Question

Create a valuation model for a new issuance of $100 million dollar corporate bonds with a face value of par.

1) Develop and present a valuation model for corporate debt with a face value of $100 million dollars. The model should use hypothetical assumptions for the coupon rate and other characteristics as well as a hypothetical market interest rate. You must also select a maturity for the bonds and the frequency of the coupon payments. The market rate should be justifiable/reasonable given current market conditions. Explain why the model will be important for the issuance process that is being considered.

2) Explain the possible determinants of the market interest rate that you chose. For example, you should explain how the inflation rate in the economy could be expected to impact the market rate that you chose.

3) Explain how the market rate you chose will be dependent upon the maturity. Describe what you believe to be the most persuasive theory associated with the shape of market interest rates across the maturity spectrum (i.e., the yield curve).

4) Comment on how the different bond characteristics would influence the valuation of the bond. Provide illustrations in a summary table format for how the value might adjust for call provisions and sinking funds.

Answer 1

1.)

Bond valuation is a technique for determining the theoretical fair value of a particular bond. Bond valuation includes calculating the present value of a bond's future interest payments, also known as its cash flow, and the bond's value upon maturity, also known as its face value or par value. Because a bond's par value and interest payments are fixed, an investor uses bond valuation to determine what rate of return is required for a bond investment to be worthwhile.

A bond is a debt instrument that provides a steady income stream to the investor in the form of coupon payments. At the maturity date, the full face value of the bond is repaid to the bondholder. The characteristics of a regular bond include:

• Coupon rate: Some bonds have an interest rate, also known as the coupon rate, which is paid to bondholders semi-annually. The coupon rate is the fixed return that an investor earns periodically until it matures.
• Maturity date: All bonds have maturity dates, some short-term, others long-term. When a bond matures, the bond issuer repays the investor the full face value of the bond. For corporate bonds, the face value of a bond is usually $1,000 and for government bonds, the face value is $10,000. The face value is not necessarily the invested principal or purchase price of the bond.
• Current Price: Depending on the level of interest rate in the environment, the investor may purchase a bond at par, below par, or above par. For example, if interest rates increase, the value of a bond will decrease since the coupon rate will be lower than the interest rate in the economy. When this occurs, the bond will trade at a discount, that is, below par. However, the bondholder will be paid the full face value of the bond at maturity even though he purchased it for less than the par value.

Bond valuation, in effect, is calculating the present value of a bond’s expected future coupon payments. The theoretical fair value of a bond is calculated by discounting the present value of its coupon payments by an appropriate discount rate. The discount rate used is the yield to maturity, which is the rate of return that an investor will get if s/he reinvested every coupon payment from the bond at a fixed interest rate until the bond matures. It takes into account the price of a bond, par value, coupon rate, and time to maturity.

For example, let’s find the value of a corporate bond with an annual interest rate of 5%, making semi-annual interest payments for 2 years, after which the bond matures and the principal must be repaid. Assume a YTM of 3%.

F = $1000 for corporate bond

Coupon rateannual = 5%, therefore, Coupon ratesemi-annual = 5%/2 = 2.5%

C = 2.5% x $1000 = $25 per period

t = 2 years x 2 = 4 periods for semi-annual coupon payments

T = 4 periods

Present value of semi-annual payments = 25/(1.03)1 + 25/(1.03)2 + 25/(1.03)3 + 25/(1.03)4

= 24.27 + 23.56 + 22.88 + 22.21

= 92.93

Present value of face value = 1000/(1.03)4

= 888.49

Therefore, value of bond = $92.93 + $888.49 = $981.42

2.)

Market interest rate can be defined as the rates of interests paid on deposits and other investments. The market interest rates are determined by the collaboration of supply and demand of funds in the financial market.

Determinants of market interest rate

Factors which affect the market interest rate are also known as the determinants of market interest rate. Market interest rate involves the function of several factors, which include inflation, risks and the real cost of money amongst others. The different determinants of market interest rate are as follows:

Market interest rate (K) = K* + IP +DRP + MRP + LRP, where:

• K* = Real Risk-Free Rate of Interest
• IP = Interest Premium
• DRP = Default Risk Premium
• MRP = Market Risk Premium
• LRP = Liquidity Risk Premium.

3.)

Yield Curve

A yield curve is a line that plots yields (interest rates) of bonds having equal credit quality but differing maturity dates. The slope of the yield curve gives an idea of future interest rate changes and economic activity. There are three main types of yield curve shapes: normal (upward sloping curve), inverted (downward sloping curve) and flat.

How a Yield Curve Works

This yield curve is used as a benchmark for other debt in the market, such as mortgage rates or bank lending rates, and it is used to predict changes in economic output and growth. The most frequently reported yield curve compares the three-month, two-year, five-year, 10-year and 30-year U.S. Treasury debt. Yield curve rates are usually available at the Treasury's interest rate web sites by 6:00 p.m. ET each trading day,

A normal yield curve is one in which longer maturity bonds have a higher yield compared to shorter-term bonds due to the risks associated with time.

An inverted yield curve is one in which the shorter-term yields are higher than the longer-term yields, which can be a sign of an upcoming recession.

In a flat or humped yield curve, the shorter- and longer-term yields are very close to each other, which is also a predictor of an economic transition.

4.)

Bond prices fluctuate with changing market sentiments and economic environments, but bond prices are affected in a much different way than stocks. Risks such as rising interest rates and economic stimulus policies have an effect on both stocks and bonds, but each reacts in an opposite way.

Understanding Yield

The yield is the discount rate of the cash flows. Therefore, a bond's price reflects the value of the yield left within the bond. The higher the coupon total remaining, the higher the price. A bond with a yield of 2% likely has a lower price than a bond yielding 5%. The term of the bond further influences these effects.

Changes in Interest Rates, Inflation, and Credit Ratings

Changes in interest rates affect bond prices by influencing the discount rate. Inflation produces higher interest rates, which in turn requires a higher discount rate, thereby decreasing a bond's price. Bonds with a longer maturity see a more drastic lowering in price in this event because, additionally, these bonds face inflation and interest rate risks over a longer period of time, increasing the discount rate needed to value the future cash flows.

Credit risk also contributes to a bond's price. Bonds are rated by independent credit rating agencies such as Moody's, Standard & Poor's and Fitch to rank a bond's risk for default. Bonds with higher risk and lower credit ratings are considered speculative and come with higher yields and lower prices. If a credit rating agency lowers a particular bond's rating to reflect more risk, the bond's yield must increase and its price should drop.