Question

Pension funds pay lifetime annuities to recipients. If a firm will remain 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 $2.7 million per year to beneficiaries. The yield to maturity on all bonds is 12.5%. a. If the duration of 5-year maturity bonds with coupon rates of 12.8% (paid annually) is four years and the duration 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 fully fund and immunize your obligation? (Do not round intermediate calculations. Enter your answers in millions rounded to 1 decimal place.) b. What will be the par value of your holdings in the 20-year coupon bond? (Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places.)

Answer 1

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ke - Microsoft Excel (Product Activation Failed) Add-Ins File Home Insert Page Layout Formulas Data Review View - 2x % Cut Σ AutoSum : A 11 A = = r Number A A = E *Wrap Text Merge & Center 8. $ - % Number Fill 2 Clear Formatting as Table Styles Styles Sort & Filter Editing Find & Select Alignment Cells U D Font fax AY A Z BA BB BC BD BE BF BG Calibri E Copy Paste Format Painter B I Clipboard BF374 - L AW AX 364 365 366 367 368 12.50% perpetual payments 2.7 YTM PRESENT VALUE OF ALL PERPETUAL PAYMENT = $2.7 MILLION/0.125= AND RESPECTIVE DURATION = ( 1+ RATE)/RATE = (1+0.125)/0.125 = 21.60 MILLION 9.00 YEARS 369 1-W = 15 YEAR ZERO COUPON BOND NOW SAY W = WEIGHT OF 5 YEAR ZERO COUPON BOND 9 = W(4) + (1-W)*(11) 9 = W(4) + 11-W(11) 2 = 7(W) W = 0.2857 ANS (a) SO WEIGHT OF 5 YEAR BOND = 0.2857, and WEIGHT OF 20 YEAR BOND = 0.7143 370 371 372 373 374 375 376 377 378 379 380 381 WEIGHT OF 5 YEAR BOND WEIGHT OF 20 YEAR BOND 0.2857 0.7143 6.1714 MARKET VALUE OF 5 YEAR BOND = $21.60 X 0.2857 = MARKET VALUE OF 20 YEAR BOND = $21.60 X 0.7143 = 6.2 MILLION 15.4 MILLION 15.4286 382 convexity DGM betaport future INDEX INTL CAP BUD SANDRINE LEASING PV, FV, ANNUITY DIR right clean HON Rea KE CAPM UTILITY, SHARPE, beta ferences YIELD bond portfolio WACC RI O BO. 130% 40-_+ 9 * * OENG 01-12-2019) D E R

ke - Microsoft Excel (Product Activation Failed) Add-Ins File Home Insert Page Layout Formulas Data Review View - 2x % Cut Calibri 11 A = = V A A = E Wrap Text Merge Merge & Center Center Σ AutoSum : A Fill 2 m Sort & Find & B I U SF 4:0 .00 8. Insert Delete Format $ - % % Number Conditional Format Formatting as Table Styles Cell Styles 2 Clear Filter Editing Select Alignment Cells E Copy Paste Format Painter Clipboard AX394 AW 382 D Font fax AY AX AZ BA BC BD BE BE BG 383 PRICE OF BOND = 60 X PVIFA @12.5%, 20 YEARS + 1000 X PVIF @12.5%, 20 YEARS PRICE OF BOND = 60 X 7.241353 + 1000 X 0.094831 = 529.31 384 385 386 387 MARKET VALUE = PAR VALUE X (PRICE OF BOND/FACE VALUE OF BOND) 15.4286 = PAR VALUE X (529.31/1000) PAR VALUE = $29.148348 MILLION PAR VALUE = 29.15 MILLION 388 ANS b 389 390 391 NOTE PVIFA @12.5%, 20 YEARS PVIF @12.5%, 20 YEARS 7.241353 EXCEL =PV(12.5%,20,-1) 0.094831 EXCEL =PV(12.5%,20,,-1) 392 393 394 395 396 397 398 399 400 convexity DGM betaport future INDEX INTL CAP BUD SANDRINE LEASING PV, FV, ANNUITY DIR right clean WACC HON Red KE CAPM UTILITY, SHARPE, beta ferences YIELD bond portfolio BO. 130% 9 * RI O 40-_+ DOER ENG 01-12-2019