Question

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Will a Balance Sheet Statement done quarterly as of 2019-12-31 have the same numbers as a...

  1. Will a Balance Sheet Statement done quarterly as of 2019-12-31 have the same numbers as a Balance Sheet Statement done annually as of 2019-12-31? Explain.
  1. What are the weights for ROA in the following equation?

ROA = ROE ∗equity/assets + (cost of debt)∗debt/assets

Explain why ROE>ROA>cost of debt.

  1. For time value of money problems, if the interest rate increase, will the Present Value increase? If the interest rate increase, will the Future Value increase? Explain.

Solutions

Expert Solution

(a): YES. This is because balance sheet is not prepared for a period but is prepared as for a particular date. All items in balance sheet are stock measures and not flow measures and hence pertains to a particular point in time. The point in time here is 2019-12-31 and so both the balance sheet statement will have the same numbers.

(b): ROA = (net income+interest expenses)/assets.

We know that ROE is net income/equity and cost of debt * debt = interest expenses.

Thus ROE ∗equity/assets + (cost of debt)∗debt/assets = (net income/equity * equity/assets) + (interest expenses/assets)

= (net income+interest expenses)/assets

ROE > ROA due to the presence of financial leverage. When there is no debt and the company is financially unlevered then shareholder’s equity and assets will be same and this will lead to same values for ROE and ROA. However when financial leverage is used and debt is present then total assets will exceed equity causing ROA to fall.

ROA > cost of debt because net income is always higher than the interest expenses that is paid on debt. Cost of debt is a part of equation used to compute ROA and so a fraction of cost of debt is a part of ROA.

(c ): Present Value = future value/(1+r)^n. Here r is the interest rate and n is the year. Now if the interest rate increases then the value of denominator will increase in the above equation and this will lead to a fall in the present value. Thus if interest rate increases then the present value will not increase, rather it will fall.

Future value = Present value * (1+r)^n. Now when the interest rate increases then the multiplier i.e. (1+r)^n will increase and this will cause the future value to increase as well. Thus if interest rate increases then future value will increase.

jeff jeffy answered 2 years ago
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