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#### sprintist

##### Senior Member
Assume that a firm has \$1,000,000 worth of assets, which are funded by \$600,000 of debt and \$400,000 of equity. Assume the return the firm can earn on its assets is 10% p.a. Calculate the available rate of return to equity holders of the firm.

#### night86mare

##### Deregistered
is that all the information you have?

a) tax rate
b) interest rates on the debt

##### Member
Have no real clue but as gotta wait up for someone, let me be helpless and try some geek speak.....;p So potential functions you could use in Excel and will need to calculate a schedule as well.....

IRR
XIRR
MIRR

#### kcuf2

##### Senior Member
Assume that a firm has \$1,000,000 worth of assets, which are funded by \$600,000 of debt and \$400,000 of equity. Assume the return the firm can earn on its assets is 10% p.a. Calculate the available rate of return to equity holders of the firm.
10% return on assets of \$1,000,000 = \$100,000

Notice here that the rate of return to equity to equity holders is actually 25% instead of the 10% return on assets. This is because of leverage used in this instance i.e. the equity holders took up debt to invest more and earn more returns.

#### night86mare

##### Deregistered
hrm, but don't firms pay off the interest on their debts first, before passing on returns to equity holders?

that is the reason why i asked for that additional information, along with tax rates.

unless of course, you assume that debt is interest-free, and there are no taxes on revenue..

#### eyes

##### New Member
Haha... CS has become tution centre! :bsmilie:

#### sprintist

##### Senior Member
10% return on assets of \$1,000,000 = \$100,000

Notice here that the rate of return to equity to equity holders is actually 25% instead of the 10% return on assets. This is because of leverage used in this instance i.e. the equity holders took up debt to invest more and earn more returns.
apparently the answer used debt to equity ratio which i can't figure out why, hence it wasn't as straightforward as being 25%

#### confession

##### Deregistered
Been a few years since I last revisited this. Hated Corporate Finance as wayyyyyyy too many formulas.

But something is missing.

ROE is normally calculated based on Net Income/Total equity. As with ROA is Net Income/Total Assets.

In this case, I will use the DuPont: ROE=ROA x Equity Mulitiplier = ROA x (1+Debt-Equity Ratio).

Unless Sprintist, you are asking about MM theory, then it is a whole new ball game.

#### sprintist

##### Senior Member
no wonder im into engineering... :bsmilie:
and no wonder i can't make big bucks as well

Been a few years since I last revisited this. Hated Corporate Finance as wayyyyyyy too many formulas.

But something is missing.

ROE is normally calculated based on Net Income/Total equity. As with ROA is Net Income/Total Assets.

In this case, I will use the DuPont: ROE=ROA x Equity Mulitiplier = ROA x (1+Debt-Equity Ratio).

Unless Sprintist, you are asking about MM theory, then it is a whole new ball game.
nope its not exactly the MM theory, its just about weight average cost of capital, WACC. in this the return on asset is the WACC.

cos this isn't return on equity but rather, the rate of return on equity

#### confession

##### Deregistered

nope its not exactly the MM theory, its just about weight average cost of capital, WACC. in this the return on asset is the WACC.

cos this isn't return on equity but rather, the rate of return on equity
Well, then in that case, the DuPont analysis will be the formula to use.

*I seriously hated Financial Ratios when studying corp fin.*

#### sammy888

##### Senior Member
Have no real clue but as gotta wait up for someone, let me be helpless and try some geek speak.....;p So potential functions you could use in Excel and will need to calculate a schedule as well.....

IRR
XIRR
MIRR

You helping to put out the flame or you throwing in fuel to bring the fire up? heheh :devil:

#### nemesis32

##### Senior Member
hrm, but don't firms pay off the interest on their debts first, before passing on returns to equity holders?

that is the reason why i asked for that additional information, along with tax rates.

unless of course, you assume that debt is interest-free, and there are no taxes on revenue..
You can probably assume the tax and interest already taken care in the computation for RoA so no diff. kcf2's answer shd be correct

##### Member
You helping to put out the flame or you throwing in fuel to bring the fire up? heheh :devil:
*slaps Sammy*

Anyway so is the firm sure that its assets are worth \$1mill. When was the evaluation done? ;p

#### Leong23

##### Senior Member
no wonder im into engineering... :bsmilie:
and no wonder i can't make big bucks as well
LOL...............same here. :bsmilie:

#### sprintist

##### Senior Member
You can probably assume the tax and interest already taken care in the computation for RoA so no diff. kcf2's answer shd be correct
that was what i would have done too but the answer used the debt/equity ratio.

i'll now show it here maybe someone can help explain why

Debt/Equity ratio = \$600,000/\$400,000 = 1.5
Therefore, given WACC is 10%, it must be that the cost of debt is: WACC/(D/E ratio), and the cost of equity must be: WACC x (D/E ratio). Therefore:
cost of debt = 0.10/1.5 = 0.0666 = 6.66%
cost of equity = 0.10 x 1.5 = 0.15 = 15% (available rate of return to equity holders).

#### whizzard

##### New Member
that was what i would have done too but the answer used the debt/equity ratio.

i'll now show it here maybe someone can help explain why

Debt/Equity ratio = \$600,000/\$400,000 = 1.5
Therefore, given WACC is 10%, it must be that the cost of debt is: WACC/(D/E ratio), and the cost of equity must be: WACC x (D/E ratio). Therefore:
cost of debt = 0.10/1.5 = 0.0666 = 6.66%
cost of equity = 0.10 x 1.5 = 0.15 = 15% (available rate of return to equity holders).
This is a question on how to calculate WACC. Based on the clues given in the question:-

(1) Assets = \$1,000,000 which is financed by:-
Debt = \$600,000
Equity = \$400,000

(2) Return on assets = \$100,000 (which is another word for saying return on total capital)
Capital as defined in financial terms (and not in layman's language) means Debt + Equity

(3) In other words, the question tells you that your WACC is 10%.

(4) You are now required to solve for the return on equity (or the question could also ask you to solve for the return on debt).

The formula for WACC is:-

WACC = [cost of debt x (debt/(debt + equity))] + [cost of equity x (equity/(debt + equity))]

Therefore,

Cost of Equity = WACC / (equity/debt) = 10% / 0.6667 = 15% and

Cost of Debt = WACC / (debt/equity) = 10% / 1.5 = 6.6667%

Total return = (return on debt x debt) + (return on equity x equity)
= (6.6667% x \$600,000) + (15% x \$400,000)
= \$100,000

#### sprintist

##### Senior Member
This is a question on how to calculate WACC. Based on the clues given in the question:-

(1) Assets = \$1,000,000 which is financed by:-
Debt = \$600,000
Equity = \$400,000

(2) Return on assets = \$100,000 (which is another word for saying return on total capital)
Capital as defined in financial terms (and not in layman's language) means Debt + Equity

(3) In other words, the question tells you that your WACC is 10%.

(4) You are now required to solve for the return on equity (or the question could also ask you to solve for the return on debt).

The formula for WACC is:-

WACC = [cost of debt x (debt/(debt + equity))] + [cost of equity x (equity/(debt + equity))]

Therefore,

Cost of Equity = WACC / (equity/debt) = 10% / 0.6667 = 15% and

Cost of Debt = WACC / (debt/equity) = 10% / 1.5 = 6.6667%

Total return = (return on debt x debt) + (return on equity x equity)
= (6.6667% x \$600,000) + (15% x \$400,000)
= \$100,000

pardon me but i have been trying to rearrange the formula since yesterday but i couldnt derive to simply Cost of Equity = WACC / (equity/debt)

the furthest i could get was Cost of Equity = [ WACC.(debt+equity) - cost of debt.Debt)] / [Equity]

that was what made me stuck..am i missing out any assumptions? hope you can show me the derivation if possible. Thanks!