Financial Management

Model

2/1/12
Chapter 4. Mini Case
Situation
Sam Strother and Shawna Tibbs are vice-presidents of Mutual of Seattle Insurance Company and co-directors of the company’s pension fund management division. A major new client, the Northwestern Municipal Alliance, has requested that Mutual of Seattle present an investment seminar to the mayors of the represented cities, and Strother and Tibbs, who will make the actual presentation, have asked you to help them by answering the following questions. Because the Boeing Company operates in one of the league’s cities, you are to work Boeing into the presentation.
a. What are the key features of a bond? The key features of a bond are, Par or face value, Coupon rate , Maturity, Issue date and default risk
b. What are call provisions and sinking fund provisions? Do these provisions make bonds more or less risky? A call provision is a provision in a bond contract that gives the issuing corporation the right to redeem the bonds under specified terms prior to the normal maturity date. A sinking fund provision is a provision in a bond contract that requires the issuer to retire a portion of the bond issue each year. A sinking fund provision facilitates the orderly retirement of the bond issue. The call provisions is potentially detrimental to the investor especially if the bonds were issued in a period when interest rates were cyclically high so therefore, bonds with a call provision are riskier than those without a call provision .
Call Provisions and Sinking Funds
A call provision that allows the issuer to redeem the bond at a specified time before the maturity date. If interest rates fall, the issuer can refund the bonds and issue new bonds at a lower rate. Because of this, borrowers are willing to pay more and lenders require more on callable bonds.
In a sinking fund provision, the issuer pays off the loan over its life rather than all at the maturity date. A sinking fund reduces the risk to the investor and shortens the maturity. This is not good for investors if rates fall after issuance.
c. How is the value of any asset whose value is based on expected future cash flows determined? The value of an asset is just the present value of its expected future cash flows.
d. How is the value of a bond determined? What is the value of a 10-year, $1,000 par value bond with a 10 percent annual coupon if its required rate of return is 10 percent?
Finding the “Fair Value” of a Bond
First, we list the key features of the bond as “model inputs”:
Years to Mat:10
Coupon rate:10%
Annual Pmt:$100
Par value = FV:$1,000
Going rate, rd:10%
The easiest way to solve this problem is to use Excel’s PV function. Click fx, then financial, then PV. Then fill in the menu items as shown in our snapshot in the screen shown just below.
Value of bond =$1,000.00Thus, this bond sells at its par value. That situation always exists if the going rate is equal to the coupon rate.
The PV function can only be used if the payments are constant, but that is normally the case for bonds.
e. (1.) What would be the value of the bond described in Part d if, just after it had been issued, the expected inflation rate rose by 3 percentage points, causing investors to require a 13 percent return? Would we now have a discount or a premium bond?
We could simply go to the input data section shown above, change the value for r from 10% to 13%. You can set up a data table to show the bond’s value at a range of rates, i.e., to show the bond’s sensitivity to changes in interest rates. This is done below.
To make the data table, first type the headings, then type the rates in cells in the left column. Since the input values are listed down a column, type the formula in the row above the first value and one cell to the right of the column of values (this is B73; note that the formula in B73 actually just refers to the bond pricing formula above in B60). Select the range of cells that contains the formulas and values you want to substitute (A73:B78). Then click Data, What-If-Analysis, and then Data Table to get the menu. The input data are in a column, so put the cursor on “column input cell” and enter the cell with the value for r (B37), then Click OK to complete the operation and get the table.
Bond Value
Going rate, r:$1,000
0%$2,000.00
7%$1,210.71
10%$1,000.00
13%$837.21
20%$580.75
We can use the data table to construct a graph that shows the bond’s sensitivity to changing rates.
Put B37 here.
(2.) What would happen to the value of the 10-year bond over time if the required rate of return remained at 13 percent, or if it remained at 7 percent? Would we now have a premium or a discount bond in either situation? You pick a rate.
Value of Bond in Given Year:
N7%10%13%
0$1,211$1,000$837
1$1,195$1,000$846
2$1,179$1,000$856
3$1,162$1,000$867
4$1,143$1,000$880
5$1,123$1,000$894
6$1,102$1,000$911
7$1,079$1,000$929
8$1,054$1,000$950
9$1,028$1,000$973
10$1,000$1,000$1,000
You pick the rate for a bond:
Your choice:
20%
Resulting bond prices
$581
$597
$616
$640
$667
$701
$741
$789
$847
$917
$1,000
If rates fall, the bond goes to a premium, but it moves towards par as maturity approaches. The reverse hold if rates rise and the bond sells at a discount. If the going rate remains equal to the coupon rate, the bond will continue to sell at par. Note that the above graph assumes that interest rates stay constant after the initial change. That is most unlikely–interest rates fluctuate, and so do the prices of outstanding bonds.
Yield to Maturity (YTM)
f. (1.) What is the yield to maturity on a 10-year, 9 percent annual coupon, $1,000 par value bond that sells for $887.00? That sells for $1,134.20? What does the fact that a bond sells at a discount or at a premium tell you about the relationship between rd and the bond’s coupon rate? What is the yield-to-maturity of the bond?
Use the Rate function to solve the problem.
Years to Mat:10
Coupon rate:9%
Annual Pmt:$90.00Going rate, r =YTM:10.91%See RATE function at right.
Current price:$887.00
Par value = FV:$1,000.00
(2.) What are the total return, the current yield, and the capital gains yield for the discount bond? (Assume the bond is held to maturity and the company does not default on the bond.)
Current and Capital Gains Yields
The current yield is the annual interest payment divided by the bond’s current price. The current yield provides information regarding the amount of cash income that a bond will generate in a given year. However, it does not account for any capital gains or losses that will be realized if the bond is held to maturity or call.
Simply divide the annual interest payment by the price of the bond. Even if the bond made semiannual payments, we would still use the annual interest.
Par value$1,000.00
Coupon rate:9%Current Yield =10.15%
Annual Pmt:$90.00
Current price:$887.00
YTM:10.91%
The current yield provides information on a bond’s cash return, but it gives no indication of the bond’s total return. To see this, consider a zero coupon bond. Since zeros pay no coupon, the current yield is zero because there is no interest income. However, the zero appreciates through time, and its total return clearly exceeds zero.
YTM =Current Yield+Capital Gains Yield
Capital Gains Yield =YTMCurrent Yield
Capital Gains Yield =10.91%10.15%
Capital Gains Yield =0.76%
g. How does the equation for valuing a bond change if semiannual payments are made? Find the value of a 10-year, semiannual payment, 10 percent coupon bond if nominal rd = 13%.
Bonds with Semiannual Coupons
Since most bonds pay interest semiannually, we now look at the valuation of semiannual bonds. We must make three modifications to our original valuation model: (1) divide the coupon payment by 2, (2) multiply the years to maturity by 2, and (3) divide the nominal interest rate by 2.
Use the Rate function with adjusted data to solve the problem.