Question

"A Company has a bond outstanding with a face value of $10000 that reaches maturity in 10 years. The bond certificate indicates that the stated coupon rate for this bond is 2.5% and that the coupon payments are to be made semiannually. Assuming the appropriate YTM on the bond is 5%, then the price that this bond trades for will be closest to ________. Note: Express your answers in strictly numerical terms. For example, if the answer is $500, write enter 500 as an answer."

Answer 1

Sol:

Face value (FV) = $10,000

Coupon rate = 2.5%, semiannual = 2.5 / 2 = 1.25%

Annual coupon payment (PMT) = 10,000 * 2.5% = $250, Semiannual payment = 250 / 2 = $125

Maturity = 10 years, Semiannual = 10 * 2 = 20

Yield = 5%, Semiannual = 5 / 2 = 2.5%

To determine price that this bond trades for or present value.

Present value (PV) = (PMT x (1-(1+r)^-n)/r) + (FV/(1+r)^n)

Present value (PV) = (125 x (1-(1+2.5%)^-20)/2.5%) + (10,000 / (1+2.5%)^20)

Present value (PV) = (125 x (1-(1.025)^-20)/0.025) + (10,000 / (1.025)^20)

Present value (PV) = (125 x 15.589162) + 6,102.709429

Present value (PV) = 1,948.64525 + 6,102.709429

Present value (PV) = 8051.35

Therefore price that this bond trades for is 8051.35

You can also determine the present value in excel by using PV function:

FV	10,000
NPER	20
Monthly payment	125
Yield	2.50%
Present value	8,051.35

Working