Adjusted Present Value - Subsidised loans

The effect on the base case NPV is to add the tax benefit on the interest payments (30% x 8% per year, discounted for 4 years) and also to add the benefit of the subsidy of 2% per year for 4 years. I explain how to do this in my free lectures on APV. (and does your book not have an answer and explanation?)

So this is the solution given in the text book. As you can see the interest rate used for calculating the amount of interest is 10% and not 8%. Im arriving at $722,760 but the answer is $951,000. Solution (a) Step 2 of the APV would be as follows. We assume that the loan is for the duration of the project (four years) only. Annual interest = $6 million x 10% = $600,000 Tax relief = $600,000 x 0.3 = $180,000 This needs to be discounted over Years 1 to 4 at the normal cost of debt of 10%. NPV tax relief = $180,000 x Discount factor Years 1 to 4 = $180,000 x 3.170 = $570,600 However, we also need to take into account the benefits of being able to pay a lower interest rate. Benefits = $6 million x (10% – 8%) x 10% discount factor Years 1 to 4 = $6 million x 2% ? 3.170 = $380,400 Total effect = $570,600 + $380,400 = $951,000.

The total effect is 836,880. You can get this 2 ways. One way is as the answer in the book has done it, although there is a mistake: The tax saving on interest at 10% = 570,600 (as per the workings you have shown). The subsidy benefit is 6M x (10 - 8)% x 0.7 x 3.170 = 266,280 (the 0.7 is because the tax saving has been calculate as though the interest was 10%, the subsidy benefit gains us 2% but loses the tax saving on the 2% so is only 0.7 times the saving. Total of the two is 570,600 + 266,280 = $836,880 The other way is as follows: Tax saving on interest at 8% = 6M x 8% x 0.3 x 3.170 = 456,480 Subsidy saving: 6M x (10-8)% x 3.170 = 380,400 Total of the two is 456,480 + 380,400 = $836,880 Either way is acceptable. The examiner sometimes does it the first way in his answers and sometimes does it the second way :-)

This is another worked example I came across. Here they have considered the tax relief lost while they have calculated the PV of the interest payment at the subsidised rate. I'm a bit confused regarding the tax relief calculation for the PV of the subsidised loan. A plc requires $1 million in debt finance for 5 years. It has borrowed $700,000 in the form of 10% bonds redeemable in 5 years and the remainder under a government subsidised loan scheme at 6%. The tax rate is 30%. Assume that tax is delayed one year. (a) PV of the tax shields Although the cheap loan has a cost of 6% it has the same risk as a normal loan, therefore the appropriate discount rate is 10% pa. Annual tax relief = Total loan × interest rate × tax rate 700,000 × 0.10 × .30 = 21,000 x 3.791 x 0.909 = 72,366 300,000 × 0.06 × .30 =72,366 x 3.791 x 0.909 = 18,609 Annuity factor for 5 years @10% Discount factor for 1 year @10% PV of the tax shield (b) PV of the cheap loan Annual amount 300,000 × (10% – 6%) = 12,000 × .30 = 12,000 x 3.791 = 45,492 Annuity factor for 5 years Present value factor – PV of the cheap loan Tax relief lost = 3,600 x 3.791 x 0.909 = (12,406) Total = 124,061

That is doing exactly as I explained in my previous reply to you. The only difference is that the tax is delayed for a year and so the PV of the tax relief needs discounting for the extra year.

I get that the tax is delayed for a year but we are calculating the interest amount at the subsidised rate and wouldn't that mean while calculating the PV of the subsidised loan the tax relief part is not included because we are including only the opportunity benefit of availing the subsidised loan?

That is correct. It does seem that there is a mistake in the answer and that although the tax benefit calculation is correct, the benefit of the subsidy should be calculated on the full 4% and not on 4% after tax.

Okay. Thank you for clearing my doubts John. :)