Question

In: Finance

17. a. Equity Risk Premium – the return that investors expect to receive above the return...

17. a. Equity Risk Premium – the return that investors expect to receive above the return of the risk-free asset for investing into a risky asset. What does this mean?

b. How do we use the Expected Rate of Return from our investment to discount the expected cash flows from our investment to determine the present value (intrinsic value)? Please calculate the fair value of an investment with a dividend payout ratio of 40%, Next year’s dividend expectations of $2.40, growth rate of 3.0%, Risk-free rate is 2.4%, beta is 0.9 and ERP is 5.0%.

c. What is the difference between an Arithmetic Mean (Average) and a Geometric Mean (Average)? a. Why should investors know the difference?

d. Describe why a person must take risk to gain the potential for a higher return than they would receive for investing into the risk-free asset?

e. Be prepared to discuss which investment a reasonable person would choose to invest into over the next 5 years and why? a. Investment A has a mean return of 6% and a standard deviation of 12%. b. Investment B has a mean return of 5% and a standard deviation of 9%.

Expert Solution

a. In order to accept the uncertainty associated with returns and for taking on systematic risk/market risk, unlike in the case of a risk free instrument, investors expect a higher return. The Risk premium they expect is equal to the expected return on market minus the risk free rate of return.

b.Expected return on the stock = cost of equity

As per CAPM,

Expected Return = RFR + (Beta *(Market Risk Premium)) = 2.4 +4.5 = 6.9%

Fair value = D1 / (r-g) = 2.4 / (.069 - .03) = $61.54

c. Arithmetic mean is a simple average whereas geometric mean take into account the impact of compounding. In Finance we are generally concerned with the CAGR or compounded annual growth rate as it is assumed that money made is reinvested into the market. That is why it is important for investors to know it. If returns in year 1 is 2% and that in year 2 is 3%,

AM = (2+3) /2 = 2.5%

GM = sqrt (1.02 * 1.03) -1 = 2.49%

d. Investor has got to embrace uncertainty to make higher returns. Higher returns are a compensation of added risk taken.

e. Assuming the RFR = 0,

Sharpe ratio of investment A = 6 /12 = .5

Sharpe ratio of investment B = 5 /9 = .55

Therefore from risk-return trade off perspective (maximizing return for given risk), investor would prefer option B as it has a higher Sharpe ratio

jeff jeffy answered 1 month ago

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