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You need a new car

Finance Aug 13, 2020

You need a new car. You can either lease or buy the car for 360 000 SEK. In both cases you expect to use the car for 5 years. It will have a residual value of 120 000 SEK after 5 years. You can borrow at a rate of 3.0% APR with monthly compounding. (a) In case you buy the car you will take an annuity loan over 5 year at a borrowing rate of 3.0%. What will be your monthly payments on the loan? The monthly payments on the loan will be SEK. (round to SEK, no decimals) (b) In case you decide to lease the car from a car dealer, what monthly rate will the dealer charge assuming a perfect market? The monthly payments on the lease will be SEK. (round to SEK, no decimals) (C) You remember the corporate finance classes at JIBS that you took long time ago and you recognize that a comparison of the rates from (a) and (b) is not meaningful, in particular since in (a) you will own the car and you could sell it at its residual value. Furthermore, you also notice that you can deduct the interest payments on the loan from your income tax so that the after-tax interest rate is 0.7 times the pre-tax rate. The residual value shall be used to make a balloon payment on the remaining loan amount to repay it completely. What will be your monthly payments considering both the balloon loan repayment using the residual amount and also the tax consequences from interest payments? The monthly payments on the loan will be in this case SEK. (round to SEK, no decimals)

Expert Solution

Part (a)

Your monthly payment = PMT (Rate, NPER, PV, FV) = PMT (3%/12, 5 x 12, -360000, 0) = 6,469

Part (b)

The dealer has a FV = residual value = 120000 at the end of year 5

The monthly payment on lease = PMT (Rate, NPER, PV, FV) = PMT (3%/12, 5 x 12, -360000, 120000) = 4,612

Part (c)

Rate = Post tax interest rate = 3% x 0.7 = 2.1%

Hence, the monthly payment on loan = PMT (Rate, NPER, PV, FV) = PMT (2.1%/12, 5 x 12, -360000, 120000) =  4,427

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