Time Value of Money
MenuBondsFormulas & ExamplesBasic bond valuationExcel
functionsExamplesCopyright (c) 1997 Ian H Giddy
&APage &PBond ValuationExcel functionsPVExamplesPV
Bond ValBasic Bond ValuationBond price (PV annuity + PV
principal)PV=PMT*(1-1/(1+R)^n)/RPV=FV/(1+R)^nExampleCoupon
rate8FV100Yield8.00%Yield8.00%Periods10Periods10PV53.7PV46.32AnswerPrice$100.00Bond
price with semi-annual
paymentsPV=(PMT/m)*(1-1/(1+R/m)^n*m)/(R/m)PV=FV/(1+R/m)^n*mExampleCoupon
rate8FV100Yield8.00%Yield8.00%Frequency22Periods10Periods10PV54.4PV45.64AnswerPrice$100.00
&APage &P
Excel functionsBond calculations with Excel functionsUse PRICE
function to find a bonds priceSettle date1/1/97Mat
date1/1/07Rate8%Yield9%Frequency2Price93.50Use YIELD function to
find a bond's yield to maturitySettle date1/1/97Mat
date1/1/07Rate8%Price95Frequency2Yield8.76%Use MDURATION function
to find a bond's modified durationSettle date1/1/97Mat
date1/1/07Rate8%Price8%Frequency2Modified duration6.8
&APage &P
ExamplesExamples1Atlantic Bell issued 10-year bonds one year ago
at a coupon rate of 9.25 percent. The bonds makesemiannual
payments. If the YTM on these bonds is 7.15 percent, what is the
current bond price?Use the Excel PV function to calculate the
current value of the bond.Coupon rate8.25%Yield to
maturity12.00%Years till maturity7Bond value$82.572IBM issued
12-year bonds two years ago at a coupon rate of 8.4 percent. The
bonds make semiannualpayments. If these bonds currently sell for
97.5 percent of par value, what is the YTM?Use Excel YIELD
functionBond value$95.8841.1660629527Par value (redemption
value)$100Coupon rate (annual)4.00%Years till
maturity5Today7/14/99Maturity7/13/04Yield to maturity4.95%3Stern
Investments has 14 percent coupon bonds issued by Rotten Tree Inc
with seven years to maturity. The bonds makesemiannual payments and
currently sell for 105 percent of par. What is the current yield on
the bonds?The YTM? The effective annual yield?Use Excel YIELD and
EFFECT functionsBond value$105.00Par value (redemption
value)$100Coupon rate (annual)14.00%Years till
maturity7Today7/14/99Maturity7/14/06Current yield13.33%Yield to
maturity12.89%Effective annual yield13.31%4The YTM on a bond is the
interest rate you earn on your investment if interest rates don't
change. If you actuallysell the bond before it matures, your
realized return is known as the holding period yield (HPY).a.
Suppose that today you buy a GE 9 percent coupon bond making annual
payments of $1,200. The bond has10 years to maturity. What rate of
return do you expect to earn on your investment?b. Two years from
now, the YTM on your bond has declined by 2.5 percent, and you
decide to sell. Whatprice will your bond sell for? What is the HPY
on your investment? Compare this to the YTM when youfirst bought
the bond. Why are they different?Use Excel YIELD and PRICE
functionsBond value$120.00Par value (redemption value)$100Coupon
rate (annual)9.00%Years till
maturity10Today7/14/99Maturity7/13/09Yield to maturity6.28%2 years
laterNew yield3.78%Par value (redemption value)$100Coupon rate
(annual)9.00%Years till maturity8Today7/13/01Maturity7/13/09New
Price135.78Holding period yieldBond value$120.00Par value
(redemption value)135.78Coupon rate (annual)9.00%Years till
maturity2Today7/14/99Maturity7/13/01Holding period yield13.46%5An
EDS Corp. bond carries an 8 percent coupon,paid semiannually. The
par value is $1,000 and the bondmatures in six years. If the bond
currently sells for$911.37, what is its yield to maturity?What is
the effective annual yield?Settle date1/1/97Mat
date1/1/03Rate8%Price91.137Frequency2Yield10.00%EAY10.25%6A
callable bond pays annual interest of $60,has a par value of
$1,000,matures in 20 years but is callable in 10 yearsat a price of
$1,100, and has a value today of $911.90.The yield to call on this
bond is:Settle date1/1/97Mat
date1/1/07Rate6%Price91.19Frequency1Yield7.27%7A coupon bond which
pays interest annually,has a par value of $1,000, matures in 5
yearsand has a yield to maturity of 12%.If the coupon rate is 9%,
the value of the bond todaywill be:Settle date1/1/97Mat
date1/1/02Rate9%Yield12%Frequency1Price89.198As a portfolio manager
at Putnam Management, you bought a 10-year, 8.25% semiannual-pay
bond at issuance2 1/2 years ago. At that time the yield to maturity
was 8.23%; it's now fallen to 7.10%. How much has the
bond'smodified duration changed?OriginalPresentSettle
date1/1/977/1/99Mat
date1/1/071/1/07Rate8.25%8%Yield8.23%9%Frequency22Modified
duration6.75.59You are the risk manager at a new savings bank,
Lostyur Trust. Mr Edgar Lostyur, sole shareholder, has beentold by
the regulatory authorities to provide them with the institution's
modified duration in order to evaluate itssensitivity to interest
rate fluctuations. The Prime rate is 8.25%.You find that the
initial balance sheet of the savings bank looks like
this:Assets:Cash on deposit2million face value3-month loans at
Prime + 2%13million face value4-year, 6% s.a. Treasury bonds
yielding6.35%20million face value7-year, 7.90% s.a. IBM bonds
yielding8.23%6million face valueLiabilities:6-month CDs at
4%3million face value5-year 9% s.a. bonds33million face
valueEquity:100,000sharesWhat can you tell the regulators the
bank's modified duration of assets is?Of liabilities? And what is
the net modified duration?Based on the net duration, what would be
the effect on net worth of a 10bp increase in
rates?ItemCashLoansTreas noteIBM bond6-mo CD5-yr
bondEquityAssetsLiab.+Eq.NetFace value213206333Settle
date1/1/971/1/971/1/971/1/971/1/971/1/97Mat
date1/1/974/1/971/1/011/1/047/1/971/1/02Rate-10.25%6.00%7.90%4.00%9.00%Yield-10.25%6.35%8.23%4.00%9.00%Frequency-22222Price100100.0098.7898.27100.00100.0046.52Value213.0019.765.903.0033.004.6540.6540.65Modified
duration00.23.55.30.54.02.543.25-0.71If rates rose by0.10%value
would change by0.0286609729millionand this is0.62%of4.65net
worth
&APage &P
