Question

a. Suppose a company currently pays an annual dividend of $3.20 on its common stock in a single annual installment, and management plans on raising this dividend by 6 percent per year indefinitely. If the required return on this stock is 12 percent, what is the current share price?

b. Now suppose the company in (a) actually pays its annual dividend in equal quarterly installments; thus, the company has just paid a dividend of $.80 per share, as it has for the previous three quarters. What is your value for the current share price now? (Hint: Find the equivalent annual end-of-year dividend for each year.) Comment on whether you think this model of stock valuation is appropriate.

Please Explain in Full How you got everything PLEASE

Answer 1

This question requires application of constant growth dividend discount model, according to which the current value of share is present value of all dividends expected in future.

Part a

According to constant growth dividend discount model,

where V₀ is the value of share today, r is the required rate of return and g is the growth rate.

D₁ = D₀ * (1 + g) = $3.20 * (1 + 6%) = 3.392

Value of share today, V₀ = 3.392/(12% - 6%) = $56.53 --> Answer

Part b

When the company will pay quarterly dividend, then the expected dividend per quarter would be = $3.20 * (1 + 6%)/4 = $0.848

Now, we need to find equivalent annual dividend for this quarterly dividend. For this, you would need to assume that the quarterly dividend that you receive would be reinvested at market rate of return, which is 12% in this question. We first need to calculate the quarterly rate for an effective rate of 12%.

(1 + r)⁴ = (1 + 12%)

(1 + r)⁴ = 1.12

r = 1.12^(1/4) -1 = 0.0287

Now, in order to calculate the effective annual dividend, we need to use the FV of annuity formula, according to which:

P = 0.848, r = 2.87% (quarterly), n = 4 (1 year = 4 quarters)

FV of annuity = 0.848 * 4.1755 = $3.54 --> Equivalent annualdividend

Now, using the same concept as we used in part a,

Value of Share = 3.54/(12% - 6%) = $59.01 --> Answer