Question

The present value of an investment is estimated at about $266,300. The expected generated free cash flow from the project for next year is $5,000 and is expected to grow 15% a year for the next four years following the first generated cash flow. After the fifth year, the growth rate is expected to drop to 5% in in perpetuity. Estimate the discount rate used in valuing this project.

A. % 6.73

B. % 7.65

C. % 8.12

D. % 9.23

Answer 1

Cash flows can be set up as below:

	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6
FCF	$5,000	$5,750	$6,613	$7,604	$8,745	$9,182
Growth rate	-	15%	15%	15%	15%	5%
PV of FCF	$4,645	$4,962	$5,301	$5,662	$6,049
Terminal value					$346,501
PV of terminal value					$239,681
Total PV (r = 7.65%)					$266,300

FCF for year 2 = 5000 * (1+15%) = 5,750

FCF for year 3 = 5750 * (1+15%) = 6,613

FCF for year 4 = 6613 * (1+15%) = 7,604

FCF for year 5 = 7604 * (1+15%) = 8,745

FCF for year 6 = 8745 * (1+5%) = 9,182  

PV of FCF for year 1 = 5000 / ((1+r))

PV of FCF for year 2 = 5750 / ((1+r) ^ 2)

PV of FCF for year 3 = 6613 / ((1+r) ^ 3)

PV of FCF for year 4 = 7604 / ((1+r) ^ 4)

PV of FCF for year 5 = 8745 / ((1+r) ^ 5)

Terminal value = next year's FCF / (r - growth rate) = (8745 * 1.05) / (r - 5%) = 9182 / (r - 5%)

PV of terminal value = (9182 / (r - 5%)) / ((1+r) ^ 5))

Total PV = PV of FCF's for years 1 - 5 + PV of terminal value

$266,300 = PV of FCF's for years 1 - 5 + PV of terminal value

Using goal seek function in excel, we get r = 7.65%. [set total PV = 266,300 by changing value of r]

Hence, option B is the correct answer.