Question

# Are you thinking of bypassing a​ gasoline-fueled car in favor of a hybrid​ (gasoline and​ electric)...

Are you thinking of bypassing a​ gasoline-fueled car in favor of a hybrid​ (gasoline and​ electric) automobile?​ Let's take a look at the relative economics of your possible choice.​ Let's say the​ gasoline-fueled car sells for ​\$21,000 and gets 2525 miles per gallon​ (mpg) of​ fuel, while the competing hybrid car sells for 24,000 and averages 31.931.9mpg. The expected resale value of the hybrid car is ​\$8,400 and that of the​ gasoline-only car is ​\$6,900after five years of anticipated ownership. If you drive 14,000 miles per year and gasoline cost will average​ \$3.503.50per​ gallon, what is the internal rate of return​ (IRR) on the incremental investment in the hybrid automobile relative to the​ gasoline-only car? Assume that all other maintenance and operating costs are the same for the two vehicles.

Ans:-

Annual fuel cost of gasoline car = (14000/25)*3.5 = \$1960

Annual fuel cost of hybrid car = (14000/32.5)*3.5 = \$1507.69

Time = 5 years

Incremental investment of hybrid over gasoline care = 24000-21000 = \$3000

Time = 5 years

Incremental annual savings in fuel cost = 1960-1507.69 = \$452.31

Incremental resale value = \$2500

Let,

IRR = R

Then,

3000 = present value of the annual fuel cost savings + present value of the incremental resale value

3000 = 452.31*(1-1/(1+R)^5)/R + 2500/(1+R)^5

At R = 12%

Present value cash inflows = 3049.04

At R = 13%

Present value cash inflows = \$2947.78

As per the method of interpolation,

R = 12% + ((3049.04-3000)/( 3049.04-2947.78))*(13%-12%)

R = 12.48% or 12.5%

So,

Incremental rate of return = 12.5%

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