Question

What is the bond prices?

What is the zero discount rate?

What is the forward rate?

Par Value=1000

Maturity (yrs)	YTM	Coupon Rate
0.5	0.06	0.062
1.0	0.07	0.072
1.5	0.08	0.082
2	0.09	0.092

The market convention is semi-annual coupons and semi-annual compounding

Answer 1

Ans: 1) Value of Bond

Maturity (yrs)	YTM	Coupon Rate	Interest	Present Value Factor	Present value
0.5	0.06	0.062	$62.00	0.97	$60.19
1	0.07	0.072	$72.00	0.94	$67.54
1.5	0.08	0.082	$82.00	0.88	$71.81
2	0.09	0.092	$92.00	0.76	$70.21
					$269.75

Present value factor = ((1/(1+R1/2))^1)*((1/(1+R2/2))^2)*((1/(1+R3/2))^n)

Here R1 is Coupon rate of first six month and R2 is Interest of next six month

Computation of bond price = Issue price of the bond /( 1+ Yield till maturity) + Sum of (Interest received / ( 1+ yield till maturity))for N number of period

Computation of bond price = Present value of the bond + Present value of Interest received

Present value of Principle amount to be received = Redeemable value of the bond * Present value factor

= $1,000*0.76

= $760

Value of Bond = $760 + $269.75

= $1029.75

2) Zero discount rate

Present value of zero discounted Bond = Redeemable value of the bond * Present value factor

   1,000*(1+(1+r/2))^4 = $1,000*0.76

(1+(1+r/2))^4 = $760/1,000

  (1+(1+14%/2))^4= 0.76

So Zero Discounted rate = 14%

3) Forward rate

   Present value of Bond= Face value of the bond / ( (1+ Interest rate)*(1+Forward rate))

Maturity (yrs)	YTM/Forward rate	Coupon Rate
0.5	0.6	0.62
1	0.7	0.72
1.5	0.8	0.82
2	0.9	0.92