Question

A $1,000 par value bond was issued five years ago at a coupon rate of 10 percent. It currently has 10 years remaining to maturity. Interest rates on similar debt obligations are now 12 percent. Use Appendix B and Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods a. Compute the current price of the bond using an assumption of semiannual payments. (Do not round intermediate calculations and round your answer to 2 decimal places.) Current bond price b. If Mr. Robinson initially bought the bond at par value, what is his percentage capital gain or loss? (Ignore any interest income received. Do not round intermediate calculations and input the amount as a positive percent rounded to 2 decimal places.) % Percentage c. Now assume Mrs. Pinson buys the bond at its current market value and holds it to maturity, what will be her percentage capital gain or loss? (lgnore any interest income received. Do not round intermediate calculations and input the amount as a positive percent rounded to 2 deci mal places.) % Percentage d. Why is the percentage gain larger than the percentage loss when the same dollar amounts are involved in parts b and c? The percentage gain is larger than the percentage loss because the investment is larger. The percentage gain is larger than the percentage loss because the investment is smaller.

Answer 1

6% [12%/2 20 [10 years x 2 28 as there are 2 semiannuals in a year] a) Semiannual Interest rate, RATE as there are 2 semiannuals in a year] #of semiannuals to maturity, NPER $50 [$1000 x 10% / 2] Semiannual coupon payment, PMT $1,000 [Par value of the bond] Maturity value at the end, FV 0 0 if paid at the end of each period; 1 if paid at the beginning of each period $885.30 [Ref: NOTE Semiannual coupon type, TYPE Bond's price today NOTE: Bond price today is calculated using EXCEL FUNCTION PV(rate,nper,pmt,fv,type) where rate= 6%; nper - 20; pmt-50; fv-1000; type-0. Here, value for pmt & fv are negative as they denote cash inflows; type 0 because coupons paid at the end of each semiannual only A C D EF G 1 Semiannual Interest rate, RATE 2 #of semiannuals to maturity, NPER 3 Semiannual coupon payment, PMT 4 Maturity value at the end, FV 5 Semiannual coupon type, TYPE 6 Bond's price today 12%/2 [12%/2 as there are 2 semiannuals in a year] 10*2 [10 years x 2 = 28 as there are 2 semiannuals in a year] 84*10%/2 [$1,000 x 10% / 2] $1,000 [Par value of the bond] 00 if paid at the end of each period; 1 if paid at the beginning of each period =PV(B1,B2,-B3,-B4,B5) [Ref: NOTE]

b) Bond's initial purchase price $1,000.00 -->(u) $885.30 (v) [As calculated in Part-(a)] -$114.70(v) (u) Bond's market price now Capital gain (loss), dollars So, Capital gain (loss), percentage -11.47% -->-$114.7/ $1000=-11.47% $885.30 c) Bond's market price now (v) [As calculated in Part-(a)] --> $1,000.00->(y) [Matured at par value] $114.70 Bond's market price at maturity Capital gain (loss), dollars (y) - v) --> $114.7/ $885.3 12.96% So, Capital gain (loss), percentage 12.96% d) Option-(b): The percentage gain is larger than the percentage loss because the investment is smaller. Explanation: For Part-(b), initial investment was $1,000 whereas for Part-(c), initial investment is $885.30 in the capital gain (loss) percentage calculation. As the numerator decreases, percentage gain (loss) increases.