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Interest Rates and Bond Prices

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What is the relationship between Bonds and interest rates?
Interest rates and bond prices have what is called an "inverse relationship" which means that when one goes up, the other goes down and vice versa of course though this relation might not seem obvious at first, the reasons are fairly simple.

An example of the above is "The U.S. government sells Treasury bonds when prevailing market interest rates are 8%. So, a bond with a face value of $1,000 on issue would pay $80 a year in interest - usually in two half-yearly instalments of $40. But if market interest rates were to rise to 10%, then who would want to buy such a bond? So, the market price of the bond would have to fall to a level where that fixed $80 annual payment were the equivalent of a 10% annual yield - in this case, the price would have to fall to $800, so that the annual $80 payment would equal 10% of the purchase price of the bond. Conversely, if market interest rates were to fall to 6%, the price of the bond would rise to $1,333.33 - or 133 11/32 in market jargon".

Bonds prices and interest rate. Retrieved from http://www.leftbusinessobserver.com/Bond_supplement.html

What are the calculations involved with pricing a bond and a stock?
Calculations involved with pricing a bond

Bond Value = C x [1 - 1/(1+r)t ] /r + F/(1+r)t

Example:
Calculate the price of a bond with a par value of $1,000 to be paid in ten years, a coupon rate of 10%, and a required yield of 12%. In our example we'll assume that coupon payments are made semi-annually to bond holders and that the next coupon payment is expected in six months.

An example of Stocks:
Price of Stock A is currently $100.00 per share or (P0). The Dividends are expected to be $3.00 per share (Div) and the price of Stock A is expected to be $105.00 per share in one year's time (P1). Therefore our capital gain is expected to be $105.00 - $100.00 or $5.00 per share.

Expected Return, or R = ($3.00 + $5.00) / $100.00 = 8.0%

We can now use this expected return to calculate the price of a stock in the same risk class as Stock A using the following formula:

Stock Price = (Dividends Paid (Div) + Expected Price (P1)) / (1 + Expected Return (R))

Stock Price = ($3.00 + $105) / (1 + 0.08) = $108.00 / 1.08 = $100

Choose a stock that is publicly traded and explain how you think the future potential of the stock warrants the price it sells at today.

"Gilts Bonds" are bonds that are issued by the British government while many other bonds are issued by companies. Gilts are generally considered low risk and one of the safest types of bonds since any or no government should default on debit. They guarantee to pay the holder a fixed cash payment every six months until the bond matures, at which point the holder receives the final coupon payment and get his original investment back. It is the government's responsibility to repay capital on maturity and make interest payments throughout the term of the gilt. "If the UK government had financial difficulty, then a gilt investment may not receive interest payments and capital may not be repaid at maturity. For example, a five-year bond with a value of £100 and a coupon of 2.5% will pay you £2.50 a year for five years, after which you get your £100 back and keep the interest. As with all investment, nothing is guaranteed and you could lose some or even all of you money. That may not seem like a lot of money but at least your secured".

Calculate the current return on a stock of your choice and compare it to returns on bonds. Which is better to invest in presently a stock or a bond in this company and why?
Example:

Assume the following information for an existing ABC Group bond that provides annual coupon payments:

Par value = $1,000

Coupon rate = 11%

Maturity = 4 years

Required rate of return by investors = 11%

a. What is the present value of the bond?

Answer:

PV of Bond = PV of Coupon Payments + PV of Principal

= $110(PVIFAi = 11%,n = 4) + $1,000(PVIFi = 11%,n = 4)

= $110(3.1024) + $1,000(.6587)

= $341 + $659

= $1,000

b. If the required rate of return by investors were 14 percent instead of 11 percent, what would be the present value of the bond?

Answer:

PV of Bond = PV of Coupon Payments + PV of Principal

= $110(PVIFAi = 14%,n = 4) + $1,000(PVIFi = 14%,n = 4)

= $110(2.9137) + $1,000(.5921)

= $321 + $592

= $913

When you invest in stocks, you buy ownership shares in a company. Your return on investment, or what you get back in relation to what you put in, depends on the success or failure of that company. If the company does well and makes money from the products or services it sells, you expect to benefit from that success; however if the company loses money, then its shareholders generally expect to lose money on their investment as well.

As a bondholder you receive an interest payment at specified intervals, regardless of how the company is doing (as long as the company does not go bankrupt). In other words choosing bonds is far better than stocks because if the company is doing good or bad, as long as the company does not file for bankruptcy, you get your interest and principal payments.

References:
Bond Valuation. Retrieved from http://www.bus.tu.ac.th/department/thai/download/news/2827/FN211l.pdf

Bond pricing. Retrieved from http://www.investopedia.com/university/advancedbond/advancedbond2.asp

Bonds prices and interest rate. Retrieved from http://www.leftbusinessobserver.com/Bond_supplement.html

Gilts (UK government bonds. Retrieved from. http://monevator.com/gilts-uk-government-bonds/

How to calculate bond and stock prices? Retrieved from: http://www.ehow.com/how_7641583_chart-volatility-stock-options.html

Which investment is better? Retrieved from http://learnbonds.com/bonds-vs-stocks/

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Solution Preview

Everything you have listed here is correct including the examples.

To emphasize again, if the interest rates go down, bond prices go up and if interest rates go up, bond prices go down. Bond prices and interest rates are ...

Solution Summary

This solution assists with interest rate and bond price problems.

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Value of outstanding bonds and rates of returns

1 "The values of outstanding bonds change whenever the going rate of interest changes. In general, short-term interest rates are more volatile than long-term interest rates. Therefore, short-term bond prices are more sensitive to interest rate changes than are long-term bond prices." Is this statement true or false? Explain.

2. The rate of return you would get if you bought a bond and held it to its maturity date is called the bond's yield to maturity. If interest rates in the economy rise after a bond has been issued, what will happen to the bond's price and to its YTM? Does the length of time to maturity affect the extent to which a given change in interest rates will affect the bond's price?

3. Two inventors are evaluating General Motors' stock for possible purchase. They agree on the expected value of D1 and also on the expected future dividend growth rate. Further, they agree on the risk of the stock. However, one investor normally holds stock for 2 years, while the other normally holds stock for 10 years. Should they should both be willing to pay the same price for General Motors' stock. True or false? Explain.

4. A bond that pays interest forever and has no maturity date is a perpetual bond. In what respect is a perpetual bond similar to a no-growth common sock, and to a share of preferred stock?

5. Describe the effect on a call option's price caused by an increase in each of the following factors: (1) stock price, (2) strike price, (3) time to expiration, (4) risk-free rate, and (5) variance of stock return.

6. What is a financial option? What is the single most important characteristic of an option?

7. Consider Triple Trice's call option with a $25.00 strike price. The following table contains historical values for this option at different stock prices:

Stock price Call Option Price
$25 $3.00
$30 $7.50
$35 $12.00
$40 $16.50
$45 $21.00
$50 $25.00

(1) Create a table that shows (a) stock price, (b) strike price, (c) exercise value, (d) option price, and (e) the time value, which is the option's price less its exercise value.

(2) What happens to the time value as the stock price rises? Why?

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