This page is designed to help you master the core concepts of dividend policy, a key area of the FIM exam. The problems below cover various theories and policies, as well as the mechanics of share repurchases and stock splits. Use the interactive sections to test your knowledge before viewing the solutions.
Problem Statement: BDLimited has 31,000 shares of stock outstanding with a market price of Tk. 15 per share. If net income for the year is Tk. 155,000 and the retention ratio is 80%, what is the dividend per share on BD Limited's stock?
a) Tk. 0.68
b) Tk. 0.83
c) Tk. 1.00
d) Tk. 1.25
e) Tk. 1.89
Solution:
First, we need to determine the total dividends paid. The retention ratio is the percentage of earnings retained by the company, so the dividend payout ratio is $1 - \text{retention ratio}$.
Dividend Payout Ratio = $1 - 0.80 = 0.20$ or $20\%$
Total Dividends = Net Income $\times$ Dividend Payout Ratio
= $155,000 \times 0.20 = \text{Tk. } 31,000$
Then, we can calculate the dividend per share:
Dividend per Share = $\frac{\text{Total Dividends}}{\text{Number of Shares Outstanding}} = \frac{31,000}{31,000} = \text{Tk. } 1.00$
The correct answer is **(c) Tk. 1.00**.
Problem Statement: What should be the optimum dividend pay-out ratio, when $r=15\%$, and $k_{e}=12\%$?
a) 100%
b) 50%
c) 25%
d) Zero
e) 75%
Solution:
According to Walter's model of dividend policy, the optimum payout ratio depends on the relationship between the firm's internal rate of return ($r$) and the cost of equity ($k_e$).
- If $r > k_e$ (growth firm), the firm should retain all earnings and the optimal payout ratio is **zero**.
- If $r < k_e$ (declining firm), the firm should distribute all earnings and the optimal payout ratio is **100%**.
- If $r = k_e$ (normal firm), the dividend policy is irrelevant and any payout ratio is optimal.
In this problem, $r = 15\%$ and $k_e = 12\%$. Since $r > k_e$, the firm is a growth firm, and it should reinvest all its earnings to maximize value. Therefore, the optimal dividend payout ratio is **(d) Zero**.
Problem Statement: Dividends may be considered relevant because:
a) they increase the investor's overall return
b) a higher return will be earned than with retained earnings
c) they are preferred by investors in higher tax brackets
d) share price will be increased
e) they resolve uncertainty in the minds of investors
Solution:
The correct answer is **(e) they resolve uncertainty in the minds of investors**. The "bird-in-the-hand" theory suggests that investors prefer a certain dividend today to a potential, but uncertain, capital gain from retained earnings in the future. By paying a dividend, management signals its confidence in the firm's future cash flows, reducing investor uncertainty and potentially increasing the stock's value.
Problem Statement: According to Modigliani and Miller, the investor is indifferent between receiving dividends and having earnings retained by the firm.
Solution:
True. According to the Modigliani and Miller (M&M) dividend irrelevance theory, in a perfect capital market, an investor's total return from a stock is not affected by how the firm's earnings are split between dividends and retained earnings. The investor can create "homemade" dividends by selling a portion of their stock, making them indifferent to the firm's dividend policy.
Problem Statement: The Board of Directors of City Bank Limited (CBL) decided through a Board resolution to raise additional capital through rights issue to meet the new capital requirement by Bangladesh Bank. CBL plans to issue 1 new share for every 3 shares held by existing shareholders at 10% discount to its existing market price. CBL currently has 6 million shares in issue at a book value of Tk. 2 per share. CBL maintains a dividend payout ratio of 50% and earnings per share currently is Tk. 1.6. Dividend growth is 5% per annum and this is expected into the foreseeable future. CBL's cost of equity is 15%. The issue cost is Tk. 600,000. Required: Calculate: (i) The market price per share (ii) The capitalization of CBL (iii) The rights issue price (iv) The theoretical ex-right price (v) The market capitalization after the rights issue
Solution:
First, we need to find the current market price per share using the dividend growth model. We are given the dividend payout ratio, EPS, growth rate, and cost of equity.
Current Dividend ($D_0$) = EPS $\times$ Payout Ratio = $1.6 \times 0.50 = \text{Tk. } 0.80$
Next year's dividend ($D_1$) = $D_0 \times (1+g) = 0.80 \times (1.05) = \text{Tk. } 0.84$
i. The market price per share:
Using the dividend growth model: $P_0 = \frac{D_1}{k_e - g}$
$P_0 = \frac{0.84}{0.15 - 0.05} = \frac{0.84}{0.10} = \text{Tk. } 8.40$
The market price per share is **Tk. 8.40**.
ii. The capitalization of CBL:
Market Capitalization = Number of shares outstanding $\times$ Market price per share
= $6,000,000 \times 8.40 = \text{Tk. } 50,400,000$
The capitalization of CBL is **Tk. 50,400,000**.
iii. The rights issue price:
The issue price is a 10% discount to the existing market price.
Issue Price = Market Price $\times$ (1 - Discount Rate) = $8.40 \times (1 - 0.10) = 8.40 \times 0.90 = \text{Tk. } 7.56$
The rights issue price is **Tk. 7.56**.
iv. The theoretical ex-right price:
TERP = $\frac{(\text{Number of old shares} \times \text{Old price}) + (\text{Number of new shares} \times \text{Issue price})}{\text{Total number of shares}}$
Rights issue is 1 for 3, so Number of old shares = 3, Number of new shares = 1.
TERP = $\frac{(3 \times 8.40) + (1 \times 7.56)}{3 + 1} = \frac{25.20 + 7.56}{4} = \frac{32.76}{4} = \text{Tk. } 8.19$
The theoretical ex-right price is **Tk. 8.19**.
v. The market capitalization after the rights issue:
Total number of shares after issue = $6,000,000 + (6,000,000 \times \frac{1}{3}) = 6,000,000 + 2,000,000 = 8,000,000$ shares
New Market Capitalization = Total number of shares $\times$ Theoretical ex-right price
= $8,000,000 \times 8.19 = \text{Tk. } 65,520,000$
The market capitalization after the rights issue is **Tk. 65,520,000**.
Problem Statement: All of the following are true of stock splits EXCEPT:
a) par value of share is reduced after the split
b) the number of outstanding shares is increased
c) proportional ownership is unchanged
d) total equity remains unchanged
e) market price per share do not change after the split
Solution:
The correct answer is **(e) market price per share do not change after the split**. This is the only statement that is not true. A stock split is a corporate action that increases the number of shares outstanding while reducing the par value and the market price per share proportionally. Total equity and proportional ownership remain unchanged, but the price per share is reduced to make the stock more accessible to a wider range of investors.