Question

a. Janet purchased a 180-day $100 000 bank bill 74 days ago for $98 300.00. She sold it to Timothy today and received $99 000.00.

(i) Draw a cash flow diagram that captures the details of Janet's transactions.

(ii) 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) Without any further calculations, explain how the selling price will change if Timothy accepts a lower yield.

(iv) Calculate capital gain or capital loss component of Janet investment (in dollars and cents, to the nearest cent).

(v) Assuming Janet 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 Janet will end up with a cash surplus or cash deficit.

Answer 1

(i) Cash flow diagram

Time	0th day	74th day
Cashflow	-$98300	$99000

(ii)

Purchase yield

98300 = 100000/(1+y*180/365)

y = 3.51% pa (purchase yield)

Sale yield = ((99000-98300)/98300)*365/74 = 3.51% pa

(iii) The selling price will increase if Timothy accepts a lower yield

(iv) Capital gain = 99000-98300 = $700

(v) Let the breakeven interest rate = r

98300*r*180/365 = 700

r = 1.44% (break even interest rate)

If the borrowing cost rate is 10 basis points higher than the break-even rate, Janet will end up with a cash deficit.