You buy a car, which cost $320.000. The purchase can be financed with a payment of 20% and the remaining 80% is covered by an 8-year annuity loan. The loan bears interest rate of 3% p.a., and it has monthly terms in the following you therefore also apply a discount rate of 3% p.a.
a) Determine the size of the payment, U, and the monthly payment, Y, belonging to the loan.
You consider if it is realistic to sell the car after 3 years.
b) Calculate the present value of the paying monthly benefit, Y, for 3 years from now. What is the value of this including the payout U?
You could even rent the car for 3 years which requires a one-time payment of $10000 today and after a monthly payment of $3750
c) What is the present value of the renting deal?
If you buy the car today, you expect to sell it for $200000 after 3 years to pay back the annuity loan
d) How much do you have left after 3 years, when you payed back the loan? What is the present value of this? What will the present value today of buying the car under these conditions?
It turns out the leasing agreement includes a service agreement costs of $500 each month
e) What will the present value of today buying the car now that you include the cost of the service agreement?
Of course, it is highly uncertain what price you can sell the car for in three years
f) Set up an equation that shows what the car with a documented service agreement must be able to sell to after three years, so that the present value of resp. purchase and lease are the same. Determine (numerically) this selling price.
- Thank you so much in advance :)
Cost of Car = $320,000
a) Size of Down Payment (U) = $320,000 x 20% = $64,000
Amount of Loan = $320,000 x 80% = $256,000
Rate of Interest = 3% p.a. that is 0.25% per month n = 8 years = 96 months
Thus, 256000 = Y x PVIFA(0.25%, 96)
256000 = Y x 85.2546
Y = 256000 / 85.2546 = 3002.77 = 3003
Thus, monthly payment Y = $3,003
b) Y = 3003 n = 3 years = 36 months
Present Value = 3003 x PVIFA (0.25%, 36)
= 3003 x 34.3865 = 103262.66 = $103,263
Present Value of Y including U = $103,263 + $64,000 = $167,263
c) One Time Payment = $10,000 Monthly Rent Payment =$3,750
Present Value of Rental deal = 3750 x PVIFA (0.25%, 36) + 10,000
= (3750 x 34.3865) + 10,000 = 128,949 + 10000 = $138,949
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