Question

You need a new car. You can either lease or buy the car for 355 000 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 2.5% 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 ${col}%. 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)

Answer 1

a. Monthly loan payments = $ 6300

Using financial calculator or excel:

PV	355000
NPER	60	[12months*5years]
rate	0.21%	[2.5%/12]
PMT	6300.31	[PMT(2.5%/12,60,-355000,0)]

b. Monthly loan payments = $ 4411

Present value of the payment to be made = 355000 -( 120000/(1+0.21%) ^60) = 249086.609

PV	249086.6
NPER	60	[12months*5years]
rate	0.21%	[2.5%/12]
PMT	4411.44	[PMT(2.5%/12,60,-355000,0,1)]

c. Monthly loan payments = $ 4268

After tax rate = ( 2.5%/12)*0.7 = 0.15%

PV	355000
NPER	60	[12months*5years]
rate	0.15%	[2.5%/12]
FV	120000
PMT	4268.37	[PMT(2.5%/12,60,-355000,0)]