Question

An investor owns a 14% bond with face value 400 and semiannual coupons. The bond will mature at par at the end of 18 years. The investor decides that a ten-year bond would be preferable. Current yield rates are 6.8% convertible semiannually. The investor uses the proceeds from the sale of the 14% bond to purchase an 12% bond with semiannual coupons, maturing at par at the end of ten years.

Answer 1

Currently,

Face value(FV) = 400

PMT = Value of Coupons = 14% semiannual = 7% * 400 = 28

Yield Rate = 6.8%/2 = 3.4% semiannual

No of periods= 18*2 =36

We have to calculate the Present value(PV) in excel or financial calculator,

=PV( rate, nper,pmt,fv)

=PV(3.4%,36,-28,-400)

=$ 696.43

Now, The investor uses the proceeds from the sale of the 14% bond to purchase an 12% bond with semiannual coupons, maturing at par at the end of ten years

Let the Face value of 2nd bond be F

PMT = 12/2 = 6% of F = 0.06F

Yield Rate = 6.8%/2 = 3.4% semiannual

No of periods= 10*2 =20

The PV of this bond

=PV( rate, nper,pmt,fv)

=PV(3.4%,20,-0.06F,-F)

   Or, PV = 1.37F

  

Since The investor uses the proceeds from the sale of the 14% bond to purchase an 12% bond,

The PV of both of them are equal

So, 696.43= 1.37F

F= 696.43/ 1.37 = 507.27 $

The par value or face value of 2nd bond is 507.27 $