Two companies are identical in all respects except that X Ltd., has debt of Rs 5,00,000 borrowed at the rate of 12% whereas Y Ltd., has no debt in its capital structure. The total assets of both the companies amount to Rs 15,00,000 on which the companies have earnings of 20%. You are required to do the following:
(i) Calculate value of companies and k0 using NI approach taking ke as 18%.
(ii) Calculate value of companies and ke using NOI approach taking k0 as 18%. (iii) Compare the results and comment on the difference of the two approaches.
The correct answer and explanation is :
Explanation
In this problem, we analyze two companies, X Ltd. (leveraged) and Y Ltd. (unleveraged), under the Net Income (NI) Approach and Net Operating Income (NOI) Approach to determine their value and cost of capital.
(i) NI Approach
The NI approach assumes that the cost of equity (ke) remains constant and that the firm can increase its value by using cheaper debt financing.
- X Ltd. (Leveraged)
- Interest on debt = ( 500,000 \times 12\% = 60,000 )
- Net income = ( (15,00,000 \times 20\%) – 60,000 = 240,000 )
- Value of equity = ( 240,000 / 18\% = 1,333,333 )
- Value of firm = Equity + Debt = ( 1,333,333 + 500,000 = 1,833,333 )
- Overall cost of capital ( k_0 ) = ( 300,000 / 1,833,333 = 16.36\% )
- Y Ltd. (Unleveraged)
- Net income = ( 15,00,000 \times 20\% = 300,000 )
- Value of firm = ( 300,000 / 18\% = 1,666,667 )
- Overall cost of capital ( k_0 = 18\% )
🔹 Conclusion (NI Approach):
- X Ltd. (with debt) has a higher firm value than Y Ltd. due to lower financing costs.
- The cost of capital ( k_0 ) decreases due to cheaper debt financing.
(ii) NOI Approach
The NOI approach assumes that the firm’s overall cost of capital (k0) remains constant, irrespective of capital structure.
- Firm value for both X Ltd. and Y Ltd.:
- ( Value = EBIT / k_0 = 300,000 / 18\% = 1,666,667 )
- Cost of Equity (ke) for X Ltd.:
- ( ke = k_0 + (k_0 – Interest Rate) \times (Debt / Equity) )
- ( ke = 18\% + (18\% – 12\%) \times (500,000 / 1,166,667) = 20.57\% )
🔹 Conclusion (NOI Approach):
- The firm’s value remains the same, regardless of capital structure.
- Higher debt increases the cost of equity due to increased financial risk.
(iii) Comparison and Comments
- Under the NI approach, X Ltd. (leveraged) has a higher firm value because it benefits from cheaper debt.
- Under the NOI approach, the firm’s value remains unchanged, as it assumes an increase in the cost of equity offsets the benefit of debt financing.
- Key Difference: The NI approach supports leverage to increase firm value, while the NOI approach states that leverage does not impact the overall value.
Thus, Modigliani & Miller’s irrelevance theorem aligns more with the NOI approach, stating that in a perfect market, capital structure does not impact firm value.