In: Economics
Answer 1
MRSP of Car X is $20000 and range is 25 miles per gallon.
I drive 13000 miles per year, hence my gas consumption annually will be = 13000/25 = 520 gallons
If price of gas is x per gallon my annual cost will be 520 * x = $520x annually
Present Worth of Gas cost will be given by PV = P * (1- (1+r)^-n) / r , P= -$520x, r = 9%, n= 4 years
Hence PV = -520x * (1-(1+9%)^-4 /9%
= -520x * (1-(1.09)^-4 /0.09
= -520x * (1-0.7084) /0.09
= -520x * 0.2916/0.09
= -$1684.8x
Hence Total Present worth of Car X = Initial cost + Present Worth of Fuel cost = -20000 - 1684.8x
MRSP of Car Y is $26000 and range is 35 miles per gallon.
I drive 13000 miles per year, hence my gas consumption annually will be = 13000/35 = 371.43 gallons
If price of gas is x per gallon my annual cost will be 371.43 * x = $371.43x annually
Present Worth of Gas cost will be given by PV = P * (1- (1+r)^-n) / r , P= -$371.43x, r = 9%, n= 4 years
Hence PV = -371.43x * (1-(1+9%)^-4 /9%
= -371.43x * (1-(1.09)^-4 /0.09
= -371.43x * (1-0.7084) /0.09
= -371.43x * 0.2916/0.09
= -$1203.43x
Hence Total Present worth of Car Y = Initial cost + Present Worth of Fuel cost = -26000 - 1203.43x
I will be indifferent when Present Worth of Car X = Present Worth of Car Y
Hence -20000 - 1684.8x = -26000 - 1203.43x
or, 26000 -20000 = 1684.8x -1203.43x
or, 6000 = 481.37x
or, x = 12.46
Hence at a Gas Price of $12.46 I will be indifferent between Car X and Car Y
Answer 2
At Gas Price of $2.90,
Total Present worth of Car X = -20000 - 1684.8x= -20000 - 1684.8 * 2.9= -20000 - 4885.92 = -$24885.92
Total Present worth of Car Y = -26000 - 1203.43x = -26000 - 1203.43 * 2.90 = -26000 - 3489.947 = -$29489.947
Since the Net Present Worth of Car X is higher at Gas Price of $2.90 Car X shall be purchased