Assume that Temp Force is a constant growth company whose last dividend was $2.0

Question

Assume that Temp Force is a constant growth company whose last dividend was $2.00 and whose dividend is expected to grow indefinetely at a 6% rate. Discount rate is 13%. What is the firm's current intrinsic stock price? What are the expected dividend yield, the expected capital gains yield, and the expected totareturn during the first year? Now assume that the stock is currently selling at $30.19, what is its expected rate of return? What would the stock price be if the dividends were expected to have sero growth? Is the stock price based more on long-erm or short-erm expecctations? Answer this by finding the percentage of Temp Force's current stock price that is based on dividends expected more than 3 years in the future. Supose Temp Force is expected to experience zero growth during the first 3 years and then to resume its steady-state growth of 6% in year 4. What is the stock's intrinsicvalue now? What is its expected dividend yield and its capital gains yield in Year 1 and Year 4?

Explanation / Answer

Temp Force is a constant growth stock, and its dividend is expected to grow at a constant rate of 6 percent per year. Expressed as a time line, we have the following setup. Just enter 2 in your calculator; then keep multiplying by 1 + g = 1.06 to get D1, D2, and D3: 0 1 2 3 4 | | | | | D0 = 2.00 2.12 2.247 2.382 1.88 1.76 1.65 . . . d. 2. What is the firm’s current stock price? Answer: We could extend the time line on out forever, find the value of Temp Force’s dividends for every year on out into the future, and then the PV of each dividend, discounted at r = 13%. For example, the PV of D1 is $1.76106; the PV of D2 is $1.75973; and so forth. Note that the dividend payments increase with time, but as long as rs > g, the present values decrease with time. If we extended the graph on out forever and then summed the PVs of the dividends, we would have the value of the stock. However, since the stock is growing at a constant rate, its value can be estimated using the constant growth model: = = = = $30.29. d. 3. What is the stock’s expected value one year from now? Answer: After one year, D1 will have been paid, so the expected dividend stream will then be D2, D3, D4, and so on. Thus, the expected value one year from now is $32.10: = = = = $32.10. d. 4. What are the expected dividend yield, the capital gains yield, and the total return during the first year? Answer: The expected dividend yield in any year n is Dividend Yield = , While the expected capital gains yield is Capital Gains Yield = = r - . Thus, the dividend yield in the first year is 10 percent, while the capital gains yield is 6 percent: Total return = 13.0% Dividend yield = $2.12/$30.29 = 7.0% Capital gains yield = 6.0% e. Now assume that the stock is currently selling at $30.29. What is the expected rate of return on the stock? Answer: The constant growth model can be rearranged to this form: s= . Here the current price of the stock is known, and we solve for the expected return. For Temp Force: s= $2.12/$30.29 + 0.060 = 0.070 + 0.060 = 13%. f. What would the stock price be if its dividends were expected to have zero growth? Answer: If Temp Force’s dividends were not expected to grow at all, then its dividend stream would be a perpetuity. Perpetuities are valued as shown below: 0 1 2 3 | | | | 2.00 2.00 2.00 1.77 1.57 1.39 . . . P0 = 15.38 P0 = PMT/r = $2.00/0.13 = $15.38. Note that if a preferred stock is a perpetuity, it may be valued with this formula. g. Now assume that Temp Force is expected to experience supernormal growth of 30 percent for the next 3 years, then to return to its long-run constant growth rate of 6 percent. What is the stock’s value under these conditions? What is its expected dividend yield and capital gains yield be in year 1? In year 4? Answer: Temp Force is no longer a constant growth stock, so the constant growth model is not applicable. Note, however, that the stock is expected to become a constant growth stock in 3 years. Thus, it has a nonconstant growth period followed by constant growth. The easiest way to value such nonconstant growth stocks is to set the situation up on a time line as shown below: 0 1 2 3 4 | | | | | 2.600 3.380 4.394 4.658 2.301 2.647 3.045 46.116 54.109 Simply enter $2 and multiply by (1.30) to get D1 = $2.60; multiply that result by 1.3 to get D2 = $3.38, and so forth. Then recognize that after year 3, Temp Force becomes a constant growth stock, and at that point can be found using the constant growth model. is the present value as of t = 3 of the dividends in year 4 and beyond. With the cash flows for D1, D2, D3, and shown on the time line, we discount each value back to year 0, and the sum of these four PVs is the value of the stock today, P0 = $54.109. The dividend yield in year 1 is 4.80 percent, and the capital gains yield is 8.2 percent: Dividend yield = = 0.0480 = 4.8%. Capital gains yield = 13.00% - 4.8% = 8.2%. During the nonconstant growth period, the dividend yields and capital gains yields are not constant, and the capital gains yield does not equal g. However, after year 3, the stock becomes a constant growth stock, with g = capital gains yield = 6.0% and dividend yield = 13.0% - 6.0% = 7.0%. h. Is the stock price based more on long-term or short-term expectations? Answer this by finding the percentage of Temp Force current stock price based on dividends expected more than three years in the future. Answer: = 85.2%. Stock price is based more on long-term expectations, as is evident by the fact that over 85 percent of temp force stock price is determined by dividends expected more than three years from now.

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