Question

An investor, who is liable to income tax at 20% but is not liable to capital gains tax, wishes to earn a net effective rate of return of 5% per annum. A bond bearing coupons payable at the end of every half-yearly at a rate 6.25% per annum is available. The bond will be redeemed at par on a coupon date between 10 and 15 years after the date of issue, inclusive. The date of redemption is at the option of the borrower. Calculate the maximum price that the investor is willing to pay for the bond.

Answer 1

Per period = 6months; Assume at the end of the 11th year bond is redeemed at the option of the borrower. Assume par value of the bond is $100;

Interest per period =Par value of the bond * interest rate * (1-tax rate) =  $100*6.25%/2*(1-.08) =$2.50

Period (i)	Cashflow after tax (ii)	PVF @ 2.5% per period (iii)	Discounted cashflow (iv) = (ii * iii)
1	$      2.50	0.9756	$         2.44
2	$      2.50	0.9518	$         2.38
3	$      2.50	0.9286	$         2.32
4	$      2.50	0.9060	$         2.26
5	$      2.50	0.8839	$         2.21
6	$      2.50	0.8623	$         2.16
7	$      2.50	0.8413	$         2.10
8	$      2.50	0.8207	$         2.05
9	$      2.50	0.8007	$         2.00
10	$      2.50	0.7812	$         1.95
11	$      2.50	0.7621	$         1.91
12	$      2.50	0.7436	$         1.86
13	$      2.50	0.7254	$         1.81
14	$      2.50	0.7077	$         1.77
15	$      2.50	0.6905	$         1.73
16	$      2.50	0.6736	$         1.68
17	$      2.50	0.6572	$         1.64
18	$      2.50	0.6412	$         1.60
19	$      2.50	0.6255	$         1.56
20	$      2.50	0.6103	$         1.53
21	$      2.50	0.5954	$         1.49
22	$ 102.50	0.5809	$       59.54
Price of the bond	$    100.00

The maximum price that the investor is willing to pay for the bond is $100. The redemption period will not affect the bond price. Interest rate after tax is equal to net effective rate of return, hence the price of the bond the investor willing to pay will not be more than par value of the bond.