# APV and the discount rate of the tax shield

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• mmia
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My question refers to example 16 of the BPP practice and revision kit

I have difficulties in understanding discounting the tax relief in the APV calculations.

p. 144 of the study text tells me to discount the PV of tax relief use either the risk free rate or the cost of debt.
p. 52 the cost of debt capital is the after-tax cost of raising debt in the capital markets.

To discount tax relief on redeemable debt in example 16 the risk free rate is used as per the solution.

I used the after-tax cost of debt and calculated it as
Year 0 amount of debt raised less issue costs
Year 0-6 interest on debt
Year 6 amount of debt to be paid back

I used IRR to get to the pre-tax cost of debt.

Would my way of calculating the disount rate for tax relief be right too?

In the exam how do I know what rate to use? Can I always use the risk free rate referring to the modigliani Miller Model and a debt risk of beta = 0?

I am quite desperate, as I fear that there is something very important that I missed to understand.

Another issue on the exam and knowing whether to use APV or NPV: Will the examiner usually tell me to use APV instead of NPV?
My rule is that if a project or an acquisition affects the exposure to financial risk than use APV.
If the examiner does not tell me to use the APV I would use it any time the example states that the overall risk to investors in the company changes due to the project. Does this approach make sense?

John Moffat
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Regarding the first part of your question, you are correct. You can either use the risk free rate, or the cost of debt. In theory they should both be the same, but in practice not (because debt in real life is not completely risk free). You will get full marks for using either.

I would expect the examiner usually to tell you whether he wants APV or NPV. If he does not then your rule is fine.

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