Question

(Unleveraged returns) You plan to invest $10,000 in a security, borrowing $6,000 of the cost from a friend, thus putting up $4,000 of 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 equity investment. What would your return be without the leverage? That is, what would your return be if the entire $10,000 was your own money?

Answer 1

Given

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 and equity, the return on the investment can be considered as weighted average cost of capital (WACC)

Formula for WACC, given debt and equity investments is as shown below

Here

    R_E = cost of equity

    R_D = cost of debt

    E = amount of equity

    D = amount of debt

    T = E + D

    E/V = percentage of financing that is equity

    D/V = percentage of financing that is debt

    t = tax rate

Substituting the values in the above equation, let us find the unknown, which is cost of equity R_E

Given no taxes, hence t= 0%

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

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

2,000 = 4,000 R_E + 720

1,280 = 4,000 R_E

R_E = 0.32

i.e, cost of equity = 32%

Now, if the person finances the total investment through his own money, the equation will contain only the equity portion, debt portion will be zero

Hence WACC = E/ T * R_E + 0

E= T = $10,000

Therefore, return will be R_E = 32%

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