Question

A 7-year semi-annual coupon bond with a $1,000 face value sells at $965.65 when the market rate is 5.6 percent. The coupon rate is closest to:

(always express coupon rate as an annual rate)

Select one:

A. 2.5% p.a.

B. 5.6%p.a.

C. 5.7% p.a.

D. 5.0%p.a

Answer 1

Now we need to look at the following details of the bond:

Coupon Payment : Semi Annual i.e twice in a year

Selling Price or PV : $ 965.65

Face Value FV : $1000

Market Rate r : 5.6%

Now we know that Present Value of Coupons = ( Here t is the time for which the coupon is discounted)

This simply means

The cash flow from the bond is discounted at the required rate of return semi annually as the bond is semi annual. The first coupon payment which is paid after 6 months will have Present value of C/(1+0.028)^14. The last term is at the end of 7 years or 14 periods. (The last value is C/(1+0.028)^14 due to technical error it shows 4 below)

Now converting the above into general formula

Present Value of Face value =

Now PV of Cash flow and PV of FV will give us the market price of bond which is in our case $ 965.65

Now solving for PV of Cash Values = (Here -n is raised to (1+r))

=C *

=C *11.45

Present Value of FV = 1000 / (1 + 0.028)^14 = 679.3544034592

Now PV/Market value of Bond = PV of Cash Flow + PV of Face Value

Therefore 965.65 = 679.3544034592 + (C * 11.45)

Now, 965.65 - 679.3544034592 = (C * 11.45)

Now, 286.2955965408 = C * 11.45

268.2955/11.45 = C   

C = 25.00398

Now C = Coupon Percentage * FV

25.00398 = C% * 1000/100

C% = 2.5% (Semi Annual)

Converting to Annual = 2*2.5% = 5%