Question

Union Street Records is considering a new capital structure. The CFO has prepared a list of options:

Option	Debt-to-capital ratio	Bond rating	Interest rate
1	0	AA	0.03
2	0.25	BBB	0.04
3	0.5	B	0.06
4	0.75	C	0.08

The company currently has a debt-to-capital ratio of 0.75 (option 4) and an equity beta of 1.7. The tax rate is 34%.

The risk-free rate is 2% and the expected equity market risk premium (MRP) is 6%.

unlevered beta: 0.57, levered beta for option 2 0.696

Part 3: Find the cost of equity for each option. What is the cost of equity for option 2 (debt-to-capital ratio of 0.25)?

Part 4: Find the WACC for each option. What is the WACC for option 3 (debt-to-capital ratio of 0.5)?

Part 5: What is the WACC at the optimal capital structure (note: it is one of the four values found in part 4)?

Answer 1

The company currently has a debt-to-capital ratio of 0.75 (option 4) and an equity beta of 1.7. The tax rate is 34%.

Levered beta = 1.4; D / (D + E) = 0.75; Hence D / E = 0.75 / 0.25 = 3

Unlevered beta = Levered beta / [1 + (1 - T) x D/E] = 1.7 / [1 + (1 - 34%) x 3] = 0.5705

We need to relever the beta using the new capital structure.

Levered beta = Unlevered beta x [1 + (1 - T) x D/E] = 0.5705 x [1 + (1 - 34%) x D/E] = 0.5705 x (1 + 0.66 x D/E)

Cost of equity, Ke = Rf + Levered beta x MRP = 2% + levered Beta x 6%

WACC = Wd x Kd x (1 - T) + We x Ke

Please see the table below. All financials are in $. Please see the second row to understand the mathematics. The cells colored in yellow contain your answer. They have been calculated using the formula above:

Option	Wd = D/(D + E)	We	D/E	Bond rating	Interest rate	Unlevered Beta	Tax rate	Levered Beta	Cost of equity	WACC
		1 - Wd	Wd / We		Kd	Bu	T	B = Bu x [1 + (1 - T) x D/E]	Ke = 2% + B x 6%	Wd x Kd x (1 - T) + We x Ke
1	-	1.00	0.00	AA	3.00%	0.5705	34%	0.5705	5.42%	5.42%
2	0.25	0.75	0.33	BBB	4.00%	0.5705	34%	0.6960	6.18%	5.29%
3	0.50	0.50	1.00	B	6.00%	0.5705	34%	0.9470	7.68%	5.82%
4	0.75	0.25	3.00	C	8.00%	0.5705	34%	1.7000	12.20%	7.01%

Hence, your answers are:

Part 3: Find the cost of equity for each option. What is the cost of equity for option 2 (debt-to-capital ratio of 0.25)?

the cost of equity for each option is available in the second last column of the table above. Cost of equity for option 2 = 6.18%

Part 4: Find the WACC for each option. What is the WACC for option 3 (debt-to-capital ratio of 0.5)?

the WACC for each option is available in the last column of the table above. WACC for option 3 = 5.82%

Part 5: What is the WACC at the optimal capital structure (note: it is one of the four values found in part 4)?

The least WACC that is 5.29%