Question

16. The present value of the terminal (continuation) value cash flow that begins in 9 years is $10,000,000 assuming a cost of equity equal to 14%. The year 9 free cash flow (beginning of the growing perpetuity) is $3,137,860. What is the growth rate required for the continuation value term?

1. 1%

2. 2%

3. 3%

4. 4%

5. 5%

Answer 1

Answer: Option d is correct
Given that present value of the terminal value that begins in 9 years is $10,000,000
Now, future value=present value*(1+interest rate)^Number of years
Substituting the values, we get;

Future Value=10000000*(1+14%)^9=32519485.21

Given that, the cash flow at the beginning of the growing perpetuity=3137860
The formula for terminal value=(Cash flow at the beginning of the growing perpetuity)*(1+Growth rate)/(Cost of capital - Growth rate)
Substituting the values, we get;
Terminal value=3137860/*(1+g)/(14%-g)

Equating the values, we get;
32519485.21=3137860/*(1+g)/(14%-g)
=>(14%-g)=3137860*(1+g)/32519485.21

=>(14%-g)=(3137860/32519485.21)*(1+g)  
=>(14%-g)=(0.096491687)*(1+g)  
=>14%=(0.096491687)*(1+g) + g
=>14%=(0.096491687)*1+(0.096491687)*g + g
=>14%=0.096491687+g*(1+0.096491687)
=>14%-0.096491687=g*(1.096491687)
=>0.043508313=g*(1.096491687)
=>0.043508313/(1.096491687) =g=0.039679565 or 3.97% or 4% (Rounded to the nearest whole number)