Question

cullumber products issued $3.06 million of 8% 5-year bonds on january 1 2017. the bonds were dated janjary 1 and pay interest annually. there is no collateral secured against the bonds and cullumber products may buy back the bonds at any time.the market interest rate was 9% for these bonds.cullumber has a calender year end.
calculate the price of the bonds

Answer 1

Calculation of price of a bond
The Company has issued the 8% coupon rate bond for 5 year, so in the at the beginning of first year it will receive $ 3.06 and at the end of each year it will pay interest at the rate of 8% coupn rate i.e (3.06*8%=0.24) and at the end of the 5th Year the company will repay the $3.06
to calculate thr price of the bond we use the market rate to discount the cash flow
As per bond theoram the price of the bond will be lower than face value if the market interest rate is more than the coupon rate as market participant expect more return than the coupan rate therefore they will pay less to purchase the bond as they will get less interest every year
	Coupon rate	8%
	Market Rate	9%
Year	Cash flow and interest at 8%	Cash flow discoiunted at 9%	Working"Cash flow and interest at 8%"	Formula"Cash flow discoiunted at 9%"
0	3.06
1	0.2448	0.2246	=3.06*8%	=.2448/(1+9%)^1
2	0.2448	0.2060	=3.06*8%	=.2448/(1+9%)^2
3	0.2448	0.1890	=3.06*8%	=.2448/(1+9%)^3
4	0.2448	0.1734	=3.06*8%	=.2448/(1+9%)^4
5	0.2448	0.1591	=3.06*8%	=.2448/(1+9%)^5
5	3.0600	1.9888		=3.06/(1+9%)^5
		2.94
The formula for discounting the cashflow is=cashflow/(1+ market interest rate)^no of year discounting