The Yield on a Loan subject to Capital Gains Tax

Extract

H. O. Worger gave a simple rule (J.S.S., 5, 15 and J.S.S., 7, 116) for using tables of Bond Values for finding the equivalent gross redemption yield on a redeemable security where the dividend is subject to income tax but the capital gain is tax-free. He showed that it was unnecessary to go through the process of first finding the net yield by entering the tables at a dividend rate from which tax had been deducted. All that was needed was to reduce the unexpired term in proportion to the rate of tax payable, and enter the table for the full nominal rate of dividend. The purpose of this note is to show that a somewhat similar rule is available if both dividend and capital gain on redemption are subject to the same rate of tax.

Let P be the purchase price of a loan of 1 redeemable at par in n years time and bearing annual dividends at the rate g, and let t be the rate of tax.