Calculate The Risk For The Following Rating Classes Of Long

Calculate The Risk For The Following Rating Classes Of Long Securit

Calculate the risk for the following rating classes of long securities, assuming that the yield to maturity (YTM) for comparable treasuries is 4.51%, AAA 4.95%, BBB 5.22%, B 8.42%. The risk premium for securities class AAA is _____% (round to two decimal). The risk premium for securities class BBB is _____% (round to two decimal). The risk premium for securities class B is _____% (round to two decimal).

you have two assets and must calculate their values today based on their different payment streams and appropriate required returns. Asset 1 has a required return of 17% and will produce a stream of $800 at the end of each year indefinitely. Asset 2 has a required return of 11% and will produce an end of the year cash flow of $1300 in the first year, $1600 in the second year, and $900 in its third and final years. The value of asset 1 today is $___ (round to nearest cent).

A bond with 12 years of maturity and a coupon rate of 9% has a par, or face value of $22,000. Interest is paid annually. If you're requiring a return of 16% on this bond, what is the value of this bond? The value of the bond is $____ (round nearest cent).

Bond prices and yields—assume that the Financial Management Corporation’s $1000 par value bond has a 5.200% coupon, matures on May 15, 2023, has a current price quote of 95.589, and a yield to maturity (YTM) of 5.993%. Given this information, answer the following questions: a) What is the dollar price of the bond? b) What is the bond's current yield? c) Is the bond selling at par, at a discount, or at a premium? Why? d) Compare the bond’s current yield calculated in part b to its YTM and explain why they differ.

Basic bond valuation—Complex Systems has an outstanding issue of $1000 par value bonds with a 12% coupon interest rate. The issuer pays interest annually and has 16 years remaining to maturity. If bonds of similar risk are currently earning a rate of return of 10%, the bonds should sell today for $____________ (round nearest cent).

Lynn Parson is considering investing in either of two outstanding bonds, both with $1000 par value and 9% coupon interest rates paid annually. Bond A has exactly 6 years to maturity, and Bond B has 16 years. (1) The value of Bond A, if the required return is 6%, is $_________ (round nearest cent).

Yield to maturity—the relationship between a bond’s yield to maturity and coupon interest rate can be used to predict its pricing level. For each of the bonds listed below, state whether the price of the bond will be a premium to par, at par, or a discount to par: Bond coupon interest rate yield to maturity A 6% 10%; B 8% 8%; C 9% 7%; D 7% 9%; E 12% 10%. What is the price of the bond in relation to its par value for Bond A? Select the best answer below: The bond sells at par, at a premium to par, or at a discount to par.

Yield to maturity—each of the bonds shown in the following table has annual coupons. Bond par value is $1000, with coupon interest rates, years to maturity, and current values as follows:

  • A: Coupon rate 9%, 8 years remaining, current value $820.
  • B: Coupon rate ?, years remaining ?, current value ?.
  • C: Coupon rate ?, years remaining ?, current value ?.
  • D: Coupon rate ?, years remaining ?, current value ?.
  • E: Coupon rate ?, years remaining ?, current value ?.

a) Calculate the yield to maturity (YTM) for Bond B. b) What relationship exists between the coupon interest rate, yield to maturity, par value, and market value of a bond? Explain.

The yield to maturity (YTM) for Bond A is _________% (round to two decimal places).

Find the value of the bond maturing in 6 years with a $1000 par value and a coupon interest rate of 10% (5% paid semiannually). If the required return on similar risk bonds is 14% annually (7% paid semiannually), the present value of the bond is $______. (Round to the nearest cent).

Paper For Above instruction

Understanding the risks and valuation of securities is fundamental for investors seeking to optimize their investment portfolios. This paper examines several key aspects, including the calculation of risk premiums for different credit rating classes, valuation of assets and bonds based on payment streams and required returns, as well as the implications of yield to maturity on bond prices. Through detailed analysis, we explore how credit ratings influence the risk premiums attached to securities, the methods to value different types of assets, and the theoretical relationship between bond yields, coupon rates, and their market prices.

Risk Premiums Across Credit Ratings

Credit rating agencies assign risk levels to securities, impacting their yield spreads over risk-free treasuries. The risk premium is the additional return investors demand for bearing the risk associated with lower credit ratings. Based on the provided data, the risk premiums can be computed by subtracting the treasury yield (4.51%) from each rating class's yield to maturity: AAA at 4.95%, BBB at 5.22%, and B at 8.42%. These calculations yield:

  • Risk premium for AAA: 4.95% - 4.51% = 0.44%
  • Risk premium for BBB: 5.22% - 4.51% = 0.71%
  • Risk premium for B: 8.42% - 4.51% = 3.91%

These premiums reflect the additional compensation investors require for accepting increased credit risk. The significant difference between AAA and B ratings underscores the increased uncertainty and potential default risk associated with lower-rated securities.

Valuation of Assets with Different Payment Streams

Asset valuation is essential for investment decision-making. Asset 1, which produces perpetual payments of $800 and has a required return of 17%, can be valued using the dividend discount model for perpetuities:

V = Payment / Required Return = $800 / 0.17 ≈ $4,705.88

Asset 2 involves multiple cash flows with varying payments over three years. Its valuation involves computing the present value of each cash flow discounted at the asset's required return of 11%:

  • Year 1: $1300 / (1 + 0.11)^1 ≈ $1170.27
  • Year 2: $1600 / (1 + 0.11)^2 ≈ $1296.96
  • Year 3: $900 / (1 + 0.11)^3 ≈ $676.83

Summing these, the total present value is approximately $3144.06, representing the current worth of the cash flow stream.

Bond Valuation and Pricing

For a bond with a 12-year maturity, a 9% coupon, and a face value of $22,000, requiring a 16% return, the valuation involves calculating the present value of the future coupon payments and the par value. The annual coupon payment is 9% of $22,000, equaling $1,980. Using present value formulas for annuities and lump sums:

PV of coupons = $1,980 × [1 - (1 + 0.16)^-12] / 0.16 ≈ $11,183.45

PV of face value = $22,000 / (1 + 0.16)^12 ≈ $4,594.63

Summing these yields approximately $15,778.08 for the bond's price.

Bond Prices, Yields, and Market Conditions

Given a bond with a quote of 95.589, the dollar price is 95.589% of $1,000 par value, which equals approximately $955.89. The current yield is calculated as annual coupon payment divided by the market price: $1,980 / $955.89 ≈ 2.07%. Since the bond's price is below par, it is selling at a discount. The difference between current yield and YTM arises because the current yield reflects only the annual income relative to market price, whereas YTM considers total returns including capital gains or losses over the bond's life.

Bond Valuation with Fixed Coupons and Semiannual Payments

The value of a 6-year bond with a $1,000 par value and a 10% coupon rate paid semiannually, with a required return of 14% annually (7% semiannually), involves discounting semiannual coupon payments ($50) and the face value. Using present value formulas, the bond's price is approximately $927.45, which falls below par because the required return exceeds the coupon rate, indicative of a discount bond.

Relationship of Yield to Maturity and Bond Pricing

The relationship between coupon rate, YTM, and bond price is fundamental. When the coupon rate exceeds YTM, the bond sells at a premium; when it equals YTM, it sells at par; and when it is lower than YTM, it sells at a discount. This inverse relationship ensures bonds are priced such that the yield to maturity aligns with market conditions, balancing the present value of future cash flows with current market prices.

Conclusion

Analyzing bond risks, valuations, and their influences on pricing and yields provides investors with essential insights to make informed decisions. Credit ratings significantly impact risk premiums, and understanding the mechanics of bond valuation—through present value calculations of coupons and principal—is vital. Moreover, the relationship between coupon rates, YTM, and market value guides investors in assessing whether bonds are attractive based on their price relative to par.

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