Question

Raymond Supply, a national hardware chain, is considering purchasing a smaller chain, Strauss & Glazer Parts (SGP). Raymond's analysts project that the merger will result in the following incremental free cash flows, tax shields, and horizon values (in millions): Year 1 2 3 4 FCF $2 $3 $4 $7 Unlevered Horizon value $75 Tax shield $1 $1 $2 $3 Horizon value of tax shield $32 Assume that all cash flows occur at the end of the year. SGP is currently financed with 30% debt at a rate of 8%. The acquisition would be made immediately, and if it is undertaken, SGP would retain its current $20 million of debt and issue enough new debt to continue at the 30% target level. The interest rate would remain the same. SGP's pre-merger beta is 1.5, and its post-merger tax rate would be 40%. The risk-free rate is 5% and the market risk premium (=ErM - rRF) is 6%.

What is the unlevered cost of equity of SGP?

What is the unlevered value of operations of SGP?

What is the value of tax shield of SGP?

Answer 1

All financials below are in $ mn

What is the unlevered cost of equity of SGP?

Levered beta, BL = 1.5,

Levered cost of equity, Kel = Risk free rate + BL x market risk premium = 5% + 1.5 x 6% = 14.00%

Proportion of debt, Wd = D / (D + E) = 30%; Proportion of equity, We = 1 - Wd = 1- 30% = 70%

Cost of debt, Kd = 8%

Hence, unlevered cost of equity = We x Kel + Wd x Kd = 70% x 14% + 30% x 8% = 12.20%

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What is the unlevered value of operations of SGP?

Please see the working below. Please pay attention to the second column, it explains how each row has been caalculated.

Year	N	1	2	3	4
FCF	C	2.00	3.00	4.00	7.00
Unlevered Horizon value	HV				75.00
Total Cash flows	CF = C + HV	2.00	3.00	4.00	82.00
Discount factor (Unlevered cost of equity)	Keu (calculated in first part)	12.20%
Discount factor	DF = (1 + Keu)-N	0.8913	0.7944	0.7080	0.6310
PV of cash flows	PV = CF x DF	1.78	2.38	2.83	51.74
Unlevered value of operations	Sum of all PV	58.74

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What is the value of tax shield of SGP?

Year	N	1	2	3	4
Tax shield	TS	1.00	1.00	2.00	3.00
Horizon value of tax shield	HV				32.00
Total Tax shield	ITS = TS + HV	1.00	1.00	2.00	35.00
Discount factor (Unlevered cost of equity)	Keu	12.20%
Discount factor	DF = (1 + Keu)^(-N)	0.8913	0.7944	0.7080	0.6310
PV of cash flows	PV = ITS x DF	0.89	0.79	1.42	22.08
Value of tax shield of SGP	Sum of all PV	25.19