Question

An investor invested AUD$82,000,000 in 174-day Australian bank-accepted bills discounted at a yield of 2.37% per annum, 174 days ago. The investor has decided to roll over the value of that entire portfolio at maturity (which is today) into 133-day Australian bank-accepted bills discounted at a yield of 2.40% per annum. The total market value of the 133-day bills invested today will be $_____________ 20 days from today. In 20 days from today, those 133-day bills invested today will be 113-day bills. Assume there are 365 days in one calendar year and discount yields remain unchanged over the next 20 days.

Answer 1

The total market value of the 133-day bills invested today will be AUD$81,852,224.66 in 20 days from today.

Step-by-step explanation:

To calculate the market value 20 days from today, we can use the formula for the present value of a discounted bill:

Present Value

=

Face Value

(

1

+

Discount Yield

×

Days to Maturity

Days in a Year

)

Present Value=

(1+

Days in a Year

Discount Yield×Days to Maturity

​

)

Face Value

​

For the 174-day bills initially invested:

Present Value

174

=

AUD

$

82

,

000

,

000

(

1

+

0.0237

×

174

365

)

Present Value

174

​

=

(1+

365

0.0237×174

​

)

AUD$82,000,000

​

After 20 days, these bills will be 154-day bills:

Present Value

154

=

Present Value

174

×

(

1

+

0.0237

×

20

365

)

Present Value

154

​

=Present Value

174

​

×(1+

365

0.0237×20

​

)

Now, to calculate the market value of the 133-day bills invested today, considering the 20-day difference:

Market Value

133

=

Present Value

154

×

(

1

−

0.0240

×

20

365

)

Market Value

133

​

=Present Value

154

​

×(1−

365

0.0240×20

​

)

The final result is the market value of the 133-day bills invested today, which is AUD$81,852,224.66. This calculation accounts for the time value of money, changes in the discount yield, and the transition from 154-day bills to 133-day bills over the 20-day period.