Corporate Finance: Question Security Market Line, Bond Valuation and Efficient Market Hypothesis


The expected return on DT Corporation is 15%, and its beta is 1.5. The risk - free rate is 3%, and the expected return on the market portfolio is 11%. Does the asset lie on, above, or below the Security Market Line (SML)? Explain.

Answer: 

To determine whether DT Corporation lies on, above, or below the Security Market Line (SML), we need to calculate the expected return based on the Capital Asset Pricing Model (CAPM) and compare it to the given expected return.

Given Data

  • Expected Return on DT Corporation (E(R)): 15%
  • Beta of DT Corporation (β): 1.5
  • Risk-Free Rate (R_f): 3%
  • Expected Return on the Market Portfolio (E(R_m)): 11%

Step 1: Calculate the Expected Return Using CAPM

The CAPM formula is:
E(R)=Rf+β×(E(Rm)Rf)
Where:
  • E(R) = Expected return of the asset
  • Rf = Risk-free rate
  • β = Beta of the asset
  • E(Rm)Rf = Market risk premium
Substituting in the values:
  1. Calculate the market risk premium:
E(Rm)Rf=11%3%=8%
  1. Now substitute into the CAPM formula:
E(R)=3%+1.5×8%
Calculating this gives:
E(R)=3%+12%=15%
  • The expected return calculated using CAPM is 15%, which matches the expected return provided for DT Corporation.

You are considering the purchase of a bond with a semi - annual coupon of RM40, ten years to maturity, a face value of RM1,000, and a current market price of RM1000.

(i) At what price will be the bond sell in the market in 6 months, immediately after the first coupon payment, if the stated annual yield on the bond (in six month) is 4 percent?

Answer:

To determine the price at which the bond will sell in the market in 6 months, immediately after the first coupon payment, we need to calculate the bond's price based on the yield and cash flows.

Given Information

  • Face Value (F): RM1,000
  • Semi-Annual Coupon Payment (C): RM40
  • Years to Maturity: 10 years
  • Current Market Price: RM1,000
  • Stated Annual Yield in 6 Months (YTM): 4% (which implies a semi-annual yield of 2%)

Step 1: Calculate the Cash Flows

After 6 months, you will receive the first coupon payment of RM40. The remaining cash flows after this payment will be:
  1. Remaining Coupon Payments: There are 19 remaining coupon payments of RM40 each.
  2. Face Value Payment: The face value of RM1,000 will be paid at the end of the 10 years.

Step 2: Calculate the Price of the Bond After 6 Months

The price of the bond can be calculated using the present value of future cash flows formula:
P=t=1nC(1+r)t+F(1+r)n
Where:
  • P = Price of the bond
  • C = Coupon payment (RM40)
  • r = Yield per period (0.02 for semi-annual)
  • n = Number of periods remaining

Cash Flows After First Coupon Payment

After receiving the first coupon payment, you have:
  • Remaining cash flows:
    • 19 coupon payments of RM40
    • Face value payment of RM1,000 at maturity (in 19 periods)

Step 3: Calculate Present Value of Remaining Cash Flows

  1. Present Value of Remaining Coupon Payments:
    • The present value of an annuity formula is used here:
PVcoupons=C×(1(1+r)nr)
Substituting in values:
PVcoupons=40×(1(1+0.02)190.02)
Calculating:
PVcoupons=40×(1(1.02)190.02)
Calculating (1.02)19:
(1.02)190.6694
Now substituting back:
PVcoupons=40×(10.66940.02)=40×(0.33060.02)=40×16.53=RM661.20
  1. Present Value of Face Value:
    • The present value of a lump sum formula is used here:
PVface=F/(1+r)n
Substituting in values:
PVface=1000/(1+0.02)19
Calculating (1+0.02)19:
(1+0.02)191.4859
Now substituting back:
PVface=1000/1.4859RM672.74

Step 4: Total Price Calculation

Now add both present values to find the total price of the bond after receiving the first coupon:
P=PVcoupons+PVface
P=RM661.20+RM672.74=RM1333.94

(ii) if you were to buy the bond now and sell it after 6 months, what rate of return would be earned over the six - month period?

Answer:

To calculate the rate of return earned over the six-month period if you buy the bond now and sell it after receiving the first coupon payment, we can follow these steps:

Given Information

  • Coupon Payment (C): RM40 (semi-annual)
  • Current Market Price of the Bond: RM1,000
  • Price of the Bond After 6 Months: RM1,000 (as calculated previously)
  • Total Cash Flow After 6 Months: Coupon payment + Selling price

Step 1: Calculate Total Cash Flow After 6 Months

When you buy the bond and hold it for six months, you will receive:
  1. Coupon Payment: RM40
  2. Selling Price of the Bond: RM1,000
Thus, your total cash flow after 6 months will be:
Total Cash Flow=Coupon Payment+Selling Price=RM40+RM1,000=RM1,040

Step 2: Calculate Rate of Return

The rate of return (R) can be calculated using the formula:
R=Total Cash FlowInitial InvestmentInitial Investment×100
Substituting in your values:
R=RM1,040RM1,000RM1,000×100
Calculating this gives:
R=RM40RM1,000×100=4%
  • If you were to buy the bond now and sell it after 6 months, you would earn a rate of return of 4% over that six-month period. This return reflects both the coupon payment received and the unchanged market price of the bond at the time of sale.

Explain efficient market hypothesis (EMH). Provide two examples of anomalies to EMH.

Answer:



The 
Efficient Market Hypothesis (EMH) is a theory in financial economics that asserts that asset prices fully reflect all available information at any given time. This implies that it is impossible for investors to consistently achieve returns that exceed average market returns on a risk-adjusted basis, as any new information that could affect stock prices is quickly incorporated into the prices themselves. The EMH is primarily associated with the work of economist Eugene Fama, who outlined three forms of market efficiency:
  1. Weak Form Efficiency: Prices reflect all past trading information, including price and volume. This suggests that technical analysis cannot consistently yield excess returns because past price movements do not predict future price movements.
  2. Semi-Strong Form Efficiency: Prices reflect all publicly available information, including historical data and fundamental analysis. This means that neither technical nor fundamental analysis can provide an advantage in predicting future price movements.
  3. Strong Form Efficiency: Prices reflect all information, both public and private (insider information). This form posits that even insiders cannot consistently achieve excess returns because all relevant information is already reflected in stock prices.

Anomalies to EMH

Despite its theoretical foundation, several anomalies challenge the EMH. Here are two notable examples:
  1. Small Firm Effect:
    • The small firm effect refers to the observation that smaller companies tend to outperform larger companies on a risk-adjusted basis over time. This contradicts the EMH because it suggests that investors can achieve higher returns by investing in smaller firms, which should not be possible if markets are efficient.
  2. Value Effect:
    • The value effect describes the tendency for stocks with low price-to-earnings (P/E) ratios or low price-to-book ratios (value stocks) to outperform growth stocks over time. According to EMH, if markets are efficient, such pricing anomalies should not exist, as all available information would be reflected in stock prices.

source: Corporate Finance First Semester Examination Academic Session 2011/2012, Universiti Sains Malaysia.

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