Question

1. You purchase a 20-year, $1,000 bond with a coupon rate of 6 percent paid annually with a margin requirement of 40 percent.

a. What would be your rate of return if the interest rates decreased, immediately after purchase, to 4 percent?

b. What would be your rate of return if the interest rates increased, immediately after purchase, to 8 percent?

Answer 1

a)
Margin amount = 1000 * 40% = 400

Rate = 4%

Nper = 20

PMT = 1000 * 6% = 60

FV = 1000

Price of the bond can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(4%,20,-60,-1000)
= $1,271.81

Rate of return = (Bond Price - Face Value)/Margin amount
= ($1,271.81 - $1,000) / $400
= $271.81 / $400
= 67.95%

Rate of return = 67.95%

b)
Margin amount = 1000 * 40% = 400

Rate = 8%

Nper = 20

PMT = 1000 * 6% = 60

FV = 1000

Price of the bond can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(8%,20,-60,-1000)
= $803.64

Rate of return = (Bond Price - Face Value)/Margin amount
= ($803.64 - $1,000) / $400
= -$196.36 / $400
= -49.09%

Rate of return = -49.09%