Question

A used car that currently costs $35,000 will have a market value of $6,000 in four years. As a student, you cannot afford to pay $35,000, but you want to have a car while you are going to university for the next four years. Your father agrees to lend you $35,000 on the condition that you pay him $300 at the end of every month for the next four years and $35,000 at the end of the four years. The car dealer provides financing facilities, and you are qualified to get a lease for which you will have to make monthly, end‐of‐month payments of $850 for 48 months. (For calculation purposes, use 5 decimal places and final answers to 0 decimal places, e.g. 5,275.)

Calculate the PV of lease.

PV of lease

$

Calculate the PV of loan from father.

PV of loan from father

$

Which option will leave you better off, assuming your cost of capital is 6 percent?

You should take? the lease or the loan .

Answer 1

Solution

a. Present value of lease payments=Monthly Lease payment*((1-(1/(1+r)^n))/r)

where

n=number of periods=48

r=rate of interest per period=6/12=.5%

Present value of lease payments=850*((1-(1/(1+.005)^48))/.005)

=36193.27012

Present value of lease payments=36193

b. Present value of loan from father=Monthly payment*((1-(1/(1+r)^n))/r)+Lumpsum amount/(1+r)^n

where

n=number of periods=48

r=rate of interest per period=6/12=.5%

Monthly payment=300

Lumpsum amount=35000

Present value of loan from father=300*((1-(1/(1+.005)^48))/.005)+35000/(1+.005)^48

=40322.53972

Present value of loan from father=40323

The vehicle also has a market price of 6000 at the end of 4 years therefore the present value of 6000 will be subtracted from the present value of loan from father

Present value=Cashflow/(1+r)^n

Here cashflow=6000

r=rate of interest per period=6/12=.5%

n=number of periods=4*12=48

Present value of resale price=6000/(1+.005)^48

=4722.59047

Thus net present value in case of loan=Present value of loan from father-Present value of resale price

=40322.53972-4722.59047

=35599.94925

c Since Present value of Lease payment is more than the net present value of loan,therefore the Loan should be taken

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