Question

Data Given:

				2017	2018	2019	2020
Net sales				$500	$600	$700	$760
Selling and administrative expense				60	70	80	90
Interest				30	40	45	60
Tax rate of ACC before the merger						30%
Tax rate after merger						35%
Cost of goods sold as a % of sales						65%
Debt ratio (percent financed with debt) before the merger						30%
Cost of debt before merger						9%
Debt ratio (percent financed with debt) after the merger						40%
Cost of debt after merger						10%
Beta of ACC						1.40
Risk-free rate						7%
Market risk premium						6.5%
Terminal growth rate of free cash flow						6.0%
Pre-merger debt (in thousands)						$      400

1. What is the levered cost of equity at old capital structure?

2. What is the unlevered cost of equity?

Before we can proceed with this problem, we must generate pro forma income statements for ACC's operations after the proposed merger so we can calculate free cash flow and interest tax shields.

Fill in the chart

			2017	2018	2019	2020	2021
Sales
Cost of Goods Sold (incl. depreciation)
Gross Profit
Selling/admin. costs
EBIT
Interest
EBT
Taxes
Net Income
EBIT
NOPAT
Investment in net operating capital
FCF

We must determine the tax shields.
From this point, we can derive horizon value from the basic DCF framework.
The tax shield is the interest multiplied by the post-merger tax rate.
					2017	2018	2019	2020	2021
Interest					0.0	0.0	0.0	0.0	0.0
Tax shield
HVTS 2020	=		TS2021		*	(1+g)	/	(rsU)	-	g)
HVTS 2020	=				*		/		-
HVTS 2020	=				/
HVTS 2020	=

To calculate the value of the tax shields add the horizon value of the tax shields to the 2021 tax shield
to get the total tax shield cash flow in 2021. In the other years the total TS cash flow is just the annual TS
Then find the NPV of this stream of tax shields at the unlevered cost of equity.
			2017	2018	2019	2020	2021
Total TS Cash Flows
NPV of TS Cash Flows				This is the value of all of the tax shields.

To calculate the unlevered value of operations you need the unlevered horizon value and the

the annual free cash flows.

To calculate the unlevered horizon value, we just need the free cash flow for 2021

HVUL 2021

=

FCF2021

*

(1+g)

/

(rsU

-

g)

HVUL 2021

=

*

/

-

HVUL 2021

=

/

HVUL 2021

=

To calculate the unlevered value of operations, add the unlevered horizon value to the free cash flow

in 2021 to get the total unlevered cash flow in 2021. In the other years the unlevered cash flow is

just the annual free cash flow. The unlevered value of operations is the NPV of the unlevered

cash flows at the unlevered cost of equity.

Year

2017

2018

2019

2020

2021

Total unlevered CFs

NPV of unlevered CFs

This is the unlevered value of operations

The value of operations is the value of the interest tax shields plus the unlevered value of operations

		VTS	+	Vunlevered
Vops	=		+
Vops	=

To find the value of ACC to Wansley's shareholders take the value of operations, add in any non-operating assets (there are non for ACC) and subtract off the debt.

Vops	=
Debt	=
Equity	=

Answer 1

Risk free rate	7.00%
Beta (Considering it Company's levered beta)	1.4
market Premium	6.50%
levered cost of equity at old capital structure	16.10%

levered beta = Unlevered Beta * [1 + (1 - Tax Rate) * Debt / Equity ]

Hence Unlevered Beta = levered Beta / [1 + (1 - Tax Rate) * Debt / Equity ] = 1.1

Unlevered cost of equity at old capital structure = 14%

	2017	2018	2019	2020	2021
Sales	500	600	700	760
Cost of Goods Sold (incl. depreciation)	325	390	455	494
Gross Profit	175	210	245	266
Selling/admin. costs	60	70	80	90
EBIT	115	140	165	176
Interest	30	40	45	60
EBT	85	100	120	116
Taxes	29.75	35	42	40.6
Net Income	55	65	78	75
EBIT	115	140	165	176
NOPAT	74.75	91	107.25	114.4
Investment in net operating capital	NA	NA	NA	NA
FCF	74.75	91	107.25	114.4

Financial for Year 2021 is not given.