Corporate Finance Study Notes

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