If interest rates suddenly rise by 2 percent, what is the percentage change in both bonds?
Both the bonds are sold at par value and the yield to maturity is 8%
If interest rates rise by 2%, yield to maturity = 10%
Bond D: FV = 1000, PMT = 8%/2 of 1000 = 40, rate = 10%/2, N = 4
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Price of Bond D = 964.54
% change in price = 964.54/1000 - 1 = -3.55%
Bond F: FV = 1000, PMT = 8%/2 of 1000 = 40, rate = 10%/2, N = 30
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Price of Bond F = 846.2755
% change in price = 846.2755/1000 - 1 = -15.37%
Bond D lost 3.55% percent value while bond F lost 15.37% value.
If interest rates suddenly fall by 2 percent, what is the percentage change in both bonds?
If rates drop by 2%, yield to maturity = 6%
Bond D: FV = 1000, PMT = 8%/2 of 1000 = 40, rate = 6%/2, N = 4
Apply PV function in Excel
Price of Bond D = 1037.1710
% change in price = 1037.1710/1000 - 1 = 3.72%
Bond F: FV = 1000, PMT = 6%/2 of 1000 = 40, rate = 10%/2, N = 30
Apply PV function in Excel
Price of Bond F = 846.2755
% change in price = 1196.0044/1000 - 1 = 19.60%
Bond D gained 3.72% in value while Bond F gained 19.6% in value.
What does this tell you about the interest rate risk of longer-term bonds?
The above calculations and the solutions indicate the interest rates risk of longer-term bonds is more sensitive than that of short term bonds.
What is the dividend yield for each of the four stocks?
To calculate the dividend yield, find the initial price. However, since we used dividend growth to find the initial price, the dividend yield for stocks A, B, and C are equal to (R-g),
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Dividend yield of A = 20% - 10% = 10%
Dividend yield of B = 20% - 0% = 20%
Dividend yield of C= 20% - -5% = 25%
For Stock D, the P 0 is 90.71, applying the formulas for non-constant growth (Ross, Stephen, Westerfield, Bradford, & Randolph, 2017) . With an initial dividend of 3.75, the dividend yield to be 4.13%.
What is the expected capital gains yield?
Expected capital gains= (P 1 - P 0 )/P 0 for each stock.
Stocks A, B, and C are 21.01% , 0% , and -9.73% , respectively.
For Stock D, P 1 =103.98 and which yield the capital gains of 14.63% .
Discuss the relationship among the various returns that you find for each of the stocks.
From my calculations, I realized that a higher stock price means a lower yield result and both the dividend price and stock price change over time. One key conclusion from my calculations is that the dividend yield of stock D continues to increase even as the stock falls. Indeed, for the initial year, although the owner loses almost 10% of the stock price, the dividend yield of 25% makes the stock worth it. However, I have reservations on how such a stock behaves in the real stock market. The capital gains yield calculations were straight forward since it measures the percent change in the stock price over a year. There is a positive association between dividends and stock price.
References
Ross, F. M., Stephen, A., Westerfield, R., Bradford, D., & Randolph, W. (2017). Essentials of Corporate Finance. McGraw Hill.
