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User Dashboard x y HMW # 2 Chapter 1 1 > M McGraw-Hill Connect l eb × Y e Essentials Of Investments × how to print screen with max Exalia ezto.mheducation.com/hm.tpx?--0.347532899220294 73_15109241 58538 10.00 points 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%. a. If the duration of 5-year maturity bonds with coupon rates of 12% (paid annually) is 4.0 years and the duration of 20-year maturity bonds with coupon rates of 4% (paid annually) is 8.6 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? (Do not round intermediate calculations. Enter your answers in millions rounded to 1 decimal place.) Holdings million 5-year bond 20-year bond million b. What will be the par value of your holdings in the 20-year coupon bond? (Enter your answer in dollars not in millions. Do not round intermediate calculations Round your answer to the nearest dollar amount.) Par value References eBook & Reso urces Worksheet Learning Objective: 11-04 Formulate fixed-income immunization strategies for various investment horizons.

Explanation / Answer

The Present Value (PV) of perputual payment of $2 million with 16% interest rate then

PV = A/r

PV = 2,000,000/0.16

PV = $12,500,000

Answer to a:

The PV or YTM of $1 Bond with Coupon Rate 12% for 4 years with 16% interest rate

PV = 0.12/(1.16) + 0.12/(1.16)^2 + 0.12/(1.16)^3 + 1.12/(1.16)^4

PV = $0.888

The PV or YTM of $1 Bond with Coupon Rate 4% for 8.6 years with 16% interest rate (using above approch)

PV = $0.496

You can hold $8,769,440 of Bond with 4 years of maturity and $9,500,000 Bond with 20 years of maturity.

$8,769,440*0.888 + $9,500,000*0.496 = $12,500,00.39

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