If the normal risk free rate is 10%, and the corporate tax rate is 34%, then
assuming the company earns enough money to pay taxes, the tax shields
effectively cut the company's interest rate from 10% to 6.6%. For example if
the debt was $100, the company would pay $10 in interest, but save $3.40 in
taxes. Thus it is like only paying $6.60 in interest. Hence the effective
"After tax interest (discount) rate would be 6.6% = 10%(1-.34). I think the
answer to the below problem is ( I am assuming the project only lasts 5
years w/ straight line depreciation and the depreciation is not already
calculated into the cash flows):
present value of cash flows: 3.5M for 5 years discounted at 20%(assuming
project is all equity financed like firm
= 3.5M/(1.2) + 3.5M/(1.2)^2 + .... = 10.47M
depreciation per year = 2M
tax shields per year = 2M(.34) = .68M
after-tax discount rate for safe-nominal cash flows = 6.6%
PV of Depreciation Tax Shields: .68M for 5 years discounted at 6.6% =
..68M/1.066 + .68M/1.066^2 +.... = 2,818,251
Thus the PV of the project = 10.47M + 2818251 = 13,288,251
Hope this helps.
> -----Original Message-----
> From: Josh Metzger [SMTP:josh.metzger@ocas.com]
> Sent: Tuesday, October 19, 1999 11:11
> To: studygroup5B@lists.casact.org
> Subject: Depreciation and PV(tax shields)
>
> Take this example:
>
> Assume XYZ Corp. is considering a $10M project that they will depreciate
> for tax purposes over a five year period. They expect $3.5M of cash
> income
> each year, pay taxes at a rate of 34%, have an all-equity cost of capital
> of 20% and the risk free rate is 10%. Calculate the value of this project
> assuming that the tax shields from depreciation are risk free and that the
> firm is all equity financed.
>
> The answer explanation says that the depreciation tax shields should be
> discounted at the after-tax rate of 10% * (1-.34) = 6.6%.
>
> But aren't we calculating how much tax is saved and should therefore use
> the tax rate of 34%, not 1-34%?
>
> I do not understand B&M's explanation on page 539. It does not seem
> intuitive to me. I am looking more for intuitive reasoning here rather
> than recited formulas. Can anyone explain this in a simple way that makes
> sense?
>
> Josh
>