Part 1

Suppose that on January 15, 2021 the following information about IBM corporate bond was obtained:

Issuer = IBM CORP

Maturity = 07/15/2029,

Coupon = 4.50% (Semiannual),

Price = 108.369 (% of Par Value),

YTM = 3.36%,

Last interest payment = 01/15/2021,

Next interest payment = 07/15/2021.

Using Microsoft's Excel, create a spreadsheet that shows the value of the bond after each interest payment, from 01/15/2021 to 07/15/2029. To makes things simple, assume that Par Value = $1000 and the YTM remains the same until the maturity. Use the function PV:

= - PV(rate,nper,pmt,fv,type)

where

rate = periodic interest rate (set it to YTM/2);

nper = total number of periods;

pmt = periodic payment;

fv = future value (set fv to 1000);

type = 0 (that is, payments are made at the end of each period).

Graph the value of the bond for each period.

Part 2

As in Part 1, assume that the YTM remains the same until the maturity. Compute current yield (CY), capital gain/loss (CGL), and holding period return (HPR) of the bond after each interest payment, from 01/15/2021 to 07/15/2029. Express the three measures (CY, CGL, HPR) in annual terms (i.e., multiply periodic rate by 2) and graph them on the same plot.

Part 5

Duration tells us approximately what percent change in bond price (DP/P) will result from a given change in yield to maturity. In this part, you need to compare the duration approximation to the actual percent change in the bond price. Compute the duration approximation to the bond price's change when the new YTM is from 0% to 13%. Use the formula

DP/P₀ = - D₀ x (y₁-y₀)/(1+y₀),

where y₁ is the new YTM (which ranges from 0% to 13%), y₀ is the current YTM (3.36%), and P₀ andD₀ are the current price and duration (i.e., corresponding to y₀).

To compute the actual percent change in the bond price, use bond prices from Part 2. Graph the actual percent change in price and the duration approximation for different values of YTM. Put both graphs on the same plot.

Part 7

Using the information on term structure of interest rates in Part 6, compute the price of a 20-year bond with par value of $1000, which makes annual coupon payments at a coupon rate of 6.5%.