Computing the issue price of bonds. Compute the issue price1 answer below »

Computing the issue price of bonds. Compute the issue price of each of the following bonds. a. $1,000,000 face value, zero coupon bonds due in 20 years, priced on the market to yield 10% compounded semiannually. b. $1,000,000 face value, serial bonds repayable in equal semiannual installments of $50,000 for 20 years, priced on the market to yield 6% compounded semiannually. c. $1,000,000 face value, 10% semiannual coupon bonds with interest payable each six months and the principal due in 20 years, priced on the market to yield 8% compounded semiannually. d. $1,000,000 face value semiannual coupon bonds, with an annual coupon rate of 6% for the first ten years and 8% for the second ten years and the principal due in 20 years, priced on the market to yield 10% compounded semiannually.

Dec 17 2020 07:26 PM

1 Approved Answer

Sanjiv C
answered on
December 19, 2020

5
Ratings,(7 Votes)

a) A Zero Coupon bond due in 20 years, priced to YTM of 10% compound semiannually Price = Maturity Amount / (1 + r/2)^n where r is the YTM % and n is the number of compounding intervals. In this case, Maturity Amount = $ 1,000,000 r = 10% and n = 40. Therefore Price = 1,000,000 / (1 + 0.05)^40 = 1,000,000* 0.142046 = $ 142,046 b) Serial Bonds of Face Value $ 1,000,000 repayable in 40 equal semi annual payment of $ 50,000 each, YTM of 6 % compounded semiannually: Price = Sum of Present Values of the 40 semi annual payments of $ 50,000 each = 50,000 * (1/1.03 + 1/1.03^2+ /1.03^3 + ...........+ 1/ 1.03^40) Price = 50,000 * 23.11 = $ 1,155,738.60 c) Semiannual Coupon payment = 5 % of $ 1,000,000 = $ 50,000. Present value of Coupon payments = 50,000 * (1/1.04 + 1/ 1.04^2 + 1/1.04^3 + ............ + 1/1.04^40) = 50,000* 19.79 = $ 989,639 Present value of Maturity Amount = Maturity Amount / (1.04)^40 = 1,000,000 * 0.2083 = $ 208,289 Price of the Bond = Present Value of Coupon Payments + Present Value of Maturity Amount = $ 989,639 + $ 208,289 = $ 1,197,928 d) Semi...

annual coupon payments = 3 % of 1,000,000 = $ 30,000 Present Value of Coupon Payemnts in 1st 10 years (YTM of 6 %) = 30,000 * (1/1.03 + 1/1.03^2 +........... + 1/1.03^20) = 30,000 * 14.8775 = $ 446,324 Present Value of Coupon Payments in next 10 years (YTM of 8 %) = 30,000 * (1/1.04^21 + 1/1.04^22 + ........+ 1/1.04^40) = 30,000 * 6.20 = $ 186,073 Present value of Maturity Amount (YTM of 10%) = 1,000,000 / (1.05)^40 = 1,000,000 * 0.142046 = $ 1,42,046 Price of Bond = Present Value of Coupon Payments in 1st 10 years + Present Value of Coupon Payments in next 10 years + Present Value of Maturity Amount Price of Bond = $ 446,324 + $ 186,073 + $ 142,046 = $ 774,443 Spreadsheet attached showing the calculations.

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