•Suppose that you are a financial investor about to take over a food retailing company, how should you estimate the discount rate you use to value it?
The rate should be the rate for a food retailer. You get a sample of food retailers and estimate their costs of capital of asset betas and average them.
•Suppose that you are a clothing retailer about to enter the food retailing market, how should you estimate the discount rate?
The same as the previous question.
•Suppose that you have three types of projects:
–Cost savings
–Expansion
–New growth
What mistakes will you make if you use your WACC for all of them?
You will underinvest in low risk cost saving and overinvest in high risk new growth.
•Suppose that you have two divisions of your company:
–A water utility
–An engineering division
Suppose you allocate capital on the basis of the same required rate of return for each of them. What mistake will you make?
You will allocate too much capital to the engineering division and too little to the utility.
•Suppose that you have a retailing company and you are considering selling some property and leasing it back. What mistake will you make if you use your WACC to assess this transaction?
You should use the required return on a property lease. This will be much lower than your WACC. You will think that the present value of the lease commitments you have made is lower than it actually is and you will think the deal is better than it actually is.
•Suppose that you are about to enter a financial lease for some equipment. The lease is a 10 year fixed rate lease. What rate should you use to evaluate it?
The rate on a 10 year fixed rate secured loan. This is the rate that reflects a level of risk close to the transaction you are evaluating.
•Suppose that you are a retailer with a cost of capital of 10% and you currently own all your property. Your EV is $1 billion. Suppose that you sell and leaseback $300 million of property. The required return on property is 7%. What happens to the required return on your operating flows that are now net of the lease payments?
The total value of $1 billion is made up of 30% of an asset with a required return of 7% and 70% of an asset with a required return of X. So:
.3*7% + .7*X = 10%
X=11.3%
•
Suppose that you have two mines. One has expected operating free cash flow of $100 per annum in perpetuity. It has an asset beta of 0.7, and the riskless interest rate is 5%. The other mine is identical in every way, but it has fixed costs that are $50 higher. What is the asset beta of the second mine?
The second mine is like the first mine with an extra $50 of fixed operating costs. If we assume that the market risk premium is 5%, then the discount rate for the first mine is 5%+0.7*5%=8.5%. So the value of the first mine is 100/0.085=1,176. If we assume that the extra fixed costs have a beta of zero, then their value is 50/0.05=1,000. So the value of the second mine is 1,176-1,000=176. The cash flow per annum from this mine is 50. So its discount rate is 50/176=28%. This corresponds to an asset beta of (28-5)/5 = 4.6.
We can see how the asset betas work out. If we think of the first mine as 1,000 of fixed cash flows with a beta of 0 and 176 of leveraged cash flows with a beta of 4.6, then we get that the beta of the first mine is:
(1,000/1,176)*0 + (176/1,176)*4.6 = 0.7
Note that we need to be able to use the present value of the first mine to do this calculation, as the calculation works with market values (ie present values) and not book values.
•Suppose that you have a project with operating free cash flow of $100 per annum in perpetuity. The riskless interest rate is 5%. The asset beta is 0.6. The project costs $600 to build and you are going to borrow $300 of the construction costs. What is the equity beta of the project?
This is similar to the previous question, but the leverage here is financial rather than operating leverage. The discount rate for the project is 5%+0.6*5%= 8%. The enterprise value of the project is 100/0.08=1,250.
The net debt of the project is 300, which we will assume has zero beta. The equity is worth (1,250-300)=950. The equity beta of the project must satisfy:
(300/1,250)*0+(950/1,250)*equity beta = 0.6
Solving this gives an equity beta of 0.79.
We can see that this is the right number by checking that it gives the right equity value. The equity discount rate is 5%+0.79*5%=8.95%. The equity cash flow is 100-0.05*300=85. If we discount a perpetuity of 85 at a discount rate of 8.95%, we get 85/0.0895=950, which is the value of the equity.
Here, again, the calculations work as long as we remember to use market values (ie present values) and not book values.