Question

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 25 miles per gallon​(mpg) of​ fuel, while the competing hybrid car sells for ​$26,000 and averages 36.5 mpg. The expected resale value of the hybrid car is $9,100 and that of the​ gasoline-only car is $7,100 after five years of anticipated ownership. If you drive 16,000 miles per year and gasoline cost will average $4.00

per​ 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.

Using the​ "trial-and-error" method, the incremental IRR is

____.

​(Round to one decimal​ place.)

Based on this​ analysis, if your investments typically give you a MARR is

5​%,

which vehicle should you​ buy?

Answer 1

Gasoline fueled car

Initial Cost=$21000

Fuel Cost=(16000/25)*4=$2560 per year

Salvage=$7100

Useful life=5 years

Hybrid car

Initial Cost=$26000

Fuel Cost=(16000/36.5)*4=$1753.43 per year

Salvage=$9100

Useful life=5 years

Incremental analysis

Initial Cost=-(26000-21000)=-5000

Annual fuel savings=-(1753.43-2560)=$806.57

Salvage=(9100-7100)=$2000

NPV of incremental amounts

-5000+806.57(P/A,i,n)+2000*(P/F,i,5)=0

Let us calculate the equation at i=4% and 5%, 6%

At i=4%

(P/F,0.04,5)=1/(1+4%)^5=0.8219

NPV=-5000+806.57*4.4518+2000*8219=234.49

At i=5%

(P/F,0.05,5)=1/(1+5%)^5=0.7835

NPV=-5000+806.57*4.3295+2000*0.7835=59.04

At i=6%

(P/F,0.05,5)=1/(1+6%)^5=0.7473

NPV=-5000+806.57*4.2124+2000*0.7473=-107.80

We find that i should be between 5% and 6%

Let us try at i=5.5%

(P/F,0.055,5)=1/(1+5.5%)^5=0.7651

NPV=-5000+806.57*4.2703+2000*0.7651=-25.50

Let us try at i=5.4%

(P/F,0.054,5)=1/(1+5.4%)^5=0.7688

NPV=-5000+806.57*4.2820+2000*0.7688=-8.66

Let us try at i=5.3%

(P/F,0.053,5)=1/(1+5.3%)^5=0.7724

NPV=-5000+806.57*4.2938+2000*0.7724=8.05

So, we can say that i lies between 5.3% and 5.4%

Let us try at i=5.35%

(P/F,0.0535,5)=1/(1+5.35%)^5=0.7706

NPV=-5000+806.57*4.2879+2000*0.7706=-0.31

We can say that i lies between 5.30% to 5.35%

or Incremental IRR =5.3%