Question

Ben buys a 180-day $100 000 bank bill, 30 days after issue, for a price of $98 140.70 (the purchase yield is 4.61% p.a.). After holding the bill for 30 days Ben sells it at a yield of 4.56% p.a. (simple interest).

a. Construct a Cash flow diagram from Ben's perspective

b. Find the sale price.

c. Find Ben's simple interest yield p.a. (as a percentage, rounded to 2 decimal places) over the 30-day holding period.

d. Explain how Ben's yield calculated in b. would change (increase or decrease) if the sale yield was less than 4.56% p.a. Why would the yield change in this way?

e. When a bank bill is purchased and sold before maturity the dollar return consists of two components—a capital component and an interest component. State how to calculate the capital component.

f. Explain in your own words and with reference to the purchase yield and the sale yield when the capital component will be a gain and when it will be a loss.

g. Use your explanation in (f.) to determine whether the capital component of Ben's bank bill investment will be a gain or a loss. Note that you are not required to calculate the actual value of the capital component.

Answer 1

The Bill was purchased after 30 days of issue (150 days remaining till maturity) and sold after 30 days from purchase (120 days remaining till maturity)

Bill was sold at 4.56% yield i.e. 4.56%*120/365 =1.499178% for 120 days

As the Bill was issued at a discount , discount rate = i/(1+i) = 0.01499178/1.01499178 = 0.0147703

So, Selling price = 100000 * (1-d) = 100000 * (1-0.0147703) = $98522.97

a) The cashflow diagram from Ben's perspective is as attached

  

b) The Sale price is $98522.97 as calculated above

c) Ben's profit in 30 days holding = 98522.97 - 98140.70 =$382.27

% gain in 30 days = 382.27/98140.70 =0.003895

% gain in 1 year (365 days) = 0.003895 *365/30 = 0.047391 = 4.74% (rounded to two decimal places)

Ben's % yield in Simple interest is 4.74%

d) If the sale yield was less than 4.56% , then the selling price would be higher than $98522.97 (as yield is inversely related to price).

If Selling price is higher than $98522.97, then Ben's yield will be higher than 4.74%

So, Ben's yield will increase if sale yield is less than 4.56%   as explained above