BMAT 230 Case 10b
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Bow Valley College, Calgary *
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BMAT
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Mathematics
Date
Apr 3, 2024
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docx
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BMAT 230 Case Study – 10B
CASE 10b
Lease or Finance Option
Tamera graduated from college and found a job as an online marketing specialist in a social networking company. Within a year, she saved $2000 and was determined to buy a new car. However, she was unsure as to whether she should lease it or buy it by financing the amount from a bank.
A car salesman at the showroom gave her the following table illustrating the comparison of the lease vs. finance options for the car she liked.
Description
Losing the car
Financing the car
Manufacturer’s Suggested Retail Price (MRSP)
$21,500.00
$21,500.00
Additional purchase costs*
$1,817.00
$1,817.00
13% HST
-
$3031.21
Net Price
$23,317.00
$26,348.21
Down payment
$2000.00
$2000.00
Term in months
48
48
Monthly payments
$250.00 + 13% HST (month-
beginning payments)
$562.13 (month-end
payments)
Residual payment to own
$12,453.56 + 13% HST
Nil
*Additional purchase costs include freight & PDL, Air Conditioner Tax, Tire Tax, and registration fees.
Assume the money was worth 5.5% compounded annually.
a.
Which options would be economically better for Tamera?
b.
Which option would be economically better if the residual value was $15,000 (including HST) for the lease option?
c.
What size of equal, beginning-of-month lease payments (including HST) would make the lease option economically equivalent to the finance option? Assume the original residual value and the term is still 48 months. a.
Which options would be economically better for Tamera?
Formulas:
c
=
¿
number of payments per year
number of compounding periods per year
¿
i
2
=(
1
+
i
)
c
−
1
PV
Due
=
PMT
¿
PV
=
FV
¿¿
LEASING THE CAR
Payments at the beginning of the month
General Annuity due
MRSP
$
21,500.00
Additional costs
$
1,817.00
Down payment
$
2,000.00
PV
$
21,317.00
PMT
$
282.50
¿
250
x
0.13
j
5.50%
M = C/Y
1
i=j/m
5.50%
t, years
4
P/Y
12
n=P/Y*t
48
Fvresidual
14072.52
¿
12453.56
+(
12453.56
x
0.13
)
n=m*t
4
c
8.33%
¿
1
/
12
i2
0.45%
¿¿
Pvdue=PV Lease PMTs
PVdue
$
12,233.56
¿
282.50
∗((((
1
−(
1
+
0.45%
)
¿¿
−
48
))/
0.45
$
12,233.56
¿
PV
(
i
2
,n,
−
PMT ,
0,1
)
Pvresidual
$
11,539.58
¿
14072.52
∗
¿
Lease amount
$
25.593.14
¿
2000
+
12233.56
+
11539.58
Better option: Leasing the car.
b.
Which option would be economically better if the residual value was $15,000 (including HST) for the lease option?
Conclusion: Since the present value of payments under lease option ($25,593.14) is less than that under “financing from bank” option ($26,234.47) lease option is economically better for Tamera. However, since today she has savings of only $2,000, she will need $282.50 more to go for lease option as its first monthly payment is to be made at the start of the month, which is today. Hence, to go for lease option she should save $282.50 more.
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