Tutorial Work Sheet: Module 4: Solutions - CA Sri Lanka

[Pages:3]Tutorial Work Sheet: Module 4: Solutions

1. What is the current price of a 90-day BAB issued 11 days ago (i.e. with 80 days to maturity), given a market yield of 6.4% p.a.?

Solution: P = 100/ [1 + (.064 * 80/365)] = $98.62

Note a face value of $100 has been assumed. 2. A BAB has a face value of $1 million, a yield of 5.5% and 90 days to maturity. Assuming

that the yield does not change, what is its price (a) today, (b) in 30 days' time and (c) in 75 days' time? Explain your results.

Solution:

a) P = 1,000,000/[1 + (0.055*90/365)] = $986,619.81

b) P = 1,000,000/[1 + (0.055*60/365)] = $991,039.91

c) P = 1,000,000/[1 + (0.055*15/365)] = $997,744.82

3. Given that a bank will pay 5.1% on a three-month fixed term deposit of $50,000 with the interest compounded daily, calculate the amount the bank will pay at maturity assuming the period is 91 days.

The amount due at maturity is calculated on the basis of daily compound interest as

follows:

F

$50,000 *

1

0.051 365

91

$50,639.77

4. Using the data in question 3, calculate the effective annual interest rate.

The effective interest rate is calculated as follows:

365

reffective

50,639.77 50,000

91

1 5.23%

5. Calculate the amount of interest that would be earned on a 90-day CD of $5 million it was accepted at 5.5% per annum.

Solution: I $5m * 0.055 * 90365 $67,808.22

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6. Calculate the amount of interest that would be earned by the depositor in Q5 if the CD was sold after 60 days at 5.6%.

SOLUTION:

The interest earned is the present value of the CD's face value with 30 days to maturity at 5.6% less the $5m deposit, calculated as follows:

F $5m 1 0.055 * 90 $5,067,808.22

365

P $5,067,808.22 $5,044,589.29

1 0.056 *

30

365

I $44,589.29

7. Suppose the 90-day bank bill reference rate is 6.35%. BNZ bank accepted a company's 90day bills with a face value of $20 million and charged fees of $52447. Calculate the borrower's interest rate.

Solution:

The borrower's interest rate is the difference between the redemption payment and the net proceeds expressed as an annual rate of simple interest, calculated as follows:

P

1

$20m 0.0635 * 90

365

$19,691,677

r

$20m

1 365 7.45%

$19,691,677 52,447 90

8. Suppose an active investment manager purchased a $50 million parcel of 90-day bills at 6.25% and sold them 10 days later at 6.35%. Calculate the investment return.

Solution:

The investment yield is calculated as follows, having first calculated the selling price.

Note the answer must be less than 6.25% since the securities were sold at a higher yield

and so the return includes a capital loss:

Pbuy

1

$50m 0.0625 * 90365

$49,241,147

Psell

$50m 1 0.0635 * 80365

$49,313,662

r 49,313,662 1 365 5.38% 49,241,147 10

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9. For the data given in (8), calculate the amount of interest earned by the investment and the amount of capital loss.

Solution:

The amount of interest earned over 10 days is calculated as the hypothetical selling price at 6.25% and the buying price and the capital loss is the difference between the hypothetical selling price at 6.25% and the actual selling price at 6.35%, calculated as follows:

P6.25%

1

$50m 0.0625 * 80365

$49,324,324

Interest $49,324,324 $49,241,147 $83,177

Capital loss $49,324,324 $49,313,662 $10,662

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