Question

Answer the following questions regarding bond valuation.

a.      What is the price of a $1,000 par value bond with an 8% coupon rate paid semi-annually, if the bond is priced to yield 4% and it has 15 years to maturity? (5%)

b.      Following a, what would be the price of the bond if the yield rose to 8%? (5%)

c.       Following a, what would be the price of the bond if the coupon is paid quarterly? (5%)

d.      Explain how the calculation changes, given semi-annual coupons in a versus quarterly coupons in c. (10%)

Answer 1

Bond Valuation: The value of bond is the present value of the expected cashflows from the bond,discounted at Yield to Maturity(YTM).

a)

Year	Cash flow	PVAF/PVF@2%	Present Value (Cashflow*PVAF/PVF)
1-30	40	22.3965	895.86
30	1000	0.5521	552.10

Bond Price = Cashflow*PVAF/PVF

= 895.86+552.10

= 1447.96

Note : Since the bond makes semiannual interest payments, total no. of period is 30 (15*2), cashflow per period is 40(1000*8%/2) and cashflows are discounted at 2% (4/2)

When the YTM is less than the coupon rate then the bond will trade at premium

b)

Year	Cash flow	PVAF/PVF@4%	Present Value (Cashflow*PVAF/PVF)
1-30	40	17.2920	691.68
30	1000	0.3083	308.30

Bond Price = Cashflow*PVAF/PVF

= 691.68+308.3

= 999.98

Note : Since the bond makes semiannual interest payments, total no. of period is 30 (15*2), cashflow per period is 40(1000*8%/2) and cashflows are discounted at 4% (8/2)

When the YTM = coupon rate then the bond will trade at par

c)

Year	Cash flow	PVAF/PVF@1%	Present Value (Cashflow*PVAF/PVF)
1-60	20	44.9550	899.10
60	1000	0.5505	550.50

Bond Price = Cashflow*PVAF/PVF

= 899.10+550.50

= 1449.60

Note : Since the bond makes quarterly interest payments, total no. of period is 60 (15*4), cashflow per period is 20(1000*8%/4) and cashflows are discounted at 1% (4/4)

d) when compounding period increases the bond price also increases and vice-versa.