WARM UP QUESTIONS for Exam 2, ACFI 601 

To study for the exam: Review the lecture slides and lecture problems, then review the end-of-chapter problems; and finally try the following questions. Qts. 1-9 are missing. Sorry!

 STOCK VALUATION:

10. DIV1 = $10, P1 = $60, K = .15. What is the current price? 
      a. $43.48 
      b. $52.17 
      c. $60.87 
Solution: This is in a simple time value problem!
                                                  DIV1 + P1         10 + 60 
               Formula:             P = --------------- = ---------- 
                                                     (1+r)^1         (1+.15)^1 

 12. Suppose you are willing to pay $30 today for a share of stock which 
      you expect to sell at the end of one year for $32. If you require an 
      annual rate of return of 12 percent, what must be the amount of the 
      annual dividend which you expect to receive at the end of Year 1? 
           SAME FORMULA AS IN 10 above.
      a. $2.25
      b. $1.00 
      c. $1.60 
      d. $3.00 
      e. $1.95 

13.  Other things being equal, which of the following factors may cause an increase in the market price of a security? 
 a. An increase in the risk aversion of the market. 
 b. A decrease in the risk aversion of the market.  (Rm -Rf) decreases, so the required rate decreases; price increases. 
 c. An increase in the risk-free rate of return. 
 d. An increase in the stock's beta. 

 14.  Other things being equal, which one of the following would be consistent with a relatively low P/E ratio for a  firm? 

 a.  The stock’s beta is high (i.e., it is a very risk stock).
 b.  The growth rate of earnings is high. 
 c. The debt/equity ratio is low and the debt is rated AAA. (That is: Risk is low.)

                    P/E is a POS function of growth and ROE, but a NEG function of risk.

15. A share of common stock paid a dividend of $2.00 yesterday. If the 
      expected long-run growth rate for this stock is 15 percent, and if 
      investors require a 19 percent rate of return, what is the price of 
      the stock?  NOTE:  JUST PAID means "Last Dividend." DIV1= 2.00*(1+.15).
       a. $57.50 
      b. $62.25 
      c. $71.86 
      d. $64.00 
      e. $44.92 

Solution: 
Plug into the following: 
         Div1
P =  -------------
          k - g

16. Calculate the standard deviation of the expected returns, given the  following distribution of rates of returns: 

                        Probability            Return 
                            0.3                  35% 
                            0.4                  45% 
                            0.3                  55% 
 a.  7.74% 
 b.  8.95% 
 c. 31.00% 
 d. 59.91% 

17. Inflation, recession, and wars are economic/political events which are characterized as 

 a. Company specific risk that can be diversified away. 
 b. Market risk
 c. Systematic risk that can be diversified away. 
 d. Diversifiable risk. 

18. If investors suddenly became more averse to risk, the Security Market Line (SML) would probably: 
 a.  change in intercept but not slope 
 b.  change in intercept and slope 
 c.  change in slope, but not in intercept (it'll have a steeper slope!)
 d.  become non-linear 
 e.  none of the above. 

19. If two stocks were perfectly positively correlated: 
    a.  there would be no need to include both in a portfolio since they 
         would contribute nothing to diversification 
    b.  they would be the perfect stocks to form a two-stock portfolio 
         since all risk is diversified away 
    c.  they would have to sell at the same price 
    d.  they would have to sell at different prices 
    e.  none of the above. 

20. Other things remaining equal, a decrease in the slope of the Security Market Line (it becomes flatter) will: 
a.  reduce the required return 
b.  change the risk-free rate of return 
c.  alter the betas associated with stocks 
d.  increase the required return 

21. Diversification of risk by holding securities in portfolios: 
    a.  eliminates the market risk of holding securities 
    b.  increases the expected level of returns 
    c.  reduces the variability of the future cash flows. (this is the best answer here in this qt.)

22. If the expected rate of return on a stock is above the security market line, this is a disequilibrium situation. In moving towards equilibrium, the price of the stock should: 
    a.  increase (Undervalued, so people rush to buy the stock; as a result, its price will increase.)
    b.  decrease 
    c.  remain the same. 

23. According to the CAPM, the only portion of the risk which is relevant in requiring a rate of return is: 
    a.  market risk only 
    b.  unique risk only 
    c.  both market risk and unique risk 
   d. neither market risk nor unique risk. 

24. Portfolio A is fully diversified and has a beta of 2.  Portfolio B is  poorly diversified and has a beta of 1.  Which of the following statements must be true about these portfolios? 

 a.  A has less market risk than B. 
 b.  The required return on A will be greater than that on B.  (The required rate is a function of BETA!)
 c.  The required return on B will be greater than that on A. 

Required rate is a function of BETA. So, A cannot have less market risk as market risk is indicated by BETA!

25. Asset J has an expected return of 25% and a beta of 2.  The T-bill rate is 8%; the return on the market portfolio is 14%.  What is the asset's required rate? 

a. 10% 
b. 6.6% 
c. 5.4% 
d. 13.4%
e. 20%   (= .08 + .06 * 2)

26. From this information (qt above), you would conclude that: 

a.  Asset J is overpriced. 
b.  Asset J is not very risky. 
c.  Asset J is undervalues. (Expected to earn 25% when its fair return, given its beta, is 20%.)
d. Asset J is likely to be a food company. 

To remember: Draw the SML and specify on the graph: Where does the RF plot? Where the Mkt Portfolio plots? Its Return? Where an overvalued asset plots? Where a fairly valued asset (one with expected return = required return)? 

More question... There may be some repeats!
27. You have developed the following data on three stocks: 

                Stock       Std Dev             Beta 
                 A              0.15                0.79 
                 B              0.25                 0.61 
                 C              0.20                 1.29 

If you are a risk minimizer, you should choose Stock _____ if it is to be held in isolation (and investor has no other assets) and Stock _____ if it is to be held as part of a well-diversified portfolio. 
a. A; A 
b. A; B 
c. B; A 
d. C; A 
e. C; B 
Answer: (Lowest STD; lowest Beta)

28. Stock X and the "Market" had the following returns during the last two years, and the same relative volatility is expected to exist in the future: 
                   Year          Market           Stock X 
                      1             10.0%           15.0% 
                      2               5.0                5.0 
                      3               0.0             - 5.0 
       What is Stock X's beta? 
a. -1.0 
b.  0.5 
c.  0.0 
d.  1.0 
e.  2.0 

29. The expected return on the market portfolio is 12%, and the risk-free rate of return is 4%. An investment has a beta 
of .6.  Its expected return is 8%. 
a. This is a good investment because its expected return exceeds the market rate of return. 
b. This is a good investment because its expected return exceeds its required rate of return. 
c. This is a bad investment because its expected return is less than its required rate of return.

ANS: Find the required rate from CAPM and compare against the expected rate (IRR) of 8%.

30. Inflation, recession, and wars are economic/political events which are characterized as 
a. Company specific risk that can be diversified away. 
b. Market risk.
c. Unique risk. 
d. Diversifiable risk. 

31.  Diversification of risk by holding securities in portfolios: 
a.  eliminates the market risk of holding securities 
b.  increases the expected level of returns of the portfolio 
c.  decreases the expected level of returns of the portfolio 
d.  reduces risk only if assets were perfectly positively correlated 
e.  reduces the unique (unsystematic) risk of the portfolio 

32. Firms operating in this industry are characterized by low beta: 
a.  Automobile manufacturing 
b.  Electric power 
c.  Dow Jones Industrials 
d.  Computer software 

33. If two stocks were perfectly positively correlated: 
a.  there would be no need to include both in a portfolio since they would contribute nothing to diversification 
b.  they would be the perfect stocks to form a two-stock portfolio since all risk is diversified away. 
c.  they would have to sell at the same price 
d.  they would have to sell at different prices 
e.  none of the above. 

34.  Which of the following would be the WORST stock to be combined with Stock X if the objective was to minimize the portfolio’s risk? 
a.  a stock with a correlation coefficient of -1 with X. 
b.  a stock with a correlation coefficient of 0.0 with X. 
c.  a stock with a correlation coefficient of +1 with X. 
d.  a stock with a correlation coefficient of +2 with X. (ticky! Correlation coef. cannt be larger than +1) 

Cap Budgeting: An important topic and you'd need to do a lot on your own. (Sorry!) Below are 2-3 of the easier questions. There will be questions on NPV, IRR (calculating them and also reading them off a graph of NPV profiles). Review the handout problem we did in class - the one you tried in Excel and also Kangaroo Corp's.

35. Under the straight line method (SLM), Tomato Corp. wrote off $2,000 as depreciation, but under the ACRS method it reported a depreciation expense of $3,500.  If Tomato's marginal corporate income tax rate was 30%, the additional tax shield of ACRS over SLM would be: 
a. $150 
b. $300 
c. $350 
d. $450 

36. Projects A and B have the following cash flows: 

              t=0        t=1        t=2        t=3       t=4 
     A   -180      +100       +80       +80       +50 
     B   -200         +70      +70       +60       +60 

     If a company acceptes projects with a payback period of less than 2 years, 
     which projects would it accept? (For your to figure out!)

     a. Project A. 
     b. Project B. 
     c. Both. 
     d. Neither. 

37.  The project's IRR is 20%.  You would accept this project if the opportunity cost of capital (required rate) was _______  20%.  

a.  Greater than  
b.  Less than * 
c.  Equal to  

All else we said in class today... 

SAMPLE Problems: 

1. (Emphasis added) The Test Company is evaluating the proposed acquisition of a new milling machine.  The machine’s base price is $108,000, and it would cost another $12,500 to modify it for special use by your firm.  The machine falls into the MACR 3-year class, and it would be sold after 3 years for $65,000.  (Look up the book for MACRS recovery allowance percentages.)  The machine would require an increase in net working capital (inventory) of $5,500.  The milling machine would have no effect on revenues, but it is expected to save the firm $44,000 per year in before-tax operating costs, mainly labor.  Test’s marginal tax rate is 35 percent.  
a. What is the net cost of the machine for capital budgeting purposes? (That is, what is the Year 0 net cash flow?)  
b. What are the net operating cash flows in Years 1, 2, and 3?  
c. What is the terminal year cash flow?  
d. If the project’s cost of capital is 12 percent, should the machine be purchased?  

2.  (CFA Test Question) Historically, RR Corporation has retained 60% of its profits in the business and generated a rate of return on equity of 12.5%.  This is expected to continue.  The risk-free rate is 8%, RPm (market risk premium) is 5%, and beta is about 1.3.  The present dividend (paid yesterday) was $2.50, and the stock is selling at $45.  Should you buy or sell the stock? Emphasis added. 

P =  Div1/ (r - g)  

g= roe * Plaowback = .125 * .60 = 7.5%  
r = Rf + (Rm - Rf) * Beta = Rf + (RPm) * Beta = .08 + (.05)*1.3 = 14.5%  
DIV1 = DIV0 (1+g) = 2.50 * (1 + .075) = 2.6875  
P = $2.6875 / (.145 - .075) = $38.  
NPV = - $45 + 38 = Negative NPV. Don't buy!  

Can you use the IRR rule to find out id RR is over- (under-) valued? Where does it plot of the SML graph?  

3. The Treasury bill rate is 4%, and the expected return on the market portfolio is 12%. On the basis of Capital Asset Pricing Model:  

a. Draw a graph showing how the expected return varies with beta – i.e., draw the SML and label the graph. 
b. What is the risk premium of the market? 
c. What is the required return on an investment with a beta of 1.5? 
d. If a investment with a beta of .8 offers an expected return of 9.8%, does it have a positive NPV?2 
 
 
On the Calculation of Yield to Maturity (YTM) 

ABC’s $1,000, 9% par bonds have ten years remaining to maturity.  These are A-rated and each bond currently sells for $938.50.  Assume the bonds pay coupons annually. 

A.  What is the expected rate of return (yield) if they are held to maturity (hence YTM)? 

That is: 

Par value = $1,000 
Current price = $938.50 
Annual coupon = $90 
Term to maturity = 10 years 

YTM or K = ? 

Year             0                           1                          2                     9                       10 
                     |-------------------|------------------|---- . . .  .  . --|------------------| 
Cash Flow  -$938.50             90                          90                  90                   90+1,000 

YTM = that “r” which gives an NPV = 0, or “r” that gives Market Price = PV of inflows. 

Using the general relationships, we know that YTM must be higher than 9% (Coupon rate) because the bond is bought at less than $1000.  (Nominal return is 9% from coupons but we also buy the bond at a discount!) 

Will 10% discount rate make the PV of the inflows (right hand side of the following equation) equal to the left ($938.50)? 

$938.50 = $90 (PV interest factor, 10-yr annuity) + $1,000 (PV factor, 10-yr single sum) 

In other words: Does 10% give an NPV of zero if we re-write the equation as: 

$90 (PV interest factor, 10-yr annuity) + $1,000 (PV factor, 10-yr single sum) - $938.50 = ? 

(Note the YTM and the IRR are exactly the same concepts.  Whether you pay $938.50 for a bond or a piece of equipment, the rate that gives zero NPV gives the effective rate of return - call YTM in case of a bond and  IRR in case of a capital asset. 

Logically, we start our trial with 10%.  Try 10%.  Find the PVIF and PVIFA for 10% an 10 years.  Plug them in the above equation and you will get an NPV of zero.   So, YTM = 10 %. 

B.  What is the expected yield to maturity if each bond sold for $1,000? 

More or less than 9%?  The general rule says that a bond selling for $1,000 has a YTM equal to its coupon rate - i.e., 9%.