Question

You are valuing the operating assets of Bloom Inc. based on the following assumptions:

During the high growth period of n years, the firm has a ROIC of 15% and a NOPAT growth rate of 8%.

In the stable growth period, the firm has a RONIC of x% and a constant growth rate of 2%.

The WACC is 10% and tax rate is 25%. EBIT in Year 0 was $100 million.

Based on the above, you have valued the operating assets at $928.637 million (the Total Value). The PV of the terminal value accounts for 75.468% of the Total Value.

(a) What is the length of the high growth period n? (1.5 points)

Answer 1

NOPAT in year 0 = EBIT0*(1-tax rate) =$100 million *0.75 = $75 million

NOPAT in year 1=NOPAT in year 0 *1.08 =$75*1.08 = $81 million

and so on

NOPAT in year n = $75 *1.08^n million

Terminal Value after year n = NOPAT in year (n+1) / ( WACC - constant growth rate of 2%)

= $75*1.08^n *1.02/(0.1-0.02)

=$956.25*1.08^n million

PV of Terminal Value = $956.25*1.08^n/1.1^n million

PV of Terminal Value = 75.468% of Total Value = 75.468%* $928.637 million = $700.823771 million

=>  956.25*1.08^n/1.1^n = 700.823771

=> (1.08/1.1)^n = 0.7328876

Taking natural log of both sides

n = ln (0.7328876)/ln(0.981818) = 16.936 or 17 years

So, n= 17