Chapter 21

Mergers and Acquisitions

SOLUTIONS TO END-OF-CHAPTER PROBLEMS

21-1 D1 = $2.00; g = 5%; b = 0.9; kRF = 5%; RPM = 6%; P0 = ?

ks = kRF + RPM(b)

= 5% + 6%(0.9)

= 10.4%.

P0 =

=

= $37.04.

21-2 D1 = $2.00; g = 7%; b = 1.1; kRF = 5%; RPM = 6%; P0 = ?

ks = kRF + RPM(b)

= 5% + 6%(1.1)

= 11.6%.

P0 =

=

= $43.48.

21-3 On the basis of the answers in Problems 21-1 and 21-2, the bid for each share should range between $37.04 and $43.48.

21-4 a. The appropriate discount rate reflects the riskiness of the cash flows to equity investors. Thus, it is Vaccaro’s cost of equity, adjusted for leverage effects. Since Apilado’s b = 1, its RPM = kM - kRF = 14% - 8% = 6%, then:

ks = kRF + (kM - kRF)b = 8% + (14% - 8%)1.47 = 16.82% 16.8%.

b. The value of Vaccaro is $14.65 million:

0 1 2 3 4 5

1.30 1.50 1.75 2.00 2.12

1.11 19.63

1.10

1.10

11.62 21.63

V = $14.93 million

CF5 = CF4(1.06) = $2.00(1.06) = $2.12.

Value at t4 of CF5 and all subsequent cash flows is:

V4 = = $19.63.

Alternatively, input 0, 1.30, 1.50, 1.75, and 21.63(2.00 + 19.63) into the cash flow register, I = 16.8, NPV = ? NPV = $14.93.

c. PMax = V/N = $14.93/1.2 = $12.44.

Since Apilado is paying exactly what Vaccaro is worth, the acquisition has a zero net present value and Apilado’s share price should remain at its current price.

21-5 0 1 2 3 10

• • •

-400,000 64,000 64,000 64,000 64,000

CF0 = -$400,000; CF1 - CF10 = $64,000; and k = 10%.

Input -400,000 and 64,000 (10) into the cash flow register, I = 10, and solve for NPV = -$6,747.71. Since the NPV of the investment is negative, Stanley should not make the purchase.

21-6 a. Since the net cash flows are equity returns, the appropriate discount rate is that cost of equity which reflects the riskiness of the cash flow stream. This cost is GCC’s cost of equity:

ks = kRF + (RPM)b = 8% + (4%)1.50 = 14%.

b. The terminal value is $1,143.4:

TV =

Annual cash flows are calculated as follows:

2003 2004 2005 2006

Sales $450.0 $518.0 $555.0 $600.0

COGS (292.5) (336.7) (360.7) (390.0)

Gross profit $157.5 $181.3 $194.3 $210.0

Selling/Admin (45.0) (53.0) (60.0) (68.0)

EBIT $112.5 $128.3 $134.3 $142.0

Interest (18.0) (21.0) (24.0) (27.0)

EBT $ 94.5 $107.3 $110.3 $115.0

Taxes (35%) (33.1) (37.6) (38.6) (40.3)

Net income $ 61.4 $ 69.7 $ 71.7 $ 74.8

The value of GCC to TransWorld’s shareholders is the present value of the cash flows that accrue to the shareholders:

V = = $877.2.

Alternatively, input 0, 61.4, 69.7, 71.7, and 1218.2 (74.8 + 1143.4) into the cash flow register, I = 14, and solve for NPV = $877.2.

Mergers and Acquisitions

SOLUTIONS TO END-OF-CHAPTER PROBLEMS

21-1 D1 = $2.00; g = 5%; b = 0.9; kRF = 5%; RPM = 6%; P0 = ?

ks = kRF + RPM(b)

= 5% + 6%(0.9)

= 10.4%.

P0 =

=

= $37.04.

21-2 D1 = $2.00; g = 7%; b = 1.1; kRF = 5%; RPM = 6%; P0 = ?

ks = kRF + RPM(b)

= 5% + 6%(1.1)

= 11.6%.

P0 =

=

= $43.48.

21-3 On the basis of the answers in Problems 21-1 and 21-2, the bid for each share should range between $37.04 and $43.48.

21-4 a. The appropriate discount rate reflects the riskiness of the cash flows to equity investors. Thus, it is Vaccaro’s cost of equity, adjusted for leverage effects. Since Apilado’s b = 1, its RPM = kM - kRF = 14% - 8% = 6%, then:

ks = kRF + (kM - kRF)b = 8% + (14% - 8%)1.47 = 16.82% 16.8%.

b. The value of Vaccaro is $14.65 million:

0 1 2 3 4 5

1.30 1.50 1.75 2.00 2.12

1.11 19.63

1.10

1.10

11.62 21.63

V = $14.93 million

CF5 = CF4(1.06) = $2.00(1.06) = $2.12.

Value at t4 of CF5 and all subsequent cash flows is:

V4 = = $19.63.

Alternatively, input 0, 1.30, 1.50, 1.75, and 21.63(2.00 + 19.63) into the cash flow register, I = 16.8, NPV = ? NPV = $14.93.

c. PMax = V/N = $14.93/1.2 = $12.44.

Since Apilado is paying exactly what Vaccaro is worth, the acquisition has a zero net present value and Apilado’s share price should remain at its current price.

21-5 0 1 2 3 10

• • •

-400,000 64,000 64,000 64,000 64,000

CF0 = -$400,000; CF1 - CF10 = $64,000; and k = 10%.

Input -400,000 and 64,000 (10) into the cash flow register, I = 10, and solve for NPV = -$6,747.71. Since the NPV of the investment is negative, Stanley should not make the purchase.

21-6 a. Since the net cash flows are equity returns, the appropriate discount rate is that cost of equity which reflects the riskiness of the cash flow stream. This cost is GCC’s cost of equity:

ks = kRF + (RPM)b = 8% + (4%)1.50 = 14%.

b. The terminal value is $1,143.4:

TV =

Annual cash flows are calculated as follows:

2003 2004 2005 2006

Sales $450.0 $518.0 $555.0 $600.0

COGS (292.5) (336.7) (360.7) (390.0)

Gross profit $157.5 $181.3 $194.3 $210.0

Selling/Admin (45.0) (53.0) (60.0) (68.0)

EBIT $112.5 $128.3 $134.3 $142.0

Interest (18.0) (21.0) (24.0) (27.0)

EBT $ 94.5 $107.3 $110.3 $115.0

Taxes (35%) (33.1) (37.6) (38.6) (40.3)

Net income $ 61.4 $ 69.7 $ 71.7 $ 74.8

The value of GCC to TransWorld’s shareholders is the present value of the cash flows that accrue to the shareholders:

V = = $877.2.

Alternatively, input 0, 61.4, 69.7, 71.7, and 1218.2 (74.8 + 1143.4) into the cash flow register, I = 14, and solve for NPV = $877.2.

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