You currently have $15,000 that you plan to use to buy a car. You prefer a new c

Question

You currently have $15,000 that you plan to use to buy a car. You prefer a new car, but you are also open to a used car. Either way you will pay cash. The cost of a new car today (in 2012) is $22,500, but the cost for new versions of this car is projected to rise by 2% per year through 2017. Instead of a new car, you could buy a 2012 model later in the used-car market. The price of the 2012 model is expected to decline by 15% per year through 2017. You plan to invest your $15,000 into BBB-rated bonds, but you are not sure whether you should invest in successive one-year bonds, or in longer-term bonds. The five-year yield curve for zero coupon bonds rated BBB is given below to help you make your decision. Use this data for the following question

Term 1 year 2 years 3 years 4 years 5 years
YTM 10.00% 11.00% 12.00% 13.00% 14.00%

Which bond, if held to maturity, provides the earliest expected opportunity to buy a new car?
a. The two-year bond
b. The three-year bond
c. The four-year bond
d. The five-year bond
e. None of the above

Explanation / Answer

Future Value (FV) = current value(1 + .rate) = New value


For 2012

FV(2012 new ) = 22500 new, FV(2012 used in 2012) = n/a

FV(2013 new) = 22950 FV(2012 used 2013 ) =19125

FV(2014) = 23409 new, FV(2012 used 2014) =16256.25

FV (2015 new) = 23877.18 FV(2012 used 2015) = 13817.812

FV(2016 new) = 24354.723 new, FV(2012 used 2016) = 11745.14

FV(2017 new) = 24841.817 FV(2012 used 2017) = 9983.369

1 year bond: 16500 (2013)
2 year bond: 18315 (2014)
3 year bond: 20146.5 (2015)
4 year bond: 23179.464 (2016)
5 year bond: 26424.588 (2017)

Calculation :

Base 15000 and the year's rate (15000 x 1.10 = 16500) for year 1, (16500 x 1.11 = 18315) for year 2 etc...

Using this data the 5 year bond (2017), to maturity, is the only way to afford a brand new car.

d. The five-year bond

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