Question 3 OR (a)

Optimum capital structure under the traditional approach

6 marks

Time to write: About 12 minutes
Topic: Theories of capital structure

Question

Question 3 OR (a) · 6 marks

You are given the following information.

Cost of Debt (%)	Cost of Equity	Proportion of Debt
16.5	19.5	0
17.4	21	0.2
18	22.5	0.3
19.5	24	0.4
22.5	27	0.5
27	30	0.6

Assuming a 30% corporate tax rate, determine the optimum capital structure using the Traditional Approach.

Reworded from the university paper: names and figures differ, the task is the same. The original paper belongs to the University of Delhi. See DU's question bank.

Before you write

Read off the question and its marks

12 minfor 6 marks

Read from the question

Assuming a 30% corporate tax rate,…The paper fixes this: use it as given, and say so in your answer.
determineFormula first, then the working, then the answer with its unit (₹, %, units).

What the paper leaves open

The costs of debt in the table are read as before tax; the 30% tax rate is applied to them.

Write it in this order

Read the data; note exactly what is asked 1 min
1 After-tax cost of debt 1 mark 2 min
2 Overall cost of capital at each level of debt 4 marks 7 min
3 Optimum structure identified 1 mark 1 min
Check: arithmetic, units (₹, %), final answer underlined 1 min

123

Short on time? Step 2 carries 4 of the 6 marks: guard its minutes.

Try it first. About 12 minutes for 6 marks. Write it out, then open the solution.

Solution

Hover or tap a marked figure, like 72,000, to see how it is made and where else it appears.

Under the traditional approach, a moderate use of cheaper debt lowers the overall cost of capital (ko) at first; beyond some point the rising cost of equity, and later of debt, outweighs that advantage and ko rises. The optimum capital structure is where ko is lowest.

The costs of debt are before tax (paper note), so the after-tax cost is kd × (1 − 0.30). Then ko = after-tax kd × proportion of debt + ke × proportion of equity.

Proportion of debt	kd (before tax) %	kd after tax %	ke %	Proportion of equity	ko %
0.0	16.5	11.55	19.5	1.0	19.500
0.2	17.4	12.18	21.0	0.8	2.436 + 16.800 = 19.236
0.3	18.0	12.60	22.5	0.7	3.780 + 15.750 = 19.530
0.4	19.5	13.65	24.0	0.6	5.460 + 14.400 = 19.860
0.5	22.5	15.75	27.0	0.5	7.875 + 13.500 = 21.375
0.6	27.0	18.90	30.0	0.4	11.340 + 12.000 = 23.340

Optimum capital structure: 20% debt and 80% equity, where the overall cost of capital is lowest at 19.236%. Up to that point the saving from cheaper debt exceeds the rise in ke; beyond it the rising costs of equity and debt push ko up, as the traditional approach predicts.

Where the 6 marks sit

#	Component	Marks
1	After-tax cost of debt	1
2	Overall cost of capital at each level of debt	4
3	Optimum structure identified	1
	Total	6

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