Essentials Of Investments
Essentials Of Investments
11th Edition
ISBN: 9781260013924
Author: Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher: Mcgraw-hill Education,
Bartleby Related Questions Icon

Related questions

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?

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
expand button
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
Expert Solution
Check Mark
Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Essentials Of Investments
Finance
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Mcgraw-hill Education,
Text book image
FUNDAMENTALS OF CORPORATE FINANCE
Finance
ISBN:9781260013962
Author:BREALEY
Publisher:RENT MCG
Text book image
Financial Management: Theory & Practice
Finance
ISBN:9781337909730
Author:Brigham
Publisher:Cengage
Text book image
Foundations Of Finance
Finance
ISBN:9780134897264
Author:KEOWN, Arthur J., Martin, John D., PETTY, J. William
Publisher:Pearson,
Text book image
Fundamentals of Financial Management (MindTap Cou...
Finance
ISBN:9781337395250
Author:Eugene F. Brigham, Joel F. Houston
Publisher:Cengage Learning
Text book image
Corporate Finance (The Mcgraw-hill/Irwin Series i...
Finance
ISBN:9780077861759
Author:Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Jeffrey Jaffe, Bradford D Jordan Professor
Publisher:McGraw-Hill Education