Question

You will be paying $9,400 a year in tuition expenses at the end of the next 2 years. Bonds currently yield 7%.

  

a.	What is the present value and duration of your obligation? (Do not round intermediate calculations. Round "Present value" to 2 decimal places and "Duration" to 4 decimal places. Omit the "$" sign in your response.)

  

Present value	$
Duration	years

  

b.	What maturity zero-coupon bond would immunize your obligation? (Do not round intermediate calculations. Round "Duration" to 4 decimal places and "Face value" to 2 decimal places.Omit the "$" sign in your response.)

  

Duration	years
Face value	$

  

Suppose you buy a zero-coupon bond with value and duration equal to your obligation.

  

c-1.

Now suppose that rates immediately increase to 8%. What happens to your net position, that is, to the difference between the value of the bond and that of your tuition obligation? (Do not round intermediate calculations. Input the amount as a positive value. Round your answer to 2 decimal places. Omit the "$" sign in your response.)

  

Net position (Click to select)increasesdecreases in value by

$

  

c-2.

Now suppose that rates immediately falls to 6%. What happens to your net position, that is, to the difference between the value of the bond and that of your tuition obligation? (Do not round intermediate calculations. Input the amount as a positive value. Round your answer to 2 decimal places. Omit the "$" sign in your response.)

  

Net position (Click to select)decreasesincreases in value by

$

Answer 1

(b)

The conditions for immunization are-

•The present value of assets should equal the present value of liabilities

•The duration of the portfolio should equal that of liabilities

So, to immunize the obligation, if we choose a zero coupon bond as the asset, the present value will be $16995.37 and the duration will be 1.4831 years.

So, Face Value= 16995.37x [(1+0.07)^(1.4831)]

= $18789.26

Duration (Maturity)= 1.4831 years

(Maturity= Duration for zero coupon bond)

(c1)

When the interest rate changes to 8 percent

Present Value of the obligation= 9400/ [(1+0.08)^1]    +     9400/ [(1+0.08)^2]

= $16762.69

Present Value of the asset= 18789.26/[(1.08)^(1.4831)]

= $16762.50

Net Position= $16762.50- $16762.69= -$0.18

(This is negligible and should be equal to zero when rounded off to zero decimal place. This is because we have immunized the portfolio)

(c2)

When the interest rate changes to 6 percent

Present Value of the obligation= 9400/ [(1+0.06)^1]    +     9400/ [(1+0.06)^2]

= $17233.89

Present Value of the asset= 18789.26/[(1.06)^(1.4831)]

= $17233.70

Net Position= $17233.70- $17233.89= -$0.19

(This is negligible and should be equal to zero when rounded off to zero decimal place. This is because we have immunized the portfolio)