You Need To Present To Your Client Alice Cartwright Some Inv
You Need To Present To Your Client Alice Cartwright Some Investment
You need to present to your client, Alice Cartwright, some investment options for her to choose from. Her choices are between the following 2 bonds: Bond Description Face Value Coupon Rate Years to Maturity Bond A corporate bond in ABA company $1,000 10% coupon 12 years, paying annual payments Bond B corporate bond in ABA company $1,000 10% coupon 2 years, paying annual payments For each bond, answer the following questions: What is the valuation of the bond if the market interest rates are 12%? What is the valuation of the bond if the market interest rates are 6%? What is the valuation of the bond if the market interest rates are 2%? What is the value of the bond at the present time? What will the bond be worth at maturity? Are there differences in bond prices? If so, explain why. Paper has to be APA style and at least 1000 words, plus calculations showing all work.
Paper For Above instruction
Introduction
Investing in bonds is a common strategy for diversification and income generation in a portfolio. Bonds, as fixed-income securities, promise periodic interest payments and the return of principal at maturity. Their valuation depends heavily on prevailing market interest rates, the bond's coupon rate, maturity period, and time to repayment. This paper analyzes two bonds issued by the ABA company, providing comprehensive valuation under different interest rate scenarios, understanding valuation at issuance, and the implications of interest rate changes on bond prices. The goal is to help Alice Cartwright make an informed investment decision based on quantitative valuation and qualitative understanding of bond pricing mechanisms.
Bond Descriptions and Basic Features
The two bonds under consideration are issued by the ABA company with the same face value of $1,000 and a coupon rate of 10%. However, they differ in terms of maturity: Bond A has a 12-year maturity, while Bond B matures in 2 years. Both pay annual coupons, reflecting a consistent annual interest of $100 (10% of $1,000). These bonds are typical fixed-income instruments that will be evaluated under three market interest scenarios: 12%, 6%, and 2%.
Understanding Bond Valuation
Bond valuation involves calculating the present value (PV) of future cash flows, which include annual coupon payments and the face value, discounted at the current market interest rate (Yields). The general formula for the price of a bond is:
\[ P = \sum_{t=1}^{n} \frac{C}{(1 + r)^t} + \frac{F}{(1 + r)^n} \]
Where:
- \( P \) = bond price
- \( C \) = annual coupon payment
- \( r \) = market interest rate (discount rate)
- \( n \) = number of years to maturity
- \( F \) = face value of the bond
This method considers that, as market rates change, bond prices fluctuate inversely. When interest rates rise, prices fall, and vice versa.
Valuation of Bond A: 12-Year Maturity
At a 12% Market Rate:
The bond's cash flows comprise 12 annual coupons of $100 and a principal repayment of $1,000 at maturity.
Calculations involve discounting the coupons and face value:
\[
PV_{coupons} = 100 \times \left[ \frac{1 - (1 + 0.12)^{-12}}{0.12} \right]
\]
\[
PV_{face} = \frac{1,000}{(1 + 0.12)^{12}}
\]
Using calculator or financial software:
\[
PV_{coupons} \approx 100 \times 6.194 \approx \$619.40
\]
\[
PV_{face} \approx \frac{1,000}{3.895} \approx \$256.66
\]
\[
P_{A,12\%} \approx 619.40 + 256.66 = \$876.06
\]
At a 6% Market Rate:
\[
PV_{coupons} = 100 \times \left[ \frac{1 - (1 + 0.06)^{-12}}{0.06} \right]
\]
\[
PV_{face} = \frac{1,000}{(1 + 0.06)^{12}}
\]
Calculations:
\[
PV_{coupons} \approx 100 \times 9.646 \approx \$964.60
\]
\[
PV_{face} \approx \frac{1,000}{1.895} \approx \$527.57
\]
\[
P_{A,6\%} \approx 964.60 + 527.57 = \$1,492.17
\]
At a 2% Market Rate:
\[
PV_{coupons} = 100 \times \left[ \frac{1 - (1 + 0.02)^{-12}}{0.02} \right]
\]
\[
PV_{face} = \frac{1,000}{(1 + 0.02)^{12}}
\]
Calculations:
\[
PV_{coupons} \approx 100 \times 10.423 \approx \$1,042.30
\]
\[
PV_{face} \approx \frac{1,000}{1.268} \approx \$788.99
\]
\[
P_{A,2\%} \approx 1,042.30 + 788.99 = \$1,831.29
\]
Current Price:
At the present moment, marking to market with current market rates, the bond's intrinsic value fluctuates depending on the prevailing rate. As observed, at 12%, the bond is valued at approximately $876.06; at 6%, about $1,492.17; and at 2%, around $1,831.29.
Value at Maturity:
The value at maturity is straightforward—the face value of $1,000 plus the last coupon payment, totaling $1,100, as the bondholder receives the face amount and final coupon.
Valuation of Bond B: 2-Year Maturity
At 12% Market Rate:
\[
PV_{coupons} = 100 \times \left[ \frac{1 - (1 + 0.12)^{-2}}{0.12} \right]
\]
\[
PV_{face} = \frac{1,000}{(1 + 0.12)^2}
\]
Calculations:
\[
PV_{coupons} \approx 100 \times 1.782 \approx \$178.20
\]
\[
PV_{face} \approx \frac{1,000}{1.254} \approx \$798.47
\]
\[
P_{B,12\%} \approx 178.20 + 798.47 = \$976.67
\]
At 6% Market Rate:
\[
PV_{coupons} \approx 100 \times 1.888 \approx \$188.80
\]
\[
PV_{face} \approx \frac{1,000}{1.123} \approx \$890.00
\]
\[
P_{B,6\%} \approx 188.80 + 890.00 = \$1,078.80
\]
At 2% Market Rate:
\[
PV_{coupons} \approx 100 \times 2.000 \approx \$200
\]
\[
PV_{face} \approx \frac{1,000}{1.040} \approx \$961.54
\]
\[
P_{B,2\%} \approx 200 + 961.54 = \$1,161.54
\]
Value at maturity:
This is simply the face value plus the last coupon: $1,000 + $100 = $1,100.
Discussion of Bond Price Differences
The variations observed in bond prices under different market interest rates highlight the inverse relationship between bond prices and yields. When market rates increase beyond the coupon rate, bonds typically trade at a discount—less than face value—since their fixed coupons become less attractive. Conversely, when market rates decrease below the coupon rate, bonds rise in price, often exceeding face value, reflecting higher relative yields. The longer the time to maturity, the more pronounced these price swings. Bond A, with its longer 12-year maturity, exhibits greater sensitivity to interest rate changes than Bond B, which matures in 2 years. This phenomenon, known as duration risk, underscores the importance of time horizon in bond investment strategies.
Conclusion
Understanding bond valuation is crucial for investment decision-making, particularly in fluctuating interest rate environments. This analysis demonstrates how the same bond can vary significantly in market value depending on prevailing rates, which influence both the discounting process and investor preferences. For Alice Cartwright, recognizing that longer-term bonds like Bond A are more sensitive to interest rates can help align her investment choices with her risk tolerance and income objectives. Ultimately, bond prices fluctuate inversely with interest rates, and investors should consider both the current rate environment and their financial goals when investing in bonds.
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