(Unleveraged returns) You plan

(Unleveraged returns) You plan to invest $10,000 in a security,borrowing $6,000 of the cost from a friend, thus putting up $4,000of your own money. The cost of debt is 12%, and there are no taxes.With this arrangement, you expect a return of 20% on your equityinvestment. What would your return be without the leverage? Thatis, what would your return be if the entire $10,000 was your ownmoney?



Total investment = $10,000

Of total,

Debt = $6,000

Equity = $4,000

Cost of debt = 12%

Tax rate = 0%

Return on investment = 20%

As it is mentioned that the investment contains both debt andequity, the return on the investment can be considered as weightedaverage cost of capital (WACC)

Formula for WACC, given debt and equity investments is as shownbelow


    RE = cost of equity

    RD = cost of debt

    E = amount of equity

    D = amount of debt

    T = E + D

    E/V = percentage of financing that isequity

    D/V = percentage of financing that isdebt

    t = tax rate

Substituting the values in the above equation, let us find theunknown, which is cost of equity RE

Given no taxes, hence t= 0%

0.2 = ($4,000/$10,000) * RE + ($6,000/$10,000) *0.12

0.2 * 10,000 = 4,000 RE + 6,000 * 0.12

2,000 = 4,000 RE + 720

1,280 = 4,000 RE

RE = 0.32

i.e, cost of equity = 32%

Now, if the person finances the total investment through his ownmoney, the equation will contain only the equity portion, debtportion will be zero

Hence WACC = E/ T * RE + 0

E= T = $10,000

Therefore, return will be RE = 32%

Hence, if the person is financing the total investment throughhis/her own money, the expected retuirn will be 32%.

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