Question

What would you pay for a bond that pays an annual coupon of $35, has a face value of $1,000, matures in 7 years, and has a yield to maturity (YTM) of 8%?

Answer 1

The bond value of the bond is based on the present value of coupon payment plus the present value of the face value to be received at maturity
Therefore, the payment for the bond would be calculated using the below formula
Price of bond = Sum of present value of coupon payment + Present value of face value
Present value is the present worth of future payment calculated using the discount rate, for bonds it is yield to maturity
Calculation of price of bonds is shown below
Year	Cash inflow	Discount factor @ 8%	Working for discount factor	Present Value
1	$          35	0.92593	1/(1.08^1)	$          32.41
2	$          35	0.85734	1/(1.08^2)	$          30.01
3	$          35	0.79383	1/(1.08^3)	$          27.78
4	$          35	0.73503	1/(1.08^4)	$          25.73
5	$          35	0.68058	1/(1.08^5)	$          23.82
6	$          35	0.63017	1/(1.08^6)	$          22.06
7	$     1,035	0.58349	1/(1.08^7)	$        603.91
				$        765.71
At the 7th year we would receive the coupon payment of $35 and the face value of $1,000 and therefore cash inflow of $1,035 is considered
Discount factor is calculated as (1/[1+r]^n), where r is the yield to maturity and n is the year
The value to be paid for the bond would be $765.71