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Essentials Of Investments
Found in: Page 361
Essentials Of Investments

Essentials Of Investments

Book edition 9th
Author(s) Zvi Bodie, Alex Kane, Alan Marcus, Alan J. Marcus
Pages 748 pages
ISBN 9780078034695

Short Answer

Pension funds pay lifetime annuities to recipients. If a firm remains in business indefinitely, the pension obligation will resemble perpetuity. Suppose, therefore, that you are managing a pension fund with responsibilities to make perpetual payments of $2 million per year to beneficiaries. The yield to maturity on all bonds is 16%.

a. If the duration of 5-year maturity bonds with coupon rates of 12% (paid annually) is four years and the time of 20-year maturity bonds with coupon rates of 6% (paid annually) is 11 years, how much of each of these coupon bonds (in market value) will you want to hold to both entire fund and immunize your obligation?

b. What will be the par value of your holdings in the 20-year coupon bond?


a. $6.7 m and $5.8 m

b. $14.25 m

See the step by step solution

Step by Step Solution

Step by Step Solution Step 1: Given information

Perpetual payment = 2m

YTM = 16%

Present value (PV) of obligation = Payment/ YTM% = 2m/ 16% = $12.5 m

Duration of Obligation = ΔP/P = 1.16/ 16% = 7.25 years

Step 2: Calculation of five years & 20-year maturity bond ‘a’

To find the weight (w) of five year maturity period (with duration 4 years-given)

= (w x 4) + [(1 – w) x 11] = 7.25

w = 0.5357

So to find maturity of 5 year bond = 0.5357 x $12.5 = $6.7 m and

the maturity of 20 year bond = (1- 0.5357) x $ 12.5 = 0.4643 x $12.5 = $5.8 m

Step 3: Calculation of price of 20-year bond ‘b’

The price of 20 year bond can be calculated by:

[60 x annuity factor (16%, 20) + [1000 x PV factor (16%, 20)]

= $407.12

This implies that the bond sells for 0.4071 times par value.

Market value = Par value x 0.4071

To find its par value, let’s substitute its values,

$5.8 m = Par value x 0.4071

= $14.25 m

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