Question

The Mayflower Corporation has two different bonds currently outstanding. Bond A has a face value of $50,000 and matures in 5 years. The bond makes no payments for the first 2 years, then pays $2,000 every 6 months over the next 3 years until maturity. Bond B also has a face value of $50,000 and matures in 5 years; it makes $750 of coupon payment every 6 months over the life of the bond. If the annual required rate of return for both of these bonds is 10%, what is the value of Bond A? Bond B?

Answer 1

To calculate Price of a $ 50,000 Par value bond, present value of all interest payments and maturity amount shall be calculated.
All interest coupon and maturity amount shall get discounted with required rate of return to calculate Present Value of all interest payment and maturity amount.
Required rate of return =			10%
Coupon payment is in 6 months, So Half yearly discount rate = 5.00 % or							0.05
Calculation of Present Value of Bond A
					Amount		Present value
Interest payment for first 2 years =					0
So, Present value of interest is also zero.							0
Interest payment six monthly for 3 years					2000
Cumulative P.V.F. @ 5.00 % for 5th to 10 th period =						4.175784
Present Value of All Interest payments (2000 * 4.175784) =							8351.568
Bond maturity amount					50000
P.V.F. @ 5.00 % for 10th period						0.613913
Present Value of Bond Maturity amount							30695.65
							_________
Total of Present Value of Interest and Bond Maturity amount =							39047.22
							__________
So, Value of Bond A is $39,047.22.
Calculation of Present Value of Bond B
					Amount		Present value
Interest payment six monthly for 5 years					750
Cumulative P.V.F. @ 5.00 % for 1 to 10 th period =						7.721735
Present Value of All Interest payments (750 * 7.721735) =							5791.301
Bond maturity amount					50000
P.V.F. @ 5.00 % for 10th period						0.613913
Present Value of Bond Maturity amount							30695.65
							_________
Total of Present Value of Interest and Bond Maturity amount =							36486.95
							__________
So, Value of Bond B is $ 36,486.95
Note (1) :Cumulative P.V. F. @ 5.00% for 1 to 10 period = 1/(1.05)^1 + 1/(1.05)^2 + 1/(1.05)^3 ……………………..1/(1.05)^10
Note (2) : Cumulative P.V. F. @ 5.00% for 5th to 10 period = 1/(1.05)^5 + 1/(1.05)^6 + 1/(1.05)^7……………………..1/(1.05)^10