FIM Exam: Valuation of Bonds & Stocks Practice

Problem Statement: Newline Plc is expected to pay equal dividends at the end of each of the next two years. Thereafter, the dividend will grow at a constant annual rate of 3.5 percent, forever. The current stock price is \$59. What is next year's dividend payment if the required rate of return is 11 percent?

Solution:

We can use the multi-stage dividend discount model to solve for the dividend payment ($D_1$). The price of the stock is the sum of the present values of the dividends over the next two years, plus the present value of the stock price at the end of year 2 (which is the start of the constant growth phase).

Given: $P_0 = \$59$, $k_e = 11\%$, $g = 3.5\%$. $D_1 = D_2$.

$P_0 = \frac{D_1}{(1+k_e)} + \frac{D_2}{(1+k_e)^2} + \frac{P_2}{(1+k_e)^2}$

where $P_2$ is the price at the end of year 2, calculated using the Gordon Growth Model ($P_t = \frac{D_{t+1}}{k_e-g}$):

$P_2 = \frac{D_3}{k_e - g} = \frac{D_2(1+g)}{k_e - g}$

Since $D_1 = D_2$, we can substitute into the main formula:

$59 = \frac{D_1}{1.11} + \frac{D_1}{1.11^2} + \frac{D_1(1.035)}{(0.11 - 0.035) \times 1.11^2}$

$59 = 0.9009D_1 + 0.8116D_1 + \frac{1.035D_1}{0.075 \times 1.2321}$

$59 = 1.7125D_1 + 11.1991D_1 = 12.9116D_1$

$D_1 = \frac{59}{12.9116} \approx \$4.57$

The next year's dividend payment ($D_1$) is approximately **\$4.57**.

Problem Statement: The constant growth model of equity valuation assumes that:

a) the dividends paid by the company remain constant

b) the dividends paid by the company grow at a constant rate

c) the cost of equity may be less than or equal to the growth rate

d) the cost of equity remains constant

e) the dividend payout ratio remains constant

Solution:

The correct answer is **(b) the dividends paid by the company grow at a constant rate**. The constant growth model, or Gordon Growth Model, is a method of valuing a stock that assumes dividends will grow at a fixed, constant rate forever. It also assumes that the cost of equity is greater than the growth rate, and that the firm's required return remains constant.

Problem Statement: What is the intrinsic value of a Tk. 1,000 face value, 8% coupon paying perpetual bond if an investor's required rate of return is 6%? (Assume annual interest payments and discounting)

a) Tk. 1,333.33

b) Tk. 1,000

c) Tk. 750

d) Tk. 75.47

e) cannot be determined

Solution:

The intrinsic value of a perpetual bond (or consol) is calculated by dividing the annual coupon payment by the investor's required rate of return. The face value is only used to calculate the coupon payment.

Annual Coupon Payment = Face Value $\times$ Coupon Rate

= Tk. $1,000 \times 8\% = \text{Tk. } 80$

Intrinsic Value = $\frac{\text{Annual Coupon Payment}}{\text{Required Rate of Return}} = \frac{80}{0.06} = \text{Tk. } 1,333.33$

The correct answer is **(a) Tk. 1,333.33**.

Problem Statement: Sorbond Industries has a beta of 1.45. The risk-free rate is 8 percent and the expected return on the market portfolio is 13 percent. The company currently pays a dividend of Tk. 2 a share, and investors expect it to experience a growth in dividends of 10 percent per annum for many years to come. Required: (i) What is the stock's required rate of return according to the CAPM? (ii) What is the stock's present market price per share, assuming this required return? (iii) What would happen to the required return and to market price per share if the beta were 0.80? (Assume that all else stays the same.)

Solution:

i. Required rate of return (CAPM):

We use the Capital Asset Pricing Model formula to find the required rate of return ($k_e$).

$k_e = R_f + \beta \times (R_M - R_f)$

Given: $R_f = 8\%$, $R_M = 13\%$, $\beta = 1.45$.

$k_e = 0.08 + 1.45 \times (0.13 - 0.08) = 0.08 + 1.45 \times 0.05 = 0.08 + 0.0725 = 0.1525$ or $15.25\%$

The required rate of return is **15.25%**.

ii. Present market price per share:

We use the Gordon Growth Model with the required return from part (i).

$P_0 = \frac{D_1}{k_e - g}$

Given: $D_0 = \text{Tk. } 2$, $g = 10\%$.

$D_1 = D_0 \times (1+g) = 2 \times 1.10 = \text{Tk. } 2.20$

$P_0 = \frac{2.20}{0.1525 - 0.10} = \frac{2.20}{0.0525} \approx \text{Tk. } 41.90$

The present market price is approximately **Tk. 41.90**.

iii. Impact of beta change:

If beta changes to 0.80, the new required return is:

$k_{e\_new} = 0.08 + 0.80 \times (0.13 - 0.08) = 0.08 + 0.80 \times 0.05 = 0.08 + 0.04 = 0.12$ or $12\%$

The new market price is:

$P_{0\_new} = \frac{2.20}{0.12 - 0.10} = \frac{2.20}{0.02} = \text{Tk. } 110.00$

The required return would **decrease** to 12%, and the market price per share would **increase** to Tk. 110.00.

Problem Statement: United Airlines will pay a Tk. 4 dividend next year on its common stock, which is currently selling at Tk. 100 per share. What is the market's required return on this investment if the dividend is expected to grow at 5% forever?

a) 12 percent

b) 9 percent

c) 7 percent

d) 5 percent

e) 4 percent

Solution:

We can use the Gordon Growth Model (or Dividend Discount Model) to find the required return ($k_e$).

$P_0 = \frac{D_1}{k_e - g}$

Given: $P_0 = \text{Tk. } 100$, $D_1 = \text{Tk. } 4$, $g = 5\% = 0.05$.

We rearrange the formula to solve for $k_e$:

$k_e = \frac{D_1}{P_0} + g = \frac{4}{100} + 0.05 = 0.04 + 0.05 = 0.09$ or $9\%$.

The market's required return is **(b) 9 percent**.

Problem Statement: Just today, Acme Rocket, Inc.'s common stock paid a Tk.1 annual dividend per share and had a closing price of Tk. 20. Assume that the market expects this company's annual dividend to grow at a constant 6 percent rate forever. Required: (i) Determine the implied yield on this common stock. (ii) What is the expected dividend yield? (iii) What is the expected capital gains yield?

Solution:

Given: $D_0 = \text{Tk. } 1$, $P_0 = \text{Tk. } 20$, $g = 6\% = 0.06$.

i. Implied yield:

The implied yield is the required rate of return, which we can find using the Gordon Growth Model formula:

$k_e = \frac{D_1}{P_0} + g$

First, we need to calculate $D_1$: $D_1 = D_0 \times (1+g) = 1.00 \times (1.06) = \text{Tk. } 1.06$

$k_e = \frac{1.06}{20} + 0.06 = 0.053 + 0.06 = 0.113$ or $11.3\%$

The implied yield is **11.3%**.

ii. Expected dividend yield:

The dividend yield is the next period's dividend divided by the current price.

$\text{Dividend Yield} = \frac{D_1}{P_0} = \frac{1.06}{20} = 0.053$ or $5.3\%$

The expected dividend yield is **5.3%**.

iii. Expected capital gains yield:

In the Gordon Growth Model, the capital gains yield is equal to the constant growth rate.

$\text{Capital Gains Yield} = g = 6\%$

The expected capital gains yield is **6%**.