Question

-N7 Bond Value = cl 1- Bord Volet c [013]. Come (148) Cl+on Bond value = 935.08 R = 1000 100 30 N 12 Calculate & ?

Answer 1

We are given the equation:

1-(1+r)-n] Bond Value = 0 (1+r)"

Substituting the values we get:

1-(1+r) -12 935.08 = 100 1000 (1+r)12

If the coupon is 100 and the par value is 1000 then the coupon rate is 10%

If the price is 935.08 that is less than the par value of 1000, r will be greater than the the coupon rate of 10%

After this we need to use hit and trial for a few rates to come to the required value of r or we can use a financial calculator or Excel's goalseek or rate functions.

Through hit and trial we can create a table as follows:

r	10%	11%	12%	13%	14%
Sum of PV of coupons	$         681.37	$         649.24	$         619.44	$         591.76	$         566.03
PV of par value	$         318.63	$         285.84	$         256.68	$         230.71	$         207.56
Bond value	$     1,000.00	$         935.08	$         876.11	$         822.47	$         773.59

So we see that r = 11%

Or we can feed in excel this formula =rate(12,100,-935.08,1000) and we will get the same answer

Or else we can use the financial calculator and feed:

N = 12, PMT = 100, PV = -935.08, FV = 1000 and CPT I/Y

As we need to pay the bond value to purchase the bond, and then only will we be able to get the coupon payments and the part value at maturity, PV is fed in as a negative number because it is a cash outflow.