Question

bond interest payments are semi-annual, and maturity and face value are $1,000

John has a 3-year, 4.9% bond with a yield to maturity of 4.03%.

a. What is the price of the bond?

b. Is the bond selling at a premium or a discount?

c. What is the current yield on this bond?

Answer 1

a. What is the price of the bond?

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

Prima facie, the bond will trade at Premium as YTM<coupon rate

Year	Cash flow	PVAF/[email protected]%	Present Value (Cashflow*PVAF/PVF)
1-6	24.5	5.5986	137.17
6	1000	0.8872	887.19

Current Market Price of Bonds = $\sum$Cashflow*PVAF/PVF

= 137.17+887.19

= 1024.35

Note : Since the bond makes semiannual interest payments, total no. of period is 6 (3*2), cashflow per period is 24.50(1000*4.9%/2) and cashflows are discounted at 2.015%(4.03/2).

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

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

b. Is the bond selling at a premium or a discount?

The bonds are selling at premium, that is above face value.

c. What is the current yield on this bond?

Current Yield = Annual Coupons / Current Bond Price

= (1000*4.9%)/1024.35

= 49/1024.35

= 0.04783521257

= 4.78%