Dec 2012, COEDEN, Part (a)

It seems you have misunderstood the previous posts that you have looked at. The market value of debt is always calculated as the present value of the pre-tax flows discounted at the pre-tax cost of debt (which is the investors required rate of return) because it is investors who determine the market value and they are not affected by company tax. The cost of debt is the cost to the company and is after tax. If the debt is irredeemable, then the cost of debt is Kd (1-T) where Kd is the pre-tax cost of debt and T is the rate of tax. (Although it is more normally calculated as I(1-T)/ MV, where I is the interest and MV is the market value, because this is faster). However, if the debt is redeemable the cost of debt is calculated as the IRR of the after tax interest and redemption flows to the company (and most exam questions have redeemable debt rather than irredeemable). The reasons for this are all explained (with examples) in my free Paper FM lectures on the valuation of securities and on the cost of capital, because this is revision from Paper FM, and in my Paper AFM cost of capital lectures.

Thank you for your reply. I've revisited the lecture notes and understood the points you mentioned. That is why I'm confused with the approach used since 4.9% is the pre-tax cost of debt and is later used as the discount rate to arrive at the market value of debt. However, the way it calculated WACC is 10.6% x 0.5 + 4.9% x 0.8 x 0.5 = 7.3%. Here, the cost of debt suggested is Kd (1-T) where Kd = 4.9% and (1-T) = 0.8 but the debt in question is irredeemable. As you stated, "if the debt is redeemable the cost of debt is calculated as the IRR of the after-tax interest and redemption flows to the company" but the answer did not use this approach.

You are correct, and strictly the examiners answer should have calculated the after-tax IRR. However, because the debt is repayable at par and the debt is not traded, which means that the market value is the same as the par value, then the IRR of the post-tax flows will be exactly the same at the pre-tax cost as reduced by the rate of tax. Try it yourself and you will see that it is the same :-)