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I thought I had understood apv but I came across this example in bpp textbook and i am very confused!
A company is considering a project that would cost $100,000 to be financed 50% by equity (Ke 21.6) and 50% by debt (12% pre-tax cost). financing method would maintain co’s Wacc. Cash flow from project is $36,000 in perpetuity, before interest. Tax is 30%. Appraise using APV.I calculated the cost of ungeared equity as 17.647%, then I calculated the NPV to $42,800
but i am confused as to calculation of tax shield…
I assumed that since the project is to be financed by 50% debt so 50% of $100,000 should be debt so,
$50,000* 8.4%* 30%= $1,260so APV= $(42,800+1,260) = $44,060
but the solution in book has calculated the value of debt as $84,000 and tax shield as $84,000* 30%.
Please help!!!
I am sorry, but I do not have the BPP Study Text (only the Revision Kit).
From what you have written it does seem that they have made a mistake and that your answer is correct (have you checked their website to see if there is an errata sheet? I know they produce one correcting errors in their Revision Kit.)
However, without seeing the whole question and answer I obviously cannot be certain.Sorry 🙁
Whole QUESTION from BPP text book as below:
A company is considering a project that would cost $100,000 to be financed 50% by equity (cost 21.6%) and 50% by debt (pre-tax cost 12%). The financing method would maintain the company’s WACC unchanged. The cash flows from the project would be $36,000 a year in perpetuity, before interestcharges. Tax is at 30%.
Appraise the project using firstly the NPV method and secondly the APV method.
Whole ANSWER from BPP text book:
Before tax 36,000
Less tax (30%) 10,800
After tax 25,200
NPV of project = –$100,000 + (25,200 / 0.15)
= –$100,000 + $168,000
= $68,000
Note that the tax relief that will be obtained on debt interest is taken account of in the WACC, not in theproject cash flows.Since $100,000 of new investment is being created, the value of the company will increase by $100,000 + $68,000 = $168,000, of which 50% must be debt capital.
The company must raise 50% x $168,000 = $84,000 of 12% debt capital, and (the balance) $16,000 ofequity. The NPV of the project will raise the value of this equity from $16,000 to $84,000 thus leaving the gearing ratio at 50:50.The APV approach to this example is as follows.
(a) First, we need to know the cost of equity in an equivalent ungeared company. The MM formula we can use to establish this is as follows.MM formula to get ke = 17.647%
(b) Next, we calculate the NPV of the project as if it were all equity financed. The cost of equity would be 17.647%.
NPV = ($25,200 / 0.17646) – $100,000 = $42,800(c) Next, we can use an MM formula for the relationship between the value of geared and ungeared companies to establish the effect of gearing on the value of the project. $84,000 will be financed by debt.
Vg (APV) = Vu + (value of debt × corporate tax rate)
= $42,800 + ($84,000 x 0.30)
= $42,800 + $25,200
= $68,000
The value of debt x corporate tax rate represents the PV of the tax shield on debt interest; that is, the PV of the savings arising from tax relief on debt interest.This can be proved as follows.
Annual interest charge = 12% of $84,000 = $10,080
Tax saving (30% x $10,080) = $3,024.00
Cost of debt (pre-tax) = 12%
PV of tax savings in perpetuity =3,024/ 0.12 = $25,200
(by coincidence only this equals the project net of tax cash flows)Now I see the full question, the BPP answer is correct, although it is badly worded.
If the $100,000 was to be raised 50% equity, 50% debt, then your answer would have been correct.
However, what they intended (but again it is badly worded) is that 50% of the value of the project is raised from debt. Since the project cost 100,000 and gives a gain of 68,000, it means that the value of the project to the business is 168,000, and therefore 50% i.e. 84,000 is to be raised from debt.
if the same question happen in exam? what should we do? show we follow our own answer which the PV of the tax shield is 100,000*50% * 30% = $15,000
The exam will make it more clear (but if you are not sure then state your assumption and you will still get the credit – always in P4 (especially in question 1) there are different assumptions you could make, and that is why almost always the question asks you to state your assumptions in the report).
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