Question

Stubborn Motors, Inc. is asking a price of $91 million to be purchased by Rubber Tire Motor Corp. Stubborn Motors currently has total cash flows of $3 million that are expected to grow indefinitely by 1 percent annually. Managers estimate that, because of synergies, the merged firm’s cash flows will increase by $5 million in the first year after the merger and that these cash flows will grow by an additional 5 percent in years 2 through 4 following the merger. After the first four years, these incremental cash flows will grow at a rate of 1 percent annually. The WACC for the merged firms is 11 percent.

Calculate the NPV of the merger.

Should Rubber Tire Motor Corporation agree to acquire Stubborn Motors for the asking price of $91 million?

Answer 1

Calculation of NPV of the merger:

Purchased price = $91 millions

Value generated by merger:

Year	Growth rate	Expected cash flow	Discounting factor@ 11%	Present value of cash flows
1		8.00	0.90	7.21
2	6%	8.48	0.81	6.88
3	6%	8.99	0.73	6.57
4	6%	9.53	0.66	6.28

Value at 4^th year through Expected cash flow generated in the 5^th year = Expected cash flow at 5^th year/WACC-g

Expected cash flow at 5^th year = (9.53*1.01)/(0.11-0.01)

= 9.62/0.10

= 96.23

Current price of Forever Cash flow generated after 4^th year = 96.23*(PVFA_{11%, 4 years})

= 96.23*0.66

= $63.39 million

Current price = $7.21+$6.88+$6.57+$6.28+$63.39

= $90.33 million

NPV = Current price – acquisition value

= $90.33 million – $91 million

= -$0.67 million

Since NPV of the merger is negative, therefore Rubber Tire Motor Corporation shoul not agree to acquire Stubborn Motors.