Question

Hybrid cars are touted as a "green" alternative; however, the financial aspects of hybrid ownership are not as clear. Consider a 2015 Lexus RX 450h, which had a list price of $5,765 (including tax consequences) more than a Lexus RX 350. Additionally, the annual ownership costs (other than fuel) for the hybrid were expected to be $320 more than the traditional sedan. The mileage estimate was 5.2 litre/100 km for the hybrid and 6.9 for the traditional sedan. a. Assume that gasoline costs $1.55 per litre and you plan to keep either car for six years. How many kilometres per year would you need to drive to make the decision to buy the hybrid worthwhile, ignoring the time value of money? (Do not round intermediate calculations. Round the final answer to nearest whole number.) Kilometres per year b. If you drive 15,200 km per year and keep either car for six years, what price per litre would make the decision to buy the hybrid worthwhile, ignoring the time value of money? (Do not round intermediate calculations. Round the final answer to 2 decimal places.) Price per litre c-1. Gasoline costs $1.55 per litre and you plan to keep either car for six years. How many kilometres per year would you need to drive to make the decision to buy the hybrid worthwhile? Assume the appropriate interest rate is 12 percent and all cash flows occur at the end of the year. (Do not round intermediate calculations. Round the final answer to the nearest whole number.) Kilometres per year c-2. If you drive 15,200 kilometres per year and keep either car for six years, what price per litre would make the decision to buy the hybrid worthwhile? Assume the appropriate interest rate is 12 percent and all cash flows occur at the end of the year. (Do not round intermediate calculations. Round the final answer to 2 decimal places.) $ Price per litre d. Not available in Connect

Hybrid cars are touted as a “green” alternative; however, the financial aspects of hybrid ownership are not as clear. Consider a 2015 Lexus RX 450h, which had a list price of $5,765 (including tax consequences) more than a Lexus RX 350. Additionally, the annual ownership costs (other than fuel) for the hybrid were expected to be $320 more than the traditional sedan. The mileage estimate was 5.2 litre/100 km for the hybrid and 6.9 for the traditional sedan.

Answer 1

a). To make the hybrid worthwhile, the total cost (including list price + annual ownership cost + gasoline cost) has to equal or be lower than the total cost for the traditional sedan.

Let the kilometres driven/year be x. Then, total gasoline cost will be x*mileage*number of years*gasoline cost

Hybrid sedan gasoline cost = x*5.2*6*1.55 = 0.4836x

Traditional sedan gasoline cost = x*6.9*1.55 = 0.6417x

Extra list price for the hybrid sedan = 5,765

Extra ownership cost for the hybrid sedan for 6 years = extra annual ownership cost*number of years = 320*6 = 1,920

Total cost for hybrid sedan = Total cost for traditional sedan

0.4836x + 5,765 + 1,920 = 0.6417x

0.1581x = 7,685

x = 7,685/0.1581 = 48,608.48 or 48,609 kms

b). Again, we need to equate the costs of the two sedans.

Let the gasoline cost be y ($/lt)

Total gasoline cost will be distance per year*number of years*mileage*gasoline cost/100

Then, for hybrid sedan, gasoline cost will be (15,200*6*5.2*y)/100 = 4,742.40y

Traditional sedan, gasoline cost will be (15,200*6*6.9*y)/100 = 6,292.80y

4,742.40y + 5,765 + 1,920 = 6,292.80y

1,550.4y = 7,685

y = 7,685/1,550.4 = 4.96

Gasoline cost needs to be at least $4.96/lt

c-1). In this case, time value of money will be considered. So, annual cash flows will be discounted back to the present time and the NPVs of both sedans will be calculated. The distance per year at which difference in NPVs is zero will be the minimum driving distance which will justify buying a hybrid sedan.

Use excel Solver for this: Condition to be checked is NPV of hybrid sedan - NPV of traditional sedan = 0. Variable to be changed will be distance per year.

Formula		Hybrid	Traditional
		Lexus RX450h	Lexus RX 350
D	Distance/year (km)	65,358.49	65,358.49
M	Mileage (lt/100 km)	5.20	6.90
N	Number of years	6.00	6.00
C	Gasoline cost ($/lt)	1.55	1.55
AOC	Extra annual ownership cost ($)	320.00	-
LP	Extra List price ($)	5,765.00	-
r	Interest rate	12%	12%
GC = (D*M*C)/100	Gasoline cost per year	5,267.89	6,990.09
TC = GC + AOC	Total cost per year	5,587.89	6,990.09
PV = TC*(1 - (1+r)^-N)/r	PV of total cost per year	22,974.11	28,739.11
NPV = PV + LP	NPV	28,739.11	28,739.11
	Difference	-

Distance per year which makes buying a hybrid worthwhile = 65,358

c-2). Again use Solver for this. Changing variable will now be the gasoline cost per lt.

Formula		Hybrid	Traditional
		Lexus RX450h	Lexus RX 350
D	Distance/year (km)	15,200.00	15,200.00
M	Mileage (lt/100 km)	5.20	6.90
N	Number of years	6.00	6.00
C	Gasoline cost ($/lt)	6.66	6.66
AOC	Extra annual ownership cost ($)	320.00	-
LP	Extra List price ($)	5,765.00	-
r	Interest rate	12%	12%
GC = (D*M*C)/100	Gasoline cost per year	5,267.89	6,990.09
TC = GC + AOC	Total cost per year	5,587.89	6,990.09
PV = TC*(1 - (1+r)^-N)/r	PV of total cost per year	22,974.11	28,739.11
NPV = PV + LP	NPV	28,739.11	28,739.11
	Difference	0.00

Gasoline cost has to be $6.66/lt to justify buying a hybrid sedan.