Question

Juicers Inc. is thinking of acquiring Fast Fruit Company. Juicers has determined that Fast Fruit's current cost of equity is 17.5%; Fast Fruit currently has no debt outstanding. In Year 1, Juicers expects Fast Fruit to generate $9 million in NOPAT and invest $50 million in total net operating capital. Fast Fruit will borrow to finance this expansion, with the first interest payment ($5 million) due at Year 2. (There will be no interest due at Year 1.) In Year 2, Fast Fruit will generate $25 million in NOPAT and invest $10 million in total net operating capital. Fast Fruit's marginal tax rate is 25%. After the second year, the free cash flows and the tax shields each will grow at a constant rate of 4%. Assume that all cash flows occur at the end of the year. If Juicers must pay $90 million to acquire Fast Fruit, what is the NPV of the proposed acquisition? (Report your answer in millions of dollars.)

Answer 1

The unleverd cost of equity = 17.5%

Free cash flow to equity for year 1 = NOPAT - Operating capital

=$9 million - $50 million

=$ -41 million

Free cash flow to equity for year 2 = NOPAT - Operating capital - Interest(1-t)

= $25 million - $10 million - $5 million (1-0.25)

= $25 million - $10 million - $5 million (0.75)

=$25 million - $10 million - $3.75 million

= $11.25 million

Now after year 2 , the free cash flows and the tax shields each will grow at a constant rate of 4%

hence horizon value = [NOPAT - interest expense(1-tax rate)] x (1+g) / Ke-g

g = growth rate = 4% , Ke = required rate of return = 17.5%

Thus horizon value =[$25 million - $5 million (0.75)] x (1+4%) / 17.5%-4%

=[$25 million - $3.75 million] x (1.04) / 13.5%

= $21.25 million/13.5%

= $157.41 million

Statement showing PV of FCFE

Year	FCFE	PVIF @ 17.5%	PV
1	-41	0.8511	-34.89
2	11.25	0.7243	8.15
Terminal / Horizon value	157.41	0.7243	114.01
Total PV of FCFE	87.27

NPV of acquisition = Total PV of FCFE - Consideration paid

=$87.27 million - $90 million

=$ - 2.73 million