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Nonconstant Dividends Bucksnort, Inc., has an odd dividend policy. The company has just paid a dividend of \(\$ 10\) per share and has announced that it will increase the dividend by \(\$ 3\) per share for each of the next five years, and then never pay another dividend. If you require an 11 percent return on the company's stock, how much will you pay for a share today?

Short Answer

Expert verified
The current share price of Bucksnort, Inc. is equal to the present value of the future dividend payments. Given its odd dividend policy and a required rate of return of 11%, the present value of the dividends is $67.89. Therefore, you would be willing to pay $67.89 for a share of Bucksnort, Inc. stock today.

Step by step solution

01

1. Understand the dividend payment pattern

The company has just paid a dividend of \(10 (D_0)\) and has announced that it will increase the dividend by \(3\) per share for each of the next five years. So, the dividend payments are as follows: 1. Dividend in 1 year (D_1) = \(10 + 3 = \)13 2. Dividend in 2 years (D_2) = \(13 + 3 = \)16 3. Dividend in 3 years (D_3) = \(16 + 3 = \)19 4. Dividend in 4 years (D_4) = \(19 + 3 = \)22 5. Dividend in 5 years (D_5) = \(22 + 3 = \)25
02

2. Calculate the present value of the dividends

As the required rate of return is 11%, we'll use this discount rate to calculate the present value (PV) of the future dividend payments: PV = D_1 / (1+r)^1 + D_2 / (1+r)^2 + D_3 / (1+r)^3 + D_4 / (1+r)^4 + D_5 / (1+r)^5 where r is the required rate of return (11% or 0.11). Plugging in the numbers: PV = \(13 / (1+0.11)^1 + 16 / (1+0.11)^2 + 19 / (1+0.11)^3 + 22 / (1+0.11)^4 + 25 / (1+0.11)^5\)
03

3. Calculate the present value of the dividends

Solve the equation for the present value (PV): PV = \(13 / 1.11 + 16 / 1.2321 + 19 / 1.3675 + 22 / 1.5189 + 25 / 1.6856\) PV = \(11.71 + 12.98 + 13.88 + 14.49 + 14.83\) PV = $67.89
04

4. Find the current share price

The current share price is equal to the present value of the future dividend payments. Therefore, the price you would be willing to pay for a share of Bucksnort, Inc. stock today is: Share price = PV = $67.89

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Present Value
Present value refers to the current worth of a future sum of money or stream of payments, given a specified rate of return. It reflects the principle of time value of money which holds that a dollar today is worth more than a dollar in the future due to its potential earning capacity. Calculating the present value of future dividends involves discounting each of those future cash flows back to their value today. This is essential in finance for making informed investment decisions.
To compute the present value of a series of future dividends, like in Bucksnort, Inc.'s case, you apply a discount rate, which in this scenario is the required rate of return. By discounting the future dividends of $13, $16, $19, $22, and $25 using the 11% rate, we determine their worth in today's terms, adding them up to find the total present value at $67.89.
Dividend Policy
A company's dividend policy outlines how it distributes its earnings to shareholders. Dividends can be issued as cash payments, shares of stock, or other forms. The policy affects how much money shareholders receive directly and speaks to how much trust the company has in reinvesting profits back into its business.
  • Odd Dividend Policy: Bucksnort, Inc. follows an "odd" dividend policy where it pays increasing dividends for a limited period and then ceases dividends entirely. This policy may attract certain investors looking for short-term dividend returns rather than long-term growth.
  • Implications: It suggests a lack of future expansion plans or using earnings for growth, which might deter long-term investors who prefer companies with continual dividends or growth prospects.
Understanding such policies helps investors predict future cash flows from dividends, crucial for accurate stock valuation.
Required Rate of Return
The required rate of return is the minimum percentage return an investor expects to receive from an investment to justify the risk taken. It factors in the opportunity cost of capital, inflation, and risk level associated with the investment.
For Bucksnort, Inc., the required rate is 11%. This means investors demand at least an 11% return annually to compensate for the potential risks involved in investing in the company's stock.
  • Calculation Use: This rate is critical in the present value calculation, serving as the discount rate. Higher required returns decrease the present value of future dividends, thus affecting the stock price investors are willing to pay.
  • Investor's Perspective: It reflects how much return investors need to feel comfortable risking their capital, balancing between desired profitability and acceptable risk.
Understanding this rate is vital for evaluating whether an investment meets personal financial goals and risk appetite.
Stock Valuation
Stock valuation involves determining the intrinsic value of a company's shares, thereby guiding investment decisions. The aim is to calculate what a stock is truly worth based on current and future financial metrics, like dividends.
Bucksnort, Inc.'s valuation relies heavily on the calculation of the present value of its expected dividends, reflecting what an investor should pay today. This approach treats the sum of the present value of all future dividends as the fair price for the stock today.
  • Valuation Techniques: Common methods include discounted dividend models (like our example), and other approaches considering earnings, cash flow, or asset values.
  • Impact of Dividends: Nonconstant or unconventional dividend patterns, like Bucksnort's, necessitate more complex valuations to accurately reflect the fleeting dividend cash flows.
Accurate stock valuation ensures investors make informed decisions, basing the purchase price on calculated, realistic future cash returns.

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Most popular questions from this chapter

Nonconstant Dividends North Side Corporation is expected to pay the following dividends over the next four years: \(\$ 9, \$ 7, \$ 5\), and \(\$ 2.50\). Afterwards, the company pledges to maintain a constant 5 percent growth rate in dividends forever. If the required return on the stock is 13 percent, what is the current share price?

Capital Gains versus Income Consider four different stocks, all of which have a required return of 20 percent and a most recent dividend of \(\$ 4.50\) per share. Stocks \(W, X\), and \(Y\) are expected to maintain constant growth rates in dividends for the foreseeable future of 10 percent, 0 percent, and -5 percent per year, respectively. Stock \(Z\) is a growth stock that will increase its dividend by 30 percent for the next two years and then maintain a constant 8 percent growth rate thereafter. What is the dividend yield for each of these four stocks? What is the expected capital gains yield? Discuss the relationship among the various returns that you find for each of these stocks.

Dividend Growth Four years ago, Bling Diamond, Inc., paid a dividend of \(\$ 1.20\) per share. Bling paid a dividend of \(\$ 1.93\) per share yesterday. Dividends will grow over the next five years at the same rate they grew over the last four years. Thereafter, dividends will grow at 7 percent per year. What will Bling Diamond's cash dividend be in seven years?

Negative Growth Antiques \(R\) Us is a mature manufacturing firm. The company just paid a \(\$ 12\) dividend, but management expects to reduce the payout by 6 percent per year, indefinitely. If you require an 11 percent return on this stock, what will you pay for a share today?

Stock Valuation Most corporations pay quarterly dividends on their common stock rather than annual dividends. Barring any unusual circumstances during the year, the board raises, lowers, or maintains the current dividend once a year and then pays this dividend out in equal quarterly installments to its shareholders. 1\. Suppose a company currently pays a \(\$ 3.60\) annual dividend on its common stock in a single annual installment, and management plans on raising this dividend by 5 percent per year indefinitely. If the required return on this stock is 14 percent, what is the current share price? 2\. Now suppose that the company in (a) actually pays its annual dividend in equal quarterly installments; thus, this company has just paid a \(\$ .90\) dividend 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 or not you think that this model of stock valuation is appropriate.

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