Question

Zeta Technologies has the following projections. It has no non-operating assets. Calculate Zeta's intrinsic value of equity using the FCFE model.

	Current year	Year 1	Year 1	Year 3
FCF	NA	1,000	1,200	1,248
Total debt	3,000	3,900	4,290	4,462
Interest rate on debt	6%	6%	6%	6%
Tax rate	25%	25%	25%	25%
Long-term growth rate	4%
Required return on equity	9%

	a.	$21,165
	b.	$28,171
	c.	$23,282
	d.	$30,988
	e.	$25,610

Answer 1

value of equity = present value of FCFE

FCFE for 3 years are known. After that, they grow at a constant long-term growth rate. Hence we calculate the value of equity at the end of year 3 by calculating the terminal value. Then we discount the terminal value back to the present.

FCFE = FCFF - (interest * (1 - tax rate)) + net borrowings

interest paid in each year = interest rate * total debt

FCFE of year 1 = 1,000 - (234 * (1 - 0.25)) + 900 ==> 1,725

FCFE of year 2 = 1,200 - (257 * (1 - 0.25)) + 390 ==> 1,397

FCFE of year 3 = 1,248 - (268 * (1 - 0.25)) + 172 ==> 1,219

PV of year 1 FCFE = 1,725 / (1.09^1) ==> 1,582

PV of year 2 FCFE = 1,397 / (1.09^2) ==> 1,176

PV of year 3 FCFE = 1,219 / (1.09^3) ==> 941

sum of the PVs of FCFE = $3,699

Now, we calculate the terminal value at end of year 3

terminal value = FCFE of year 3 * (1 + longterm growth rate) / (required return - longterm growth rate)

terminal value = (1,219 * (1 + 0.04) / (0.09 - 0.04)

terminal value = 25,359.57

PV of terminal value = 25,359.57/(1.09^3) ==> 19,582

Value of equity now = sum of PVs of FCFE + PV of terminal value

Value of equity = 3,699 + 19,582

Value of equity = $23,282

the answer is (c)