I have located essentially what is in essence the identical problem
and its solution, except that the current risk-free rate is 9% instead
of 6% as in your problem.
"4. LimeAde Corporation, a large soft drink manufacturing firm, is
faced with the decision of how much to pay out as dividends to its
stockholders. It expects to have a net income of $ 1000 (after
depreciation of $500), and it has the following projects:
Project Initial Investment Beta IRR (to equity investors)
A $ 500 2.0 21%
B $600 1.5 20%
C $ 500 1.0 12%
The firm's beta is 1.5 and the current risk-free rate is 9%. The firm
plans to finance net capital expenditures (cap ex -depreciation) and
working capital with 20% debt. The firm also has current revenues of
$5000, which it expects to grow at 8 %. Working capital will be
maintained at 25% of revenues. How much should the firm return to its
stockholders as a dividend?"
"Problems and Questions"
http://pages.stern.nyu.edu/~adamodar/New_Home_Page/problems/divfr.htm
"Problem 4
Project IRR (to Equity) Beta Cost of Equity
A 21% 2 20.00%
B 20% 1.5 17.25%
C 12% 1 14.50%
Accept projects A and B. The total capital expenditures are $ 1100.
Estimated FCFE next year
Net Income next year = $1,000
- (Cap Ex - Depr) (1-.2) = 480
- Chg in WC (1-.2) = 80
= FCFE $440
The firm should pay out a dividend of $ 440."
"Dividend Framework: Solutions"
http://pages.stern.nyu.edu/~adamodar/pdfiles/divfr.pdf
The cost of equity for each project is calculated using the CAPM
formula: r(project) = r (risk free) + Beta(project)[r(market)-r(risk
free)]. In this case, the author has used an r(market)-r(risk free)
rate of 5.5%. The IRR to equity investors exceeds the cost of equity
for projects A and B, so they are accepted.
The total capital expenditure required is $1,100. The change in
working capital is calculated by first figuring out the initial
working capital. For $5,000 in revenue, the working capital is 25% of
$5,000, or $1,250. With 8% growth, revenues become $5,000*1.08 or
$5,400. Therefore, working capital becomes 25% of $5,400 or $1,350.
Therefore, the change in working capital equals $1,350 - $1,250 or
$100.
Using the formula FCFE = Net Income - (Capital Expenditures -
Depreciation) (1-debt/equity ratio) - (Change in Working Capital)
(1-debt/equity ratio), we find that FCFE = $1,000 - ($1,100 - $500)
(!-0.20) - ($100) (1-0.20) = $440. Therefore, to maintain its ratio
of working capital to revenue at 25%, $440 in dividends should be
paid.
For your problem, if you use an r(market)-r(risk free) rate of 5.5%
and the risk-free rate of 6%, Project C also becomes attractive, which
increases the capital expenditures. This decreases the dividend
payment by $400 to $40 to reflect (1-0.2) ($500) required to determine
the cash flow from Project C.
Sincerely,
Wonko |
