Corporate Finance Study Notes

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Solutions to Chapter 10 Introduction to Risk, Return, and the Opportunity Cost of Capital capital gain + dividend ($44 − $40) + $2 = = 0.15 = 15.0% initial share price $40

1.

Rate of return =

Dividend yield = dividend/initial share price = $2/$40 = 0.05 = 5% Capital gains yield = capital gain/initial share price = $4/$40 = 0.10 = 10%

2.

Dividend yield = $2/$40 = 0.05 = 5% The dividend yield is unaffected; it is based on the initial price, not the final price. Capital gain = $36 – $40 = −$4 Capital gains yield = –$4/$40 = –0.10 = –10% capital gain + dividend ($38 − $40) + $2 = = 0% initial share price $40 1 + nominal rate of return 1+ 0 −1 = − 1 = −0.0385 = −3.85% 1 + inflation rate 1 + 0.04

3.

a.

Rate of return =

Real rate of return =
Rate of return =

b.

($40 − $40) + $2 = 0.05 = 5% $40 1 + nominal rate of return 1.05 −1 = − 1 = 0.0096 = 0.96% 1 + inflation rate 1.04

Real rate of return = Rate of return =

c.

($42 − $40) + $2 = 0.10 = 10% $40 1 + nominal rate of return 1.10 −1 = − 1 = 0.0577 = 5.77% 1 + inflation rate 1.04

Real rate of return =

10-1

4.

Real rate of return =

1 + nominal rate of return −1 1 + inflation rate 1.95 − 1 = 0.0833 = 8.33% 1.80

Costaguana: Real return = U.S.: Real return =

1.12 − 1 = 0.0980 = 9.80% 1.02

The U.S. provides the higher real rate of return despite the lower nominal rate of return. Notice that the approximate relationship between real and nominal rates of return is valid only for low rates: real rate of return ≈ nominal rate of return – inflation rate This approximation incorrectly suggests that the Costaguanan real rate was higher than the U.S. real rate.

5.

We use the following relationship:
Real rate of return = 1 + nominal rate of return −1 1 + inflation rate

Asset class Treasury bills Treasury bonds Common stocks

Nominal rate of return 4.0% 5.3% 11.7%

Inflation rate 3.0% 3.0% 3.0%

Real rate of return 0.97% 2.23% 8.45%

6.

The nominal interest rate cannot be negative. If it were, investors would choose to hold cash (which pays a rate of return equal to zero) rather than buy a Treasury bill providing a negative return. On the other hand, the real expected rate of return is negative if the inflation rate exceeds the nominal return.

7. Average price of Quarter stocks in market 1 902.50 2 866.67 3 888.33 4 876.67 Index (using DJIA method) 100.00 96.03 98.43 97.14 Total market value of stocks 628,880 608,260 607,760 569,100 Index (using S&P method) 100.00 96.72 96.64 90.49

10-2

8.

a. b. c.

For the period 1900-2004, Average rate of return = 11.7% (See Table 10-1) For the period 1900-2004, Average risk premium = 7.6% (See Table 10-1) For the period 1900-2004, Standard deviation of returns = 20.0%. (See Table 10-5)

9.

a. Year 2000 2001 2002 2003 2004 b. c. Stock market return -10.89 -10.97 -20.86 31.64 12.62 T-bill return 5.89 3.83 1.65 1.02 1.20 Average Risk premium -16.78 -14.80 -22.51 30.62 11.42 -2.41 Deviation from mean -14.37 -12.39 -20.10 33.03 13.83 Squared deviation 206.4969 153.5121 404.0100 1,090.9809 191.2689 409.2538

The average risk premium was: -2.41% The variance (the average squared deviation from the mean) was 409.2538 (without correcting for the lost degree of freedom). Therefore: standard deviation = 409.2538 = 20.23%

10. In early 2004, the Dow was substantially more than three times its 1990 level. Therefore, in 2004, a 40-point movement was far less significant in percentage terms than it was in 1990. We would expect to see more 40-point days in 2004 even if market risk as measured by percentage returns is no higher than it was in 1990.

11.

Investors would not have invested in bonds during the period 1977-1981 if they had expected to earn negative average returns. Unanticipated events must have led to these results. For example, inflation and nominal interest rates during this period rose to levels not seen for decades. These increases, which...
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