Question

A semi-annual corporate bond has a coupon rate of 9 percent per year. The face value is $1,000. The market interest rate (yield to maturity) for this bond today is 10.5 percent. This bond has 25 years before maturity.

a. What is the price of this bond today?

b. What is the current yield for this bond?

c. Why is the current yield different from the current market rate of this bond?

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Answer 1

a. What is the price of this bond today?

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 discount as YTM>coupon rate

Year	Cash flow	PVAF/[email protected]%	Present Value (Cashflow*PVAF/PVF)
1-50	45	17.5728*	790.78
50	1000	0.0774**	77.42

Current Market Price of Bonds = Cashflow*PVAF/PVF

= 790.78+77.42

= $868.20

Note : Since the bond makes semiannual interest payments, total no. of period is 50 (25*2), cashflow per period is 45(1000*9%/2) and cashflows are discounted at 5.25% (10.5/2)

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

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

b. What is the current yield for this bond?

Current Yield = Annual cash inflows/Current market price

= 90/868.20

= 10.37%

c. Why is the current yield different from the current market rate of this bond?

Current market rate is based on expected future cash flows. It includes both coupon payment and capital appreciation/depreciation.

current yield does not take into account any capital gains or losses that a bondholder would realize if the bond were purchased at a discount or premium.