In: Finance
Private Corp. is a privately held firm that builds and sells widgets globally. The business has prospered in the last few years, but the owners are afraid the growth may be slowing down. To that end, the Finance division started looking at competitors and came up with the following table:
EPS | Dividends/Share | Stock Price | ROE | R | Debt Rating | Yield | |
ABC Corp. | $1.30 | $0.16 | $25.34 | 8.50% | 8.00% | AA | 3.15% |
XYZ Inc. | $1.95 | $0.23 | $29.85 | 10.50% | 13.00% | A | 3.56% |
Widgets Inc. | -$0.37 | $0.14 | $22.13 | 9.78% | 12.00% | BBB+ | 4.04% |
JKL Corp. | $0.50 | $0.05 | $28.56 | 9.00% | 11.50% | BB+ | 6.12% |
RTS Systems | $1.00 | $0.17 | $25.12 | 11.00% | 14.00% | BB | 8.02% |
OAZ Technologies | $1.10 | $0.18 | $23.54 | 9.20% | 10.50% | BB | 7.14% |
Industry Average | $0.91 | $0.16 | $25.76 | 9.66% | 11.50% | - | 5.34% |
While gathering the data above, the Finance division noted that Widgets Inc. took an accounting write-off last year that caused the negative earnings. According to the same note, the impact of that write-off was $1.20 per share.
In the past year Private Corp. had Earnings per Share of $3.25 and paid a total dividend of $40,000. The company is supported only by equity with no debt. There are a total of 50,000 shares outstanding. Last year the Return on Equity was 18% and the owners believe the required rate for the whole company is 15%. Private Corp's debt rating is regarded by investors as BB.
It may be useful to use the identity:
which says that the growth rate in dividends depends on the ROE and the retention rate.
1]
dividend per share = $40,000 / 50,000 = $0.80
retention ratio = (EPS - dividend per share ) / EPS = ($3.25 - $0.80) / $3.25 ==> 0.75
growth rate = ROE * retention ratio = 18% * 0.75 ==> 13.5%
value per share = next year dividend / (required return - growth rate)
next year dividend = current year dividend + growth rate = $0.80 + 13.5% ==> $0.908
value per share = $0.908 / (0.15 - 0.135) ==> $60.53
2]
First we compute the industry average growth rate
Before that, EPS of Widgets Inc. needs to be adjusted for the one-time loss. Adjusted EPS = -$0.37 + $1.20 ==> $0.83
industry average growth rate = average retention ratio * average ROE
industry average growth rate = (($1.11 - $0.16) / $1.11 ) * 9.66% ==> 8.27%
value of share = present value of dividends for 5 years + present value of share value at after 5 years
share value after 5 years = 6th year dividend / (required return - growth rate)
growth rate for five years is 13.5%, and after that it is 8.27%. Required return is the industry average of 11.50%
share value after 5 years = ($1.33 * 1.0827) / (0.1150 - 0.0827) ==> $44.58
Present value of share value after 5 years = $44.58 / (1 + 0.1150)^5 ==> $29.96
we calculate the dividends and share value and their present values (using 11.50% discount rate) as below :
present value of dividends = $4.07
value of share now = $4.07 + $29.96 ==> $34.03
3]
Average PE ratio = Average price / average EPS = $25.76 / $1.11 ==> 23.21
Private PE ratio (with high growth) = stock price / EPS = $60.53 / $3.25 ==> 18.62
Private PE ratio (with average growth) = stock price / EPS = $34.03 / $3.25 ==> 10.47
4]
growth rate = retention ratio * ROE
ROE = growth rate / retention ratio
industry average retention ratio = ($1.11 - $0.16) / $1.11 = 0.86
ROE = 8.27% / 0.86 ==> 9.6%