## Ratings of the corporate bond

Bonds are usually rated according to their credit worthiness. Letters are assigned to the bonds expressing their respective credit worth for investments. Bonds with the highest credit-quality are normally assigned the letters AAA whereas those bonds with average credit worth are given letters BBB. Further, bonds that have low credit quality do not attract any investment and are thus assigned the letters C or D. Bonds that normally have longer maturity posses greater risks than those that have a short time to mature hence attracting higher interest rates or yields to maturity (Ehrhardt & Brigham, 2009). Liquid markets also pose greater risks to the investors and therefore bonds that are issued in such a market condition attract greater interest rates.

Accordingly, bond W which is rated AAA has a long time maturity and therefore poses greater risks which enable it to attract higher interest rates. Conversely, X which is rated BBB will have lower interest rates as compared to W, and therefore W will be rated higher using interest rate as a bench mark. However, bonds with short maturity time have low risks hence attract lower interest rates than those bonds that take a longer time to mature (Ehrhardt & Brigham, 2009). In such a case, bond Y that takes a shorter time to mature than both bonds W and X will be given lower ratings. In addition, the bonds sold in a liquid market though take a shorter time to mature as bond Z will, it has more risks than Y meaning that it will have higher earnings and therefore will be rated higher than Y.

## The Yield Curves Slopes

Yield curves are usually being used by investors to predict the behavior of interest rates given the economic conditions. Yield curves depict the relationships between the interest rates and the corresponding maturity dates of the treasury fixed returns securities. Basically, the fixed returns securities for the treasury bonds are used as yardsticks because they bear lower risks, and hence the savvy investors are unlikely to lose their investments. What makes up the credit spread that is ideally used to forecast the potential economic conditions is the difference between the corporate fixed return earnings and the treasury securities. In a graph, it is indicated by the gap between the corporate and treasury securities slopes.

According to Ehrhardt and Brigham (2009), economists are capable of predicting future economic conditions by analyzing the behavior of the credit spread. If the gap between the corporate and the treasury securities is wide, then the economy is shrinking or is undergoing a recession. In other words, low demand and higher interest rates discourage investments. Companies are investing in long term and secure treasury bonds that promise better returns. Investing in long term secure treasury bonds also implies that companies are protected against more losses in case the economy shrinks further in recession. Furthermore, a shrinking economy results in increased risks that relate to long term corporate bonds investments (Ehrhardt & Brigham, 2009). Conversely, an expanding economy results in a declining interest rate thus the credit spread narrows. This implies that the expanding economy results in increased investment in the long term corporate bonds due to reduced risks as well as interest rates.

## The bond’s real return

Given that the initial bond principal was $10,000, we can take this value to be equivalent to P while the received interest remains at $400. However, the summation of the initial principal and interest received will be equal to the nominal return value of $10,400. From this value, the nominal return rate may be obtained through {40÷10,000} ×100% = 4%. Since the inflation rate is given to be 5%, the real return rate will be 4%-5%=-1%. A quick look at this return might make an individual feel that $400 has been made from the initial principal but this accruing interest often hinges on the inflation rate and the tax bracket. Thus, the calculation of the real value of $10,400 calls for the incorporation of a 5% inflation rate. According to Ehrhardt and Brigham (2009), in order to convert the nominal amount received into real worth (R), the amount is deflated using the modus operandi R=P (1+π) where: R is the real amount or the deflated amount

P is equivalent to the nominal amount; π is the rate of inflation

The deflated amount is therefore, R=$10400÷ [1+0.05] =$9904.76. Nevertheless, by dividing the deflated amount by the principal and multiplying it by 100%, we obtain the real return rate. Thus, real return is (9904.76/10,000) ÷ 100% =.009904×100=0.9904%.

## The return on the stock, the current stock yield, and the gain on capital yield

From the specified stock current price along with the dividend paid, the current stock yield is obtainable using the formula: [paid dividend ÷ beginning stock price] ×100. In this case, this stock’s current yield is given by [$2÷$50] ×100%=4%.

This stock’s capital gains yield can conversely be obtained by getting the price difference for instance (P2-P1) and then dividing the result by the initial price (Ehrhardt and Brigham, 2009). Where P2 = Ending stock Price and P1= Beginning stock Price. Thus, capital-gains yield= [{$53-$50} ÷50] ×100%=6%

This stock’s total return can be found by adding the capital gain to the dividend and then dividing the sum by the initial price. The annualized capital gain is similar to the stock’s discount and is given by $53-$50 =$3. This difference is subsequently added to the paid dividend of $2 to get $5. Finally, the stock return is equal to ($5/50) ×100% =10%

## Using the CAPM (Capital Asset Pricing) model to forecast stock returns

Consistent with Ehrhardt and Brigham (2009), the CAPM is given by the addition of risk free rate (Rf) to the beta (β) multiplied by the stock return (Rs) less the risk free rate. Through the formula R=Rf + β (Rs – Rf), and given that β= -0.3; 0.7; 1.6 while Rs=12% and Rf =2%, the expected returns on the stock that has the following beta are obtained as follows: Beta (β) = -0.3 gives Rs = 2% -0.3[12%-2%] = -1%

Beta (β) = 0.7 gives Rs = 2% + 0.7[12% – 2%] = 9%

Beta (β) = 1.6 gives Rs = 2% + 1.6[12% – 2%] = 18%

## References

Ehrhardt, M., C. & Brigham, E., F. (2009). *Corporate Finance: A Focused Approach*. Auckland, New Zealand: Cengage Learning.