3. If the required real annual rate of interest on one year Treasury Bills is 5%

Question

3. If the required real annual rate of interest on one year Treasury Bills is 5% and the expected domestic inflation rate is 8%, based upon the exact relationship between real and nominal rates, what is the required nominal risk-free rate of interest?

6. A share very recently paid a dividend of $4.00. If the dividend is expected to grow at an annual rate of 5% and the required return is 15%, what is the intrinsic value of the share?

7. A share is expected to pay a dividend of $4.00. If the dividend is expected to grow at an annual rate of 5% and the required return is 15%, what is the intrinsic value of the share?

11. You buy 100 shares of Pink Bismol, Inc. stock at $35 per share on a margin of 50 percent. If the price of Pink Bismol stock immediately rises to $50 per share, what is your percentage return? In other words, what is your percentage gain on the initial equity?

16. If you invest 35% of your holdings in a security with an expected return of 8% and the remainder in a security with an expected return of 13%, what is the expected return on your portfolio?

17. Suppose that we have identified two important systematic risk factors: the growth rate of gross domestic product, labeled GDP, and the 30-year bond interest rate, labeled BR. Whole Hog Farms, Inc. has a beta 1.1 on GDP and 0.9 on BR. Whole Hog has an expected stock return of 12%. GDP is expected to be 5.5% and BR 6%. If gross domestic product grows by 3% and the 30-year bond rate turns out to be 9%, and no unexpected news specifically concerning Whole Hog occurs, within the Arbitrage Pricing Theory framework, what is your best guess for the realized rate of return on Whole Hog stock?

18. Assume two factors have been identified as the important sources of systematic risk: the growth rate in industrial production, IP, and the rate of change in the price of West Texas crude oil, OIL. Suppose also that the expected return on a well-diversified IP factor portfolio, E(rIP) is 8% and E(rOIL) is 12%. Now consider the Low Ride Automobile Co. with ?IP = 1.3 and ?OIL = -0.2. Assume rf = 6%. Within an Arbitrage Pricing Theory framework, what is the fair rate of return on Low Ride?

28. A portfolio has a beta of 1.4. The portfolio is made up of securities X and Y. 40% of the portfolio is in X and 60% in Y. The beta of security Y is 0.9. What is the beta of security X?

- Selected answers:

3. 13.4%
6. $42
7. $40

11. 85.7%

14. 1.281
16. 11.25%
17. 11.95%
18. 7.4%
28. 2.15

Explanation / Answer

3. (1 + Nominal) = (1 + Real) x (1 + Inflation rate)

So,

(1 + Nominal) = 1.05 x 1.08 = 1.134

So Nominal rate = 13.4%

6 & 7.

Share value = (Dividend x (1 + growth rate) / (required return - growth rate)

= $4 x 1.05 / (0.15 - 0.05) = $ 42

11. Gain = ($50 - $35) / $35 = 42.86%

16. Portfolio expected return = 35% x 8% + 65% x 13% = 2.8% + 8.45% = 11.25%

28. Portfolio Beta = weighted average beta of both securities

So

1.4 = 40% x Beta(X) + 60% x 0.90

Or Beta(X) = 1.4 - 0.54 = 0.86

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