Question

An investor bought a stock for $13 (at t=0) and one year later it paid a $0 dividend (at t=1). Just after the dividend was paid, the stock price was $23 (at t=1). Inflation over the past year (from t=0 to t=1) was 8% pa, given as an effective annual rate. Which of the following statements is NOT correct? The stock investment produced a:

Select one:
a. Nominal capital return of 76.923077% pa.
b. Nominal income return of 0% pa.
c. Real capital return of 91.076923% pa.
d. Real income return of 0% pa.
e. Real total return of 63.817664% pa.

Answer 1

The incorrect statement is option 'c' which claims the real capital return is 91.076923% pa. The proper calculation shows the real capital return is actually 63.817664% pa, when adjusting for an 8% inflation rate.

Step-by-step explanation:

The question pertains to calculating the nominal and real returns on a stock investment, including concepts such as capital return, income return, and total return. An investor bought a stock for $13 and sold it a year later for $23 while receiving a $0 dividend. With an inflation rate of 8%, we need to determine which statement about the stock's returns is incorrect. The nominal capital return is calculated as (($23 - $13) / $13) * 100% = 76.923077% pa. Since no dividend was paid, the nominal income return is indeed 0% pa. The real capital return can be approximated using the Fisher equation: (1 + nominal rate) / (1 + inflation rate) - 1, which for the capital gain is (1 + 0.76923077) / (1 + 0.08) - 1 = 63.817664% pa, showing option 'c' as incorrect. The real income return remains 0% pa because there were no dividends. Lastly, the real total return should combine both capital gains and income returns after adjusting for inflation, but this calculation requires the correct real capital return first.