Question

If the firm’s expected future free cash flows in year 1 is $1.2 million, in year 2 it is expected to equal $1.6 million, in year 3 it is expected to equal $2.0 million and then the expected future free cash flows are expected to increase at a constant rate of 3%/year into perpetuity. Assume the firm’s WACC is 8%/year. Provide an equation, including all of the inputs, to calculate the present value of the expected future free cash flows of this firm.

Answer 1

	Amt $Million
Particulars	Year 1	Year 2	Year 3	Year 4
Given Cash flow	1.20	1.60	2.00
Year 4 Cash flow with 3% growth =2*1.03=
Given that from year 4 cash flows will increase at constant
rate of 3% pa perpetually.
Here perpetual Growth rate =g=3%
Cash flow in first year of perpetual growth Gowth =C1=2*(1+g)=2.06				2.06
Given : WACC =8%=k
PV of Terminal Cash flows at year 3 end =D1/(k-g)=2*(1+3%)/(8%-3%)=			41.20

	We can arrange the cash flows and terminal cash flows this way:	Amt $Million
	Cash flows	Year 1	Year 2	Year 3
	Annual Cash flows	1.20	1.60	2.00
	PV of Terminal Cash at year 3 end			41.20
a	Total future Cash flow and Terminal Cash flow=	1.20	1.60	43.20
b	PV factor @8% =1/1.08^n=	0.9259	0.8573	0.7938
c	PV of Future Cash flow and terminal cash flows =a*b	1.1111	1.37	34.29
	Sum of PV of cash flows & terminal cash flow	36.7764
	Sum of PV of Cash flows & terminal cash flow =$36.7764 Million

In Equation form we can Write : PV of all future Cash flows =$1.2Million*[1/(1+8%)^1] +$1.6Million*[1/(1+8%)^2]+$2.0Million*[1/(1+8%)^3]+[$2Million*(1+3%)/(8%-3%)]*[1/(1+8%)^3]