Pension funds pay lifetime annuities to recipients. If a firm remains in busines

Question

Pension funds pay lifetime annuities to recipients. If a firm remains in business indefinitely, the pension obligation will resemble a perpetuity. Suppose, therefore, that you are managing a pension fund with obligations to make perpetual payments of $2.0 million per year to beneficiaries. The yield to maturity on all bonds is 16%.

If the duration of 5-year maturity bonds with coupon rates of 12% (paid annually) is 4 years and the duration of 25-year maturity bonds with coupon rates of 4% (paid annually) is 16 years, how much of each of these coupon bonds (in market value) will you want to hold to both fully fund and immunize your obligation?

What will be the par value of your holdings in the 25-year coupon bond?

Pension funds pay lifetime annuities to recipients. If a firm remains in business indefinitely, the pension obligation will resemble a perpetuity. Suppose, therefore, that you are managing a pension fund with obligations to make perpetual payments of $2.0 million per year to beneficiaries. The yield to maturity on all bonds is 16%.

Explanation / Answer

Present value of the perpetual obligation of the firm is calculated as follows.

Perpetual obligation = $2 million / 0.16

                                      = $12.5 million

Now, the duration of the perpetual obligation computed as follows.

Duration of the obligation = 1.16 / 0.16

                                                = 7.25 years

Let us calculate the weight (W) of the 5 year maturity bond as below by substituting the values.

7.25 years = (W × 4) + (1-W) × 16

7.25 = W4 + 16 – W16

W of 5 year bond is = 0.7292

And

W of 25 year bond is = 0.2708.

Now, with the help of computed weights, let us find the fully fund obligation as follows.

5-year bond = 0.7292 × $12.5

                       = $9.115

25-year bond = 0.2708 × $12.5

                       = $3.385

Therefore, the total investment of $12.5 million is adjusted between 5-year and 25-year bonds are $9.115 and $3.385 respectively.

b.

Compute the par value of your holdings in the 25-year coupon bond:

The price of the 25-year bond = $40 PVAF (16% ×25) + $1,000 × PVF (16% ×25)

= (6.097092 ×$40) + (0.024465 × $1,000)

= $243.88 + $24.465

= $268.33

It means it sells for 0.26833 times its par vale.

Market value = Par value × 0.26833

$3.385 = Par value × 0.26833

Par Value = $3.385 / 0.26833

= $12.62 million

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.