Suppose you are asked to value a small start-up company that is expected to generate a Free Cash Flow of - $100 million next year, and - $50 million in the following year (year 2), before the firm turns profitable in year 3. Its first positive cash flow is equal to $2 million, and cash flows are expected to grow at a rate of 15% per year for 10 years (until year 13). Then, between year 13 and 14, the growth rate drops to 7% and stays there forever. Value the start-up company if the relevant discount rate is equal to 9%. My question is when calculating the perpetuity with a cosntant growth rate, why we muliply: 1/(1+r)^13 * E(CF_14)/0,09-0,07 Why does this make sense?
Suppose you are asked to value a small start-up company that is expected to generate a Free Cash Flow of - $100 million next year, and - $50 million in the following year (year 2), before the firm turns profitable in year 3. Its first positive cash flow is equal to $2 million, and cash flows are expected to grow at a rate of 15% per year for 10 years (until year 13). Then, between year 13 and 14, the growth rate drops to 7% and stays there forever. Value the start-up company if the relevant discount rate is equal to 9%. My question is when calculating the perpetuity with a cosntant growth rate, why we muliply: 1/(1+r)^13 * E(CF_14)/0,09-0,07 Why does this make sense?
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Question
Suppose you are asked to value a small start-up company that is expected to generate a Free Cash
Flow of - $100 million next year, and - $50 million in the following year (year 2), before the firm
turns profitable in year 3. Its first positive cash flow is equal to $2 million, and cash flows are expected to grow at a rate of 15% per year for 10 years (until year 13). Then, between year 13 and 14,
the growth rate drops to 7% and stays there forever. Value the start-up company if the relevant discount rate is equal to 9%.
My question is when calculating the perpetuity with a cosntant growth rate, why we muliply:
1/(1+r)^13 * E(CF_14)/0,09-0,07
Why does this make sense?
Transcribed Image Text:13
13
Σ
Е(CF.)
E(CF;)
+
(1+ r) ' (1+r)13
E(CF;)
1
E (CF 4)
1
E(CF4)
V =
(1+r)t
r- g
(1.09) ' (1.09)13 ^ 0.09 – 0.07
t=1
t=1
t=1
The first term in the formula above is the present value of the cash flows generated by the firm in the first 13
years. These cash flows are projected out in the table below. The second part of the last term is the continu-
ing value calculation, which reflects the present value of the cash flows generated by the firm from year 14
on, using the constant growth perpetuity formula. To get the current value of the firm as of now (i.e., at t=
0), this continuing value needs to be discounted back to the present. The first part of the last term reflects
this.
With the cash flow projections given below, it can be seen that:
13
Е (CF4)
E(CF,)
(1.09) ' (1.09)13 ^0.09 – 0.07
1
1
= -111,299,428 +
8,657,494
V =
29,895,049
(1.09)13 ^0.09 – 0.07
t=1
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