An investor purchases a 180 day T-Bill at auction for $97.50. What is the annual

ID: 2782989 • Letter: A

Question

An investor purchases a 180 day T-Bill at auction for $97.50. What is the annualized yield to maturity of the T-Bill? 1. 365 Pv 97.50 M0 Fv: 1D0 2. If the invesor sels the -Bill for .0 aftr 90 days what is the annualized yield for the holding period? 36 72.50 94.50 = ,0,50 Pi Use the following information for questions 3-5. An investor is considering the purchase of $1,000 of a newly issued 3 year corporate bond. The bond pays a 3.00% coupon annually and is rated Aa by Moody's. Other Aa rated 3 year corporate bonds currently trade at a spread of +50 basis points to the 3yr US Treasury Note which is yielding 4.00% today. 3. What should the price of the bond be? ka H.so Pnce : 972, 25 -- TV 10D0

Explanation / Answer

1. Present value=$97.50

Amount to be received after maturity( 180 days)=$100

Assume, annual yield=r

Yield in 180 days(assuming 365 days in a year)=r*(180/365)

Amount of yield=97.50*r*(180/365)

Amount of yield=Maturity value –Purchase price=100-97.5=2.5

97.5*r*(180/365)=2.5

r=(2.5*365)/(97.5*180)= 0.051994

Annualized yield in percent=0.051994*100%=5.1994% rounded to 5.2%

.2. Holding period annualized yield:

Sales price=$99.50

Number of days of holding=90 days

Original investment$97.50

Holding period gain=99.50-97.50=$2

Holding period yield=2/97.50

Annualized yield=(2/97.50)*(365/90)= 0.083191

Annualized yield in percent=8.3191% rounded to 8.32%

One basis point is =1/100 percent

50 basis point=50/100=0.5 percent

The market rate of Aa rated corporate bond=4+0.5=4.5%

Hence the yield to maturity should be 4.5%

Present Value of cash flows discounted at 4.5% should be the price of the bond

Present value(PV) of cash flows=(Cash flow)/(1+i)^N

Where i=discount rate =4.5%=0.045, N=year of cash flow

Annual coupon payment=3%=$30(0.03*1000)

Cash flows and PV of cash flows are given below:

B=A/(1.045^N)

Year

Cashflow

PV of cash flow

$30

28.70813397

$30

27.47189854

$1,030 *

902.5855022

TOTAL

958.7655347

*$1000 paid back on maturity. Hence cash flow in year 3=1000+30=$1030

Price of the bond=Total Present values of cash flows=$958.77