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Gordonbear is about to start a project requiring $6 million of initial investment. The company
normally borrows at 10% but a government loan will be available to finance the entire project at 8%.
Tax is payable at 30% with no delay. The project is scheduled to last for four years.
Calculate the effect on the APV calculation if Gordonbear finances the project by means of the
government loan.
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 ? 10%
= $600,000
Tax relief = $600,000 ? 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 ? Discount factor Years 1 to 4
= $180,000 ? 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 ? (10% – 8%) ? 10% discount factor Years 1 to 4
= $6 million ? 2% ? 3.170
= $380,400
Total effect = $570,600 + $380,400 = $951,000.
____________________-the above is tb asnwer,
however my answer is:
=6M*8%*0.3*3.170
+ 6M*2%*0.7*3.170 = 722760_________________________
please explain where am I going wrong sir? my approach is inspired by Strayer Inc (Jun 02 adapted)
Also please shed some light on the fact that we have to use Pre tax cost of debt, why had bpp bpook used 10% as disocunt factor, iu’m extremely confused now.
For the question as you have typed it, it would seem that BPP have made a mistake. However so have you in your solution.
If there had been so subsidised loan, then the PV of the tax relief would be:
6M x 10% x 0.3 x 3.170 = 570,600. (they would be paying interest at 10% and getting tax relief on that interest).
The subsidised loan means that they will be saving 2% interest, but it would also mean that they would not be getting the tax saving on that 2%. Therefore the subsidy benefit would be:
6M x 2% x 0.7 x 3.170 = 266,280So the total benefit (to add to the base case NPV) is 836,880.
An alternative approach to getting the same answer (whichever you find the most logical for you) is as follows:
They are getting a saving of 2% in interest. The PV of this alone is:
6M x 2% x 3.170 = 380,400.The actual interest on which they are getting a tax saving is the 8% they are actually paying, and so the PV of this tax saving is:
6M x 8% x 0.3 x 3.170 = 456,480So the total benefit is 836,880
(Again it doesn’t matter in the exam which of the two ways to use to get the total.)
As far as the discount rate being used (here 10%), I do explain this in my free lectures as well.
The tax benefit should be discounted at the relevant rate for the risk to the investors attaching to the tax benefit. There are two arguments as to the risk of this benefit (both of which are logical and therefore both are always allowed for full marks by the examiner).
One argument is that the tax saving carries the same risk as the interest itself. Since investors are demanding a 10% return for the level of risk or the interest itself (at normal rates) then this accounts for the risk (and investors required return is always pre-tax because they are not affected by company tax). Therefore we should discount at (in this case) 10%.
The other argument is that the tax saving is risk-free, and therefore should be discounted at the risk-free rate (which is always pre-tax).
Again the examiner always allows either of the two rates to be used (and although Strayer is a very old question and was set by the previous examiner) his answer does specifically state that 5.5% (i.e. the risk free rate) could have been used instead of the normal interest rate.
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