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 $3.4 million per year to beneficiaries. The yield to maturity on all bonds is 18.5%. a. If the duration of 5-year maturity bonds with coupon rates of 14.6% (paid annually) is four years and the duration of 20-year maturity bonds with coupon rates of 8% (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.) million 5-year bond 20-year bond million

Answer 1

SEE THE IMAGE. ANY DOUBTS, FEEL FREE TO ASK. THUMBS UP PLEASE

ke - Microsoft Excel (Product Activation Failed) Page Layout Formulas File Home Insert Data Review View Add-Ins E AutoSum - Cut AC Wrap Text Calibri 11 General E Copy Fill Merge & Center Conditional Format Formatting as Table Styles Insert Delete Format Sort & Find & Filter Select Paste в IU* 000 Cell % Format Painter Clear Number Clipboard Font Alignment Styles Cells Editing fox ВА638 ВЕ AX AY AZ BА ВВ ВС BD BF BG AW 638 639 perpetual payments (a) 640 3.4 YTM 18.50% PRESENT VALUE OF ALL PERPETUAL PAYMENT = $3.4 MILLION/0.185= 641 18.3784 MILLION AND RESPECTIVE DURATION = ( 1+ RATE)/RATE = (1+0.185)/0.185 = 642 6.4054 YEARS 643 644 NOW SAY W = WEIGHT OF 5 YEAR MATURITY BOND 1-W 20 YEAR MATURITY BOND 6.4054 = W(4) + (1-W)*(11) 645 W(4) + 11-(W)*(11) 6.4054 646 4.5946 =7 (W) 647 648 THEREFORE W = 4.5946/7 = 0.6564, 1-W 0.3436 649 SO WEIGHT OF 5 YEAR BOND 0.6564, and WEIGHT OF 20 YEAR BOND ANS (a) 650 0.3436 651 MARKET VALUE OF 5 YEAR BOND 18.3784 X 0.6564 = 12.0630 12.1 MILLION 652 MARKET VALUE OF 20 YEAR BOND 18.3784 x 0.3436 6.3154 6.3 MILLION 653 ANS (b) 654 PAR VALUE OF HOLDINGS IN 20 YEAR COUPON BOND 655 PRICE OF BOND 80 X PVIFA @18.5%, 20 YEARS 1000 X PVIE @18.5%, 20 YEARS 656 PRICE OF BOND = 80 X 5.224079 1000 X 0.033545 = 451.47 DIR right UTILITY, SHARPE, beta LEASING PV, FV, ANNUITY clean YIELD bond portfolio L 130% RI INTL CAP BUD КЕ САРМ port future INDEX beta SANDRINE cONvexity DGM WACC erences WA 09:48 ENG 28-11-2019

ke - Microsoft Excel (Product Activation Failed) Formulas File Home Insert Page Layout Data Review View Add-Ins E AutoSum - Cut A A Wrap Text Calibri 11 General Copy Fill Merge & Center Insert Delete Format Paste в IU* 000 Conditional Format Cell Sort & Find & Filter Select % Format Painter Clear Formatting as Table Styles Clipboard Font Alignment Number Styles Cells Editing fox ВА671 ВЕ AW AX AY AZ ВА ВВ ВС BD BF BG 653 ANS (b) 654 PAR VALUE OF HOLDINGS IN 20 YEAR COUPON BOND PRICE OF BOND = 80 X PVIFA @18.5%, 20YEARS+1000 X PVIF @ 18.5%, 20 YEARS 655 656 451.47 PRICE OF BOND = 80 X 5.224079 1000 X 0.033545 = 657 MARKET VALUE = PAR VALUE X (PRICE OF BOND/FACE VALUE OF BOND) 658 6.3154 PAR VALUE X (451.47/1000) 659 660 PAR VALUE = 13.9872 MILLION 661 PAR VALUE = 13.99 662 5.224079 EXCEL =PV(18.5%,20,-1) 663 NOTE PVIFA @18.5%, 20 YEARS 0.033545 EXCEL =PV(18.5%, 20,,-1) 664 PVIF @18.5%, 20 YEARS 665 666 667 668 669 670 671 DIR right CONvexity clean YIELD bond portfolio L 130% RI DGM beta port future INDEX PV, FV, ANNUITY КЕ САРМ UTILITY, SHARPE, beta INTL CAP BUD SANDRINE LEASING WACC erences WA 09:48 ENG 28-11-2019