Question

  ​(Bond valuation) A bond that matures in 11 years has a ​$1,000 par value. The annual coupon interest rate is 8 percent and the​ market's required yield to maturity on a​ comparable-risk bond is 13 percent. What would be the value of this bond if it paid interest​ annually? What would be the value of this bond if it paid interest​ semiannually? a.The value of this bond if it paid interest annually would be ​$

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).

What would be the value of this bond if it paid interest​ annually?

Year	Cash flow	PVAF/PVF@13%	Present Value (Cashflow*PVAF/PVF)
1-11	80	5.6869*	454.95
11	1000	0.2607**	260.70

Current Market Price of Bonds = Cashflow*PVAF/PVF

= 454.95+260.70

= $715.65

*PVAF = (1-(1+r)^-n)/r

**PVF = 1 / (1+r)^n

What would be the value of this bond if it paid interest​ semiannually?

Year	Cash flow	PVAF/[email protected]%	Present Value (Cashflow*PVAF/PVF)
1-22	40	11.5352*	461.41
22	1000	0.2502**	250.21

Current Market Price of Bonds = Cashflow*PVAF/PVF

= 461.41+250.21

= $711.62​​​​​​​

Note : Since the bond makes semiannual interest payments, total no. of period is 22 (11*2), cashflow per period is 40(1000*8%/2) and cashflows are discounted at 6.5% (13/2)

*PVAF = (1-(1+r)^-n)/r

**PVF = 1 / (1+r)^n