course 2 exam question

[ASA_Woman]

i don't understand part of the solution. please help if you can.

November 2000, #49

A company is considering a project that costs 88,200 at time 0 and expects a revenue stream of 11,400 at the end of each year forever. The company plans to finance the project by issuing debt of 45,000 with the remaining 43,200 coming from the issuance of common stock. This debt to equity is the same as the market value of the company's debt to equity ratio.

You are given the following info about the project:

(i) issue costs equal 4% of the gross proceeds on any new issuance of stock

(ii) the compnay must pay an 8% coupon at the end of each year on its debt

(iii) the company's weighted average cost of capital = 12%

(iv) the company's marginal tax rate = 22.5%

In order to determine the adjusted present value of the project, the company assumes that its debt will be adjusted each year to keep it at a constant fraction of the future project value.

Calculate the adjusted present value.

Solution:

APV = -(project cost) - (equity issue cost) + (project PV) + (PV of tax shields)
Project cost = 88,200
Equity issue cost = 43,200/.96 - 43,200 = 1800
Project PV = 11,400/0.12 = 95,000
PV tax shield = 45,000 (0.08/0.12) (0.225) (1.12/1.08 ) =7000

therefore APV = -88,200-1800+95000+7000 = 12000

I have bolded the parts of the solution that I do not understand.

[ASA_Woman]

where in the notes is the concept "adjusted present value" found?

[Gandalf]

You are given the following info about the project:

(i) issue costs equal 4% of the gross proceeds on any new issuance of stock

[much text deleted]

Equity issue cost = 43,200/.96 - 43,200 = 1800
Project PV = 11,400/0.12 = 95,000
PV tax shield = 45,000 (0.08/0.12) (0.225) (1.12/1.08) =7000

I have bolded the parts of the solution that I do not understand.

I don't know the syllabus, so I'm not sure what issue you are raising with Equity issue cost. Mathematically, they're saying that you need to keep 43,200 from the stock. Costs are 4% of gross proceeds, so you need .96 * gross proceeds = 43,200. So gross proceeds = 43,200 / .96; cost = 43,200 / .96 - 43,200. Maybe that's right, maybe wrong, but surely that's what they're doing.

For the second bolded section, my only suggestion is that you can avoid the emoticon with a space after the 1.08.

[ASA_Woman]

Thanks Gandalf. You must be a wizard at this :wink:

[ASA_Woman]

Can anyone help me out with the (1.12/1.08 ) part of the PV tax shield calculation?

[Macroman]

where in the notes is the concept "adjusted present value" found?

Adjusted Present Value is explained starting on p. 555 of Brealey and Myers.


PV tax shield = 45,000 (0.08/0.12) (0.225) (1.12/1.08 ) =7000

APV = NPV(equity financing) + NPV(side effects). Since the cost of debt is 8% and WACC is 12%, I would say that the (1.12/1.08) factor is adjusting the debt discount rate to the firm discount rate (WACC = 12%).

I wouldn't worry too much about this one, almost everyone (including me) who sat the exam that session missed it. The APV is far enough off the beaten path that I would expect an easier question if it is tested again.

In my opinion APV is an inferior concept like IRR and payback time. I would focus on NPV problems if I were you.

[ookawasan]

This problem bugged me for some time as well. It has to do with the Miles-Ezzel formula in chapter 19. If you read chapter 19 carefully and slowly, you will see that there are three methods of calculating APV. The key phrase is "its debt will be adjusted each year to keep it at a constant fraction of the future project value. " When you want to keep it at a constant fraction, you have to adjust the discount rate. Hope this helps.

[drctypea]

i thought that if you are discounting at the wacc that debt rebalancing was already assumed. i thought the only reason why in the text they multiply by an adjustment factor when debt rebalancing was because they discounted the interest tax shields at the opportunity cost of capital and came up with a different present value that discounting at the wacc. they then had to adjust the 2.36 million by (1.12/1.08) to make it equal to the 2.5 million gotten from discounting at the wacc. on this exam question you are already discounting at wacc so im still confused on why the adjustment is neccessary.

[bg23516]

Hi,

I just tried this problem, and I have a few problems with it.

I understand how to find issue costs.

When estimating the PV(Tax Shield), the formula is:
[(rd)(1-Tc)(debt amt) / (r)] * (1+r / 1+rd)

Here's my problem with this. According to the book, we are to use the opportunity cost of capital as r, but here, we are expected to use the WACC. Aren't these not the same? I think that is what drctypea was saying. If we use the OCC, we should divide by r and multiply by (1+r/1+rd) as the interest is fixed for the next year but rebalanced otherwise. However, if we use the WACC, we shouldn't have to adjust because the WACC implicitely recognizes that next year's debt amount is fixed. (As drctypea said)

Given the WACC and not OCC, how are we supposed to find the base case NPV of the project? Aren't you supposed to find base case NPV at the OCC?

Also, why doesn't the solution tax the annual revenue? I thought you always discounted cf's AFTER-TAX.

It seems that we should be given the OCC, not the WACC in order to use the solution as given.

Any comments?

[Macroman]

APV is a different type of evaluation of cash flows like IRR or payback period. Please read the section of Corp Finance if you want to understand this problem.

When NEAS instructors decided to post answers to this exam shortly after the SOA released this exam they ommitted this question. I am not sure if they thought it was defective or erroneous or just to hard, but they posted answers to all 54 other questions but not this one.

I believe that the SOA's posted solution to this question is consistent with what is presented in Brealey and Myers. I also believe that understanding how to use Adjusted Present Value (APV) is not important to passing course #2. The relevant section of Brealey and Myers begins on page 555 if you are interested.