Cost of Capital. What Number Goes in the Denominator?. Discount Rate (a.k.a. Cost of Capital, or the Interest Rate). Rate at which you can move money of similar risk through time.
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What Number Goes in the Denominator?
During the middle ages, In a previous life, you ran the Tail of Fairies Caviar Import Company. Among your best customers are the besieged aristocrats in the great and wonderful town of Nottingham.
Alas, in the forests lies the evil communist Robin Hood! As a result, there is a 20% chance any shipment of yours will be intercepted by him and lost.
It takes you four months to transport caviar from Russia to Nottingham. Assume you can purchase the caviar for £10. Shipping, whether everything goes well or not comes to £5.
In Nottingham the sale price of the caviar is, on average, £25, but the actual sales price depends on how well the local economy is doing. Thus, the price has a market beta of 1.5. Assume the annual risk free rate (rf) equals 2% and the market premium (rm-rf) for the same period equals 10%. Should you proceed to ship caviar to Nottingham?
Notice that the chance Robin Hood intercepts your shipment goes into the NUMERATOR. It reduces your expected payoff. Remember the numerator in the present value equation contains the expected cash flows from the project.
I am assuming future debt levels are a <blank> and I want to make my life <blank>:
Just About Impossible
WACC is defined by:
Marginal Industries currently provides outfits for NFL backup players. It is considering the initiation of marketing project 5 at a cost of 1 million. The firm hopes that project 5 will increase sales by convincing the NCAA to purchase its clothing line. Assume sales to the NCAA will have the same level of market risk as the firm’s current business.
(1-TC)(Revenues-Costs) = .6(2) = 1.2.
The formula for beta is identical to the return formula except that the r’s are now replaced with β’s.
These are the equations for delevering absent taxes!
rA = .05+.8(.15-.05) = .13.
PV(Debt Tax Shield) = .24/.05 = 4.8.
PV(All Equity Cash Flows) + PV(Debt Tax Shield) =
10 + 4.8 = 14.8.
Today you know for sure what next period’s tax shield will be. Therefore you get its present value by discounting at the risk free rate of .05, assuming its debt is risk free.
PV(Year 1 tax shield) = .0348/1.05.
PV (tax shields) =
.0348×1.012/(1.05 × 1.21182) + …
PV(All Equity Financed) =
−1000000 + 240000/(.17-.02) = 600,000.
PV(Year 1 Tax Shield) = 14,000/1.05.
PV(Year 2 Tax Shield) = 14,000/1.052.
PV(Year 3 Tax Shield) = (14000×1.022)/(1.172×1.05).
PV(Year 4 Tax Shield) = (14000×1.022)/(1.172×1.052).
To go from line one of the above equation to line two note that 1.316 = (1.17/1.02)2.
Filling this in with the information we have:
which implies rE = 10.72, that is NOT a percent. It is 1,072% due to the very high debt equity ratio!