.46 $362.00 $1,458.91

$1,458.91 $4.38 $363.09 $1,095.82

$1,095.82 $3.29 $364.18 $731.64

$731.64 $2.19 $365.27 $366.37

$366.37 $1.10 $366.37 $0.00

Year #5 End

jeff jeffy answered 2 years ago

You’re looking to buy a 2018 Ford Fusion Titanium with sunroof and leather seats at a...

You’re looking to buy a 2018 Ford Fusion Titanium with sunroof and leather seats at a price of $32,000. Being a poor college student, you have cash to pay taxes, title, license & fees but your parents offer to give you 10% of the price, $3200, as a down payment and you need to finance the remainder of $28,800. You smartly researched your finance options and got pre-approval at a 3.3% APR for 60 months on your own so you’re...

You obtained a car loan from Ford Motor Credit Corp to buy a new Ford Explorer....

You obtained a car loan from Ford Motor Credit Corp to buy a new Ford Explorer. Give some examples of asymmetric or incomplete information as it pertains to both the buyer (you) and the seller (Ford). What are some ways the buyer or seller could mitigate this asymmetric information problem? Identify any adverse selection problem(s).

You want to buy a new SUV from your local Ford dealer. The total price of...

You want to buy a new SUV from your local Ford dealer. The total price of the SUV is $40,000 including tax ,tag ,title, and all fees. You can afford to pay 15% as a down payment and will need to finance the remainder. Ford credit offers you a special student rate 2.75% (compounded monthly) for 72 months. You will make monthly payments starting 1-month from today). What is the monthly payment? Answer choices: A.$603.28 B. $543.79 C.$500.92 D. $512.79

Say that you are looking to buy a small call and want to get a very...

Say that you are looking to buy a small call and want to get a very efficient car. You are trying to decide between a hybrids car and an electric car. Hyundai offers the Ioniq in a hybrid gas and an all-electric model. Compare these models by filling in the table below. Measure 2017 Ioniq blue 2017 Ioniq electric MPG combined (epa) MPG city (epa) MPG highway (epa) CO2 produced per mile (g/mi) in Columbia, Mo Fuel cost to drive...

You are looking for a $312,598 mortgage to buy a house. The mortgage has a 7...

You are looking for a $312,598 mortgage to buy a house. The mortgage has a 7 year term with a 22 year amortization. The rate on the mortgage is 2.75% APR with monthly compounding and monthly payments. What is the balloon payment on the mortgage? Round your answer to 2 decimal places. (For example 2.437 = 2.44)

You are looking to buy your first house. The cost of the house is $325,000. The...

You are looking to buy your first house. The cost of the house is $325,000. The bank has agreed to make a loan to you for 30 years at 3.15% if you can make a down payment of 7.00%, and the loan payments do not exceed 36% of your gross monthly income. Based upon this information: What is the amount of the mortgage loan that the bank will lend to you? What will be the amount of your monthly payments?...

You use silver wire in manufacturing. You are looking to buy 100,000 oz of silver in...

You use silver wire in manufacturing. You are looking to buy 100,000 oz of silver in three months' time and need to hedge silver price changes over these three months. One COMEX silver futures contract is for 5,000 oz. You run a regression of daily silver spot price changes on silver futures price changes and find that δS=0.03+ 0.89δF+ ϵ What should be the size (number of contracts) of your optimal futures position. Should this be long or short?

When you go buy something are you looking for the best bang for your buck as...

When you go buy something are you looking for the best bang for your buck as well? How do social influences play a role on the Utility we place in products we buy?

You are looking to buy a car. You can afford $650 in monthly payments for five...

You are looking to buy a car. You can afford $650 in monthly payments for five years. In addition to the loan, you can make a $750 down payment. If interest rates are 8 percent APR, what price of car can you afford (loan plus down payment)? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Samantha and Vikas are looking to buy a house in a new development. After looking at...

Samantha and Vikas are looking to buy a house in a new development. After looking at various models, the three models they like are colonial, split-entry, and single-story. The builder gave them the base price and the finished area in square feet of the three models. They want to know the model(s) with the least price per square foot. Instructions Write a program that accepts as input the base price and the finished area in square feet of the three...