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 questions

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

1. 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


2. Assuming implied forward rates are the best estimates of future one-year rates, how many years before you can expect to pay cash for a used car if you invest in successive one-year bonds?

a. One year b. Two years c. Three years d. Four years

3. What is the implied forward rate for the last year of your investment in question 2?

a. 10.00% b. 12.01% c. 14.03% d. 16.05% e. None of the above

4. Compared with an investment in the five-year bond, successive investments in one-year bonds over a five-year period carry
a. More credit risk
b. More interest-rate risk.
c. More reinvestment rate risk.
d. None of the above.
e. All 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

For a used car (only in "new for you" scenario)
2014 (2 year bond)is the year you can get a "new" used car.

b. Two years

(3)

1.1*1.11*1.12*1.13*1.14 =(1+r)^5

r =12.01 %

(4)

e. All of the above.

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