Question

The Frush Corporation has two different bonds currently outstanding. Bond M has a face value of $60,000 and matures in 20 years. The bond makes no payments for the first six years, then pays $2.700 every six months over the subsequent eight years, and finally pays $3,000 every six months over the last six years Bond N also has a face value of $60,000 and a maturity of 20 years; it makes no coupon payments over the life of the bond. The required return on both these bonds is 12 percent compounded semiannualy What is the current price of Bond M and Bond N? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) Current price Bond M Bond N

Answer 1

Calculate the price of the bond M as follows:

A B C Period Payment PV factors @6% ( 12 % /2) 1/((1+12% / 2)^A2) |-1/( (1+12% / 2 ) A3) - 1 / ( ( 1 + 12 % / 2 ) A4) - 1 / ( ( 1 + 12 % 2) A5) |=1 / ( ( + 12 % / 2 ) A6) - 1 / ( ( 1 + 12 % 2) A7) - 1 / ( ( 1 +12 % 2 ) A8) |-1/( (1+12% / 2 ) A9) |=1/ ( ( 1+12 % / 2) A10) |=1/ ((1+ 12%/2)^A11) |=1/ ( ( 1+12 % / 2) A12) |-1/ ( (1 + 12 % / 2 ) A13) |=1/ ( ( 1+12 % / 2) A14) |-1/((1+ 12 % /2)^A15) |- 1 / ( ( + 12 % 2 ) A16) |=1/ ((1+ 12%/2)^A17) |=1/ ( ( 1+12 % / 2) A18) |-1/((1+ 12 % /2)^A19) |- 1 / ( ( + 12 % 2 ) A20) |=1/ ( (1 + 12 % / 2 )^A21) - 1 / ( ( 1 + 12 % 2)^A22) - 1 / ( ( 1 +12 % / 2 ) A23) |=-1/ ( ( 1+12 % / 2)^A24) - 1 / ( ( 1 +12 % / 2 ) A25) |=-1/ ( ( 1+ 12 % / 2)^A26) |=1/ ( ( 1+12 % / 2) A27) |=1 / ( ( + 12 % / 2 ) A28) |- 1 / ( ( + 12 % / 2 ) A29) |=1 / ( ( + 12 % / 2 ) A30) |= 1 / ( ( + 12 % / 2 ) A31) |=1 / ( ( + 12 % / 2 ) A32) |- 1 / ( ( + 12 % / 2 ) A33) |=1/ ( (1+ 12 % /2)^A34) |= 1 / ( ( + 12 % / 2 ) A35) |- 1 / ( ( + 12 % / 2 ) A36) |-1/((1+ 12 % / 2 )^A37) |=1 / ( ( + 12 % / 2 ) A38) |=1/ ( ( 1+12 % / 2) A39) |=1/ ((1+ 12 % /2)^A40) |-1/((1+ 12 % / 2 )^A41) |=1/ ( (1 + 12 % /2 )A42) Present value 1 -B2*C2 - B3*C3 - B4*C4 - B5* C5 - B6 *C6 - B7*C7 - B8 *CS -B9*C9 -B10*C10 - B11*C11 -B12*C12 - B13 C13 -B14 * C14 - B15 *C15 -B16 *C16 - B17 *C17 = B18 *C18 -B19*C19 -B20* C20 -B21* C21 -B22*C22 - B23*C23 -B24* C24 -B25 *C25 -B26 * C26 - B27 * C27 -B28*C28 -B29 * C29 -B30*C30 - B31 *C31 -B32*C32 - B33 * C33 -B34* C34 = B35 * C35 -B36 * C36 = B37*C37 -B38 * C38 = B39* C39 |-B40*C40 =B41 * C41 - B42*C42 - SUM( D2 : D42 ) 2 3 2 3 4 5 4 6 5 7 6 7 8 9 8 10 9 11 10 0 12 11 0 13 12 14 13 2700 2700 2700 15 14 16 15 2700 2700 2700 2700 2700 2700 2700 2700 2700 2700 2700 2700 2700 3000 17 16 18 17 19 18 20 19 21 20 22 21 23 22 24 23 25 24 26 25 27 26 28 27 29 28 30 29 31 30 3000 32 31 3000 33 32 3000 34 33 3000 3000 35 34 36 35 3000 3000 37 36 38 37 3000 3000 39 38 40 39 3000 41 40 3000 42 40 60000 43 Price of the bond M

A C PV factors @ 6% ( 12% /2) Period Payment Present value 1 $ 1 0.943396226415094 2 $ 2 0.889996440014240 3 3 0.839619283032302 4 $ 4 0.792093663238020 5 0.747258172866057 6 $ 6 0.704960540439676 7 7 0.665057113622336 $ 8 0.627412371341826 9 0.591898463530025 10 10 0.558394776915118 11 11 0.526787525391621 12 12 0.496969363577001 13 2,700.00 2,700.00 13 0.468839022242453 1,265.86536005462 14 14 0.442300964379673 1,194.21260382512 15 2,700.00 2,700.00 $ 1,126.61566398596 15 0.417265060735540 16 16 0.393646283712774 1,062.84496602449 17 2,700.00 1,002.68393021178 17 0.371364418596957 18 $ 2,700.00 18 0.350343791129204 945.92823604885 19 2,700.00 19 0.330513010499249 892.38512834797 20 2,700.00 20 0.311804726886084 841.87276259243 21 $ 21 2,700.00 0.294155402722721 794.21958735135 22 22 2,700.00 0.277505096908227 749.26376165221 23 $ 23 2,700.00 0.261797261234177 706.85260533228 24 24 2,700.00 0.246978548334129 666.84208050215 25 $ 25 2,700.00 0.232998630503895 629.09630236052 26 26 2,700.00 0.219810028777260 593.48707769860 27 27 2,700.00 $ 0.207367951676660 559.89346952698 28 28 2,700.00 0.195630143091189 528.20138634621 29 $ 553.67021629582 29 3,000.00 0.184556738765272 30 3,000.00 30 0.174110130910634 522.33039273190 31 31 3,000.00 0.164254840481730 492.76452144519 32 3,000.00 3,000.00 32 0.154957396680878 464.87219004263 33 33 0.146186223283847 438.55866985154 34 3,000.00 $3,000.00 34 0.137911531399856 413.73459419957 35 0.130105218301751 35 390.31565490525 36 3,000.00 3,000.00 368.22231594835 37 36 0.122740771982784 37 0.115793181115834 347.37954334750 38 3,000.00 3,000.00 0.109238850109277 38 327.71655032783 39 39 0.103055518971016 309.16655691305 40 3,000.00 60,000.00 0.097222187708506 41 40 291.66656312552 5,833.33126251034 40 0.097222187708506 42 S 24,313.99395350600 Price of the bond M 43 et on. st n co av

Therefore, the price of bond M is $24,313.99

Calculate the price of the bond N as follows: Face value Price Period (1+Interest rate) $60,000 12% 2 1+ $60,000 (1.06 S60,000 10.2857179371259 S5,833.33126251034 or S5,833.33