Business: 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?

The growth in per-share fcfe of synk, inc. is expected

Ответ:

smolemily

13.01.2022

Business

$36.98

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) = $\frac{FCFE_{Year5} * (1 + GrowthRate)}{Rate Of Return - Growth Rate}$

= $\frac{3.6081 * (1.03)}{0.11 - 0.03}$

= $46.4543.

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

Price = $\frac{FCFE_{1} }{(1.11^{1})}$ + $\frac{FCFE_{2} }{(1.11^{2})}$ + ... + $\frac{FCFE_{6} }{(1.11^{6})}$

Price = $\frac{2.97}{1.11^{1}}$ + $\frac{3.2076}{1.11^{2}}$ + $\frac{3.3359}{1.11^{3}}$ + $\frac{3.4693}{1.11^{4}}$ + $\frac{3.6081}{1.11^{5}}$ + $\frac{46.4543}{1.11^{6}}$

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

Price = 36.9812

= $36.98.

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