Which discount rate to be used in APV for subsidized loan

Were you supplied with the risk free rate in the Kaplan example? Often the normal interest rate is the risk free rate, and has to be taken as that if the risk free rate is not supplied. I don't think the answer is clear. As you say the Kaplan text uses the normal interest rate to discount the benefit of the subsidy. However, a similar example in the BPP text uses the risk free rate. Kaplan's knowledge bank says: "As all financing cash flows are low risk they are discounted at either: the Kd or the risk free rate." So that doesn't help! This article (note 4 at the bottom of the first page) says it's open to debate, but that tutor suggests using the normal interest rate - but not deinitive: https://www.cimaglobal.com/Documents/Student%20docs/2010%20syllabus%20docs/F3/f3_fmarticle_june2014.pdf So, see what's available in the question and take you pick if forced to. Sorry not give a more definitive answer, but I don't think there is one.

Ken, do you mean Kd/risk free rate less the rate of the subsidised loan being the interest on which the shield is calculated?

Yes. That is a measure of the 'artificial cheapness' of the loan and that's where the benefit derives from. Remember, of the interest rate you pay is lower you lose out on some tax relief on that and that effect has to be taken into accont.