Question

Yolanda bought a 180-day $100000 bank bill 74 days ago for $98300.00. She sold it to George today and received $99000.00.
(i) [2 marks] Draw a cash flow diagram that captures the details of Yolanda’s transactions.

(ii) [2 marks] Calculate the purchase yield (simple interest rate) and sale yield (simple interest rate) of this bill (as a percentage, rounded to 2 decimal places).

(iii) [2 marks] Without any further calculations, explain how the selling price will change if George accepts a lower yield.

(iv) [2 marks] Calculate capital gain or capital loss component of Yolanda’s investment (in dollars and cents, to the nearest cent).

(v) [4 marks] Assuming Yolanda borrowed to purchase the bond, what is the break-even rate of interest of borrowing (simple interest, as a percentage, rounded to 2 decimal places)? If the borrowing cost rate is 10 basis points higher than the break-even rate, explain whether Yolanda will end up with a cash surplus or cash deficit.

Answer 1

Solution:

1.Cash flow of Yolanda’s transactions

Day	0	74
Purchase of Bank Bill	-$98300.00	-
Sale of Bank Bill	-	$99000.00

2.Calculation of Purchase Yield and Sale yield

Purchase Yield=Change in Price/Purchase Price

Change in price=($100,000-$98,300)/180*74

=$698.90

thus purchase yield=$698/$98,300

=.0071

Convert to Simple Interest=.0071/74*365

=.035 or 3.5% annually

Sale Yield=(Sale Price-Purchase Price)/PurchasePrice

=($99,000-$98,300)/$98,300

=.00712

Convert to simple Interest=.0071/74*365

=.0351 or 3.51% annually

3.There is inverse relationship between yield and price.Thus if if George accepts a lower yield then the selling price will increase.

4.Calculation of Capital Gain

Capital Gain=Sale price-purchase price

=$99,000-$98300

=$700