Question

Colosseum Corp. has a zero coupon bond that matures in five years with a face value of $85,000. The current value of the company's assets is $81,000, and the standard deviation of its return on assets is 44 percent per year. The risk-free rate is 7 percent per year, compounded continuously. C-1. a. What is the value of a risk-free bond with the same face value and maturity as the current bond? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) What is the value of a put option on the firm's assets with a strike price equal to the face value of the debt? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Using the answers from (a) and (b), what is the value of the firm's debt? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) c-2. What is the continuously compounded yield on the company's debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) d-1. Assume the company can restructure its assets so that the standard deviation of its return on assets increases to 53 percent per year. What happens to the value of the debt? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) What is the new continuously compounded yield on the debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) If the company restructures its assets, how much will bondholders gain or lose? (A loss should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) e-2. If the company restructures its assets, how much will stockholders gain or lose? (A loss amount should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

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e w © v ENG 00:15 16-04-2020 26 X X340 N o P a R S T U V W X Y Z AA AB A 335 336 337 338 PRESENT VALUE OF RISK FREE BOND = PRESENT VALUE OF RISK FREE BOND = PRESENT VALUE OF RISK FREE BOND = FACE VALUE * e^(-rt) 85000*e^(-0.07*5) 59898.49 339 340 341 b PRICE OF PUT OPTION 342 344 81000 CURRENT VALUE 85000 FACE VALUE 0.07 0.44 5 O(A) = 346 347 348 d. ln (5/6) + (rroso² (7) 349 350 351 352 d1 = [In(81000/85000) + (0.07 +0.5*(0.44)^2)(5)]/(0.44* (SQRT(5)] d1 = 0.79868 353 354 355 d2 = d1 - 0* SQRT(T) d2 = -0.18519 356 357 358 e^(-0.07*5)= 0.704688 N(d1) = 0.787762 N(D2) = 0.426540 BINOMIAL BS call put CALL EXCEL ... BULL SPREAD RISK NEUTRAL FLORIDA sd=0 COMPENSATION ZEVON Sheet7 BIN ... :

© v ENG 00:15 16-04-2020 26 X X383 - fix X o N P a R s T U V W X Y Z AA AB A 360 361 362 value of Put option 363 364 P = koe in(dz) - S. N(d) 365 366 367 368 369 370 371 372 VALUE OF PUT OPTION= VALUE OF PUT OPTION= VALUE OF PUT OPTION= VALUE OF PUT OPTION= 85000*e^(-0.07*(5))*(1-0.426540) 85000*(0.704688)*(1-0.426540) 34349.37 17158.11 [VALUE OF EQUITY] 81000 *(1-0.787762) 81000 *(1-0.787762) 17191.26 c-1 373 VALUE OF RISKY BOND = VALUE OF RISKY BOND = VALUE OF RISKY BOND = VALUE OF RISK FREE BOND - VALUE OF PUT OPTION 59898.49 - 17158.11 42740.38 374 375 C-2 376 377 378 379 380 381 CONTINUOUSLY COMPOUNDED COST OF DEBT FV = PV* e^r(T) 85000 = 42740.38*Ar(5) 1.98875 = e^r(5) 5r = In(1.72057) 5r = 68.75% 13.75% 382 383 ... BULL SPREAD BINOMIAL BS call put CALL EXCEL RISK NEUTRAL FLORIDA sd=0 COMPENSATION ZEVON Sheet7 BIN ... :

e © v ENG 00:15 16-04-2020 26 X *412 - X fix N O P Q R S U V W X Y I Z AA AB A d-1 PRESENT VALUE OF RISK FREE BOND = 389 390 391 392 FACE VALUE * e^(-rt) 85000* e^(-0.07*5) 59898.49 393 394 PRICE OF PUT OPTION 395 396 397 398 399 400 401 81000 CURRENT VALUE 85000 FACE VALUE 0.07 0.53 O(A) = 402 d. ln (5/6) + (r+0.50² (1) 403 404 405 406 d1 = [In(81000/85000) + (0.07 +0.5*(0.53)^2)(5)]/(0.53* (SQRT(5)] d1 = 0.84721 407 408 409 d2 = d1 - 0* SQRT(T) -0.33790 d2 = 410 411 412 e^(-0.07*5)= 0.704688 N(d1) = 0.801562 N(D2) = 0.367719 BINOMIAL BS call put CALL EXCEL ... BULL SPREAD RISK NEUTRAL FLORIDA sd=0 COMPENSATION ZEVON Sheet7 BIN ... :

© v ENG 00-16 16-04-2020 26 - X o for Pa R value of T U V W X Y Z AA AB A s Put option P= K. e ..(-d2) - S. N(di) X438 N 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 VALUE OF PUT OPTION= VALUE OF PUT OPTION= VALUE OF PUT OPTION= VALUE OF PUT OPTION= 85000*e^(-0.07*(5))*(1-0.367719) 85000*(0.704688)*(1-0.367719) 37872.69 21799.23 (VALUE OF EQUITY] 81000 *(1-0.801562) 81000 *(1-0.801562) 16073.45 VALUE OF RISKY BOND = VALUE OF RISKY BOND = VALUE OF RISKY BOND = VALUE OF RISK FREE BOND - VALUE OF PUT OPTION 59898.49 - 21799.23 38099.25 FV 432 CONTINUOUSLY COMPOUNDED COST OF DEBT = PV*er(T) 85000 = 38099.25*e^r(5) 2.23101 = er(5) 5r = In(1.92112) 5r = 80.25% 16.05% 433 434 435 436 437 438 e-1 e-2 ... BULL SPREAD BONDHOLDERS LOSE EQUITYHOLDERS GAIN BINOMIAL BS call put 38099.25 -42740.38 -4641.13 21799.23 - 17158.11 4641.13 CALL EXCEL RISK NEUTRAL FLORIDA sd=0 COMPENSATION ZEVON Sheet7 BIN ... :