You Are Considering Purchasing A Console That Promises Annua

1 You Are Considering Purchasing A Consol That Promises Annual Payme

You are considering purchasing a consol that promises annual payments of $4. (LO2).

a. If the current interest rate is 5 percent, what is the price of the consol?

b. You are concerned that the interest rate may rise to 6 percent. Compute the percentage change in the price of the consol and the percentage change in the interest rate. Compare them.

c. Your investment horizon is one year. You purchase the consol when the interest rate is 5 percent and sell it a year later, following a rise in the interest rate to 6 percent. As you read the business news, you come across an advertisement for a bond mutual fund—a fund that pools the investments from a large number of people and then purchases bonds, giving the individuals “shares” in the fund. The company claims its fund has had a return of 131½ percent over the last year. But you remember that interest rates have been pretty low—5 percent at most. A quick check of the numbers in the business section you’re holding tells you that your recollection is correct. Explain the logic behind the mutual fund’s claim in the advertisement.

LO. Given the data in the accompanying table, would you say that this economy is heading for a boom or for a recession? Explain your choice.

What are the advantages of holding stock in a company versus holding bonds issued by the same company? (LO1)

Sample Paper For Above instruction

The valuation of a consol, also known as a perpetual bond, depends fundamentally on the present value of its infinite series of fixed annual payments and prevailing interest rates. When considering purchasing a consol that promises annual payments of $4, with an interest rate of 5 percent, the key formula used is the present value of a perpetuity: PV = C / r, where C is the annual payment, and r is the interest rate. Substituting the known values: PV = 4 / 0.05 = $80. Hence, the current price of the consol, given the interest rate of 5 percent, is $80. This calculation assumes market efficiency and ignores transaction costs, reflecting a simplified valuation model common in financial theory (Bodie, Kane, & Marcus, 2014).

When the interest rate increases to 6 percent, the price of the consol decreases, illustrating the inverse relationship between bond prices and interest rates. Recalculating with the new rate: PV = 4 / 0.06 ≈ $66.67. The percentage change in the price is calculated as: ((66.67 - 80) / 80) × 100 ≈ -16.67%. The percentage change in the interest rate is ((6 - 5) / 5) × 100 = 20%. Comparing these, the price of the consol decreases by about 16.67%, whereas the interest rate increases by 20%, indicating a more sensitive response of bond prices to interest rate changes, especially over small interest rate moves.

Over a one-year investment horizon, purchasing the consol at a 5 percent interest rate and selling after the rate rises to 6 percent would result in a capital loss due to the decline in the bond’s price. If you purchased it at $80, after the rise in rates, the resale value would be approximately $66.67, leading to a loss of about $13.33, aside from any interest earned during the year. This scenario exemplifies interest rate risk, a core concern for fixed income investors. The initial yield would have been 5 percent, but after interest rates increase, the bond’s resale value drops, illustrating the principle that bond prices and interest rates move inversely (Fabozzi, 2013).

The advertisement for the bond mutual fund claiming a return of 131½ percent over the past year can be explained by the impact of capital gains resulting from falling interest rates. When interest rates are low, bond prices tend to rise as existing bonds with higher fixed coupons become more attractive compared to new issues offering lower yields. The mutual fund’s significant return likely includes capital gains from these rising bond prices as the fund manager bought bonds earlier at lower yields and sold them later at higher prices. Additionally, the reported return might incorporate reinvestment of interest payments and income generated from bond holdings, magnified by the large size of the fund and the compounding effects over the year (Elton, Gruber, & Blake, 2020).

Regarding whether the economy is heading for a boom or recession, analysis of the provided data suggests caution. If the data shows increasing unemployment, declining industrial production, and dampened consumer confidence, these are signals pointing toward a recession. Conversely, rising GDP, low unemployment rates, and high consumer confidence indicate a boom. Given the current data, if indicators lean towards economic slowdown, it predicts a recession; if they point to growth and high activity, a boom might be on the horizon. The context of low interest rates typically supports economic expansion, but other signs must be considered to draw a conclusive outlook (Mankiw, 2016).

Holding stock in a company versus bonds issued by the same company presents distinct advantages and risk profiles. Stocks provide ownership in the company, entitling shareholders to residual profits and voting rights, and tend to appreciate in value during periods of growth, offering higher potential returns. Bonds, however, are debt instruments that obligate the issuer to pay fixed interest and return principal, providing predictable income and less risk in terms of capital loss, especially during downturns. Investors seeking capital appreciation may prefer stocks, while those prioritizing income stability might favor bonds. Holding both diversifies the risk portfolio, balancing growth potential with income security (Ross, Westerfield, & Jaffe, 2019).

References

• Bodie, Z., Kane, A., & Marcus, A. J. (2014). Investments (10th ed.). McGraw-Hill Education.
• Fabozzi, F. J. (2013). Bond Markets, Analysis and Strategies (9th ed.). Pearson.
• Elton, E. J., Gruber, M. J., & Blake, C. R. (2020). Modern Portfolio Theory and Investment Analysis (10th ed.). Wiley.
• Mankiw, N. G. (2016). Principles of Economics (7th ed.). Cengage Learning.
• Ross, S. A., Westerfield, R. W., & Jaffe, J. (2019). Corporate Finance (12th ed.). McGraw-Hill Education.