risk and probability question

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mlh97

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lets say there are three possible scenarios, each with its respective liklihood of occuring:

scenario a - 5%
scenario b - 30%
scenario c - 65%

under scenario a, which would happen tomorrow, you lose $10.
under scenario b, which would happen in one year, you gain $20.
under scenario c, which would happen in two years, you gain $40.

and lets say, for the sake of argument, that the amount of gain or loss is 100% certain.

now lets say this is a company and you wanted to know the probability-weighted present value of these outcomes right now. to get the present value of scenarios a and b, would you discount them at the wacc (or cost of equity, etc) or would you discount them at a risk-free rate?

in other words, if a company has a 65% chance of having a gain of $40 in two years, what discount rate would you use to bring that $40 back to time zero?

on one hand, i could see using the cost of capital because is how you would normally discount a future cash flow. but on the other hand, is the risk the cash flow may not occur (the reason the cost of capital would be higher than the risk-free rate) captured in the fact that there is only a 65% chance it will occur?

thanks.
 
if gain or loss is 100% certain, then use the risk free rate. The probabilities that you gave already account for the "risk" (which otherwise might be in the cost of capital).
 
1). The prob. of the gain is not 100% -- not risk free
2). Presumably the company has to stay operational for two years if its going to have any chance of getting the gain. As long as it operates, the company is risking is assets.

WACC is more appropriate.

Just what I think..
 
RFR; no doubt, that's what equity options use.
 
WACC is a hack for when one is too lazy to work out actual probabilities (which is most of the time) and thus expected cash flows. Your finance professor will rail about this given the chance.

Say you have a firm with 10% wacc who's launching a large product in two years, which makes $10m with 60% likelihood or $0. Rather than trying to skew the WACC to take into account the risk, it's *much, much* better to apply the probability directly to the cash flow. Thus model it as a $6m cashflow, which you discount normally. "Normally" here usually means "at the company's wacc for similar (already-launched) projects".

Note that "normally" never means risk-free rate, because the company is facing other regular business risks (labor strike, general economy, etc.) in addition to the likelihood of the product's being a success or failure.

The problem with fiddling with the wacc instead of calculating the expected cash flows is that wacc compounds, and it's applied to other cash flows (of presumably less risk than that exhibited by the new product line).
 
1) Discount all scenario payouts to the present, using the risk free rate (could be the spot rate for those terms).

2) Use a probability weighted average of those discounted scenarios.

That's your answer.

If the outcomes are 100% certain for that specific scenario, then you use the RFR. For example, you could enter an agreement to pay these outcomes, and lend the discounted amounts to the government today, and have those sums available at payout time.

If there is additional uncertainty in those payouts, then you can do one of two things 1) get the probability-weighted average outcome for each scenario and use that, or 2) add a risk premium to the RFR. Use WACC if the expected payout comes from company operations, use R on common equity if the payout is expected from after-tax earnings.
 
> and lets say, for the sake of argument, that the amount of gain or loss is 100% certain.

> now lets say this is a company

Well, which is it? If it's a company then no cash flows can be more certain than the likelihood that the firm remains solvent, so discounting must happen at the cost of debt _minimum_, but for most problems like this you'd use wacc.

bchadwick's and MFEs' exhortations to use RFR only apply if the "company" is sovereign, e.g. Federal government. For any normal firm however no cash flow is discountable at rfr. (Even e.g. taxes require a solvent firm to be paid.)
 
so, for those who said rfr, would it make a difference if i didn't say the amount of the gain was less than 100% certain? does the uncertainty of it occuring cover the uncertainty of the amount? or, do you have to look at them each individually?
 
Don't you get it? you put the certainty in the question as probability. If the probability is wrong, then re-do the probabilty!?! DON'T SCREW WITH THE DISCOUNT RATE?!?! Isn't this intuitive?
 
sorry. didn't mean to hurt your feelings. i'll be more sensitive next time.
 
This is a waccy discussion.

Darien - In the real world, nobody ever gives you probabilities like the ones that appear in the question. Remember that the wacc is only a decent discount rate for projects with similar risk to the company's current projects.

Virgin - "you put the certainty in the question as probability" Say what? The cash-flows are certain given the scenario. It's this certainty that means that they are discounted using the RFR. The wacc is used to discount uncertain, expected cash flows.
 
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