Question

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

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

(b) Calculate the purchase yield (simple interest rate) and sale yield (simple interest rate) of this bill (as a %, rounded to 2 d.p.)

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

(d) Calculate capital gain or capital loss component of Tokio's investment (in dollars and cents, to the nearest cent).

(e) Assuming Tokio 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 Tokio will end up with a cash surplus or cash deficit.

Answer 1

(a)

Day	Cash-flows for Tokio
-74	-98300
-70	0
-60	0
-50	0
-40	0
-30	0
-20	0
-10	0
0	99000

(b)

Purchase yield r(p)

100000= 98300*(1+r(s)*T)

T=180/365

1+r(s)*T = 100000/98300

r(s)*T = (100000/98300) -1 = 0.01729399796

r(s) = 0.03506= 3.506%

Sale yield r(s)

99000 = 98300*(1+r(s)*T)

T=74/365

1+r(s)*T = 99000/98300

r(s)*T = (99000/98300) -1 = 0.00712105798

r(s) = 0.035124= 3.512%

(c) If Samuel accepts a lower yield, the selling price would be higher. This is because as the yield decrease, the price of a bank bill increases.

(d) Since Tokio has sold the bank bill at a higher price, there is a profit.

Profit =  $99,000.00 -$98,300.00 = $700

(e) The sales yield as calculated in part b) = 3.512%

This 3.512% is break-even rate of interest of borrowing as if the rate of interest of borrowing is 3.512%, then there is no profit no loss on the investment in bank bill.

If the borrowing cost rate is 10 basis points higher than the break-even rate, ie the borrowing cost is at 3.612%, then Tokio will end up with a cash deficit. This is because at the end of the 180 day period, Tokia will get an effective simple rate of interest =3.512% and she will have to pay the debtors The amount of cash-deficit = 0.1%*100,000*180/365 = $49.315