Question

You are an entrepreneur who wants to start a new firm that specializes in electric cars. Your plan is to fund this new business by offering a sizable portion of the equity ownership in this new firm. In order to correctly price this equity, you will need to calculate the value of your business. This will involve determining the proper discount rate for your expected electric car cash flows. Fortunately, there is one publicly traded electric car company (symbol: BOLT) you can use for comparison. You run a regression of BOLT excess stock returns on excess market returns and obtain an equity beta of 2.4 for BOLT. Additional research informs you that the market capitalization (i.e. market value of equity) of BOLT is $300M, the debt value of BOLT is $200M (which was issued at par and will remain a $200M in perpetuity), and the debt beta for BOLT is zero. a) What is the beta of assets for BOLT, according to the weighted beta equation? Your business partner informs you that the beta of assets you calculated in

(a) is not quite the beta we should be using to calculate the expected return (discount rate) for our electric car cash flows. The reason is that BOLT is a levered firm, implying that the beta of assets for BOLT incorporates both its electric car cash flows and tax shield cash flows. Our firm does not have tax shield cash flows because it has no debt.
(b) Assume that the operating assets (OA) of BOLT equals the total assets (A) of BOLT minus the value of their tax shield (TS). Also assume a tax rate of 40 percent, and that the beta of the BOLT tax shield equals zero. What is the beta of operating assets for BOLT? You will first need to calculate the value of the BOLT tax shield, and then use the following equation to find the beta of operating assets
(OA): VOA VTS BA -Boat -BTS VoA + VTS VoA + VTS
(c) Because your firm is all-equity, the proper discount rate to apply to your electric car cash flows is the expected return on operating assets for BOLT. Assume a risk-free rate of 3 percent and a market risk premium of 5 percent. Starting next year, your firm will produce an annual perpetual free cash flow of $20M with 25% probability, $40M with 50% probability, or $60M with 25% probability. What is the value of your firm?

Answer 1

Answer is explained in the explanation section below.

Step-by-step explanation:

a. Beta of assets = Be*Ve/(Ve+(1-tax)Vd) + Bd*Vd/(Ve+(1-tax)Vd)

Be = 2.4

Ve = 300

Vd = 200

Tax rate = 40% = 0.4

Plugging in the values in the formula.

Beta of Assets = 2.4*300/(300+(1-0.4)*200)

Beta of Assets = 1.714

b.

Operating Assets = Total assets - value of tax shield

Voa = 1000 - 40%*200 = 920

Ba = Voa*Boa/1000

Boa = Ba*1000/Voa = 1.714*1000/920

Boa = 1.863

c.

Beta of company = beta of operating assets of listed peer,

thus Beta = Boa = 1.863

Calculating cost of equity/ expected return on equity

Ce = Rf + Beta*(MRP)

Ce = 3%+ 1.863*5% = 12.315%

Expected cash flow = 20*25%+40*50%+60*25%

Expected cash flow = 40

Since the cash flow is perpetual, value of cash flow today = 40/12.315% =324.807

If 40% is sold at above valuation, cash you will get = 324.807*0.4 = 129.922 million dollars.