Question

The growth in per-share FCFE of SYNK, Inc. is expected to be 8% per year for the next two years, followed by a growth rate of 4% per year for three years; after this five-year period, the growth in per-share FCFE is expected to be 3% per year, indefinitely. The required rate of return on SYNC, Inc. is 11%. Last year's per-share FCFE was $2.75. What should the stock sell for today?

Answer 1

$36.98

Step-by-step explanation:

The price of the stock today is computed by discounting the FCFE for all years up to the 6th year.

Step 1: The FCFE for each year will be computed by compounding the FCFE of the preceding year by the appropriate growth rate.

`FCFE_(n) = FCFE_(n-1)* (1+Growth Rate)`

Therefore,

FCFE (year 1) = 2.75 * 1.08 = $2.97 (growth rate for the 1st 2 years is 8%)

FCFE (year 2) = 2.97 * 1.08 = $3.2076

FCFE (year 3) = 3.2076 * 1.04 = $3.3359 (growth rate for the next 3 years is 4%)

FCFE (year 4) = 3.3359 * 1.04 = $3.4693

FCFE (year 5) = 3.4693 * 1.04 = $3.6081

The FCFE for year 6 to infinity will be computed using the annuity formula to infinity since growth rate will remain constant henceforth.

FCFE (year 6 to infinity) =
`(FCFE_(Year5) * (1 + GrowthRate))/(Rate Of Return - Growth Rate)`

=
`(3.6081 * (1.03))/(0.11 - 0.03)`

= $46.4543.

Step 2: Discounting the FCFE (using the 11% rate of return) to get the price

Price =
`(FCFE_(1) )/((1.11^(1)))` +
`(FCFE_(2) )/((1.11^(2)))` + ... +
`(FCFE_(6) )/((1.11^(6)))`

Price =
`(2.97)/(1.11^(1))` +
`(3.2076)/(1.11^(2))` +
`(3.3359)/(1.11^(3))` +
`(3.4693)/(1.11^(4))` +
`(3.6081)/(1.11^(5))` +
`(46.4543)/(1.11^(6))`

Price = 2.6757 + 2.6034 + 2.4392 + 2.2853 + 2.1412 + 24.8364

Price = 36.9812

= $36.98.