Question

The Oko-Cocoa Corporation's equity has a beta of 1.4. Its debt has a beta of 0.2. Its debt/equity (D/E) ratio is 0.3. The Johnson Corporation's equity has a beta of 2. The company has zero beta debt, and its debt/equity ratio is 0.5. The risk free rate is 8%, and the expected return on the market portfolio is 19%. There are no taxes.

(a) The Johnson Corporation is thinking of investing in the same line of business that OkaCocoa is engaged in. What discount rate should it use?

(b) Now suppose the Johnson Corporation has decided to invest in projects of this type. These projects now constitute 10% of the overall value of the Johnson Corporation. Given that its debt/equity ratio and the beta of its debt remain unchanged, what will the beta of Johnson's equity be now?

Answer 1

(a) Discount Rate = Rf + Beta * (Rm - Rf) ...(1) {CAPM}

If Johnson Corp wants to invest in same line of business as OkaCocoa, then it should use beta values of OkaCocoa.

Beta_NewProject = {[D_Oka/(D_Oka+E_Oka) ] * Beta_DebtOka} + {[E_Oka/(D_Oka+E_Oka) ] * Beta_EquityOka}

= [3/13 * 0.2] + [10/13 * 1.4] = 1.123076923 ...(2)

Rf=6% ...(3)

Rm=19% ...(4)

From (1), (2), (3), (4):

DiscountRateNewProject = Rf + Beta * (Rm - Rf) = 8% + 1.123076923 (19% - 8%) = 20.353846%

(b)

Beta_NewProject = 1.23076923 ...(2) {from part a}

Beta_{InitialJohnson} = {[D_Johnson/(D_Johnson+E_Johnson) ] * Beta_DebtJohnson} + {[E_Johnson/(D_Johnson+E_Johnson) ] * Beta_{EquityJohnson}}

= [1/3 * 0] + [2/3 * 2] = 1.333333 ...(5)

{from (2), (5), (6), & 90%-10% given distribution}

Beta_NowJohnson = 10%*Beta_NewProject + 90%*Beta_{InitialJohnson} = 10%*1.123076923 + 90%*1.333333

=1.312307662 ...(6)

Beta_{NewDebtJohnson}=0 ...(7) {given}

Beta_NowJohnson = (1/3) Beta_{NewDebtJohnson} + (2/3) Beta_{NewEquityJohnson .}..(8)

From (6), (7), (8):

1.312307662 = (1/3) * 0+ (2/3) Beta_{NewEquityJohnson .}

Beta_{NewEquityJohnson} = 1.968461493