Question

1. a)            From the following sets of figures (i) Calculate the bank discount rate on each T-bill and

(ii) Convert that rate to the appropriate investment (or coupon equivalent) yield.

                                – A new three-month T-bill sells for US98.25 on a US$100 basis.

                                – The investor can buy a new 12-month T-bill for US$96 on a US$100 basis.

– A 30 – day bill is available from a government securities dealer at a price of US$97.50

    (per US$100).

2.             Calculate the holding – period yield for the following situations:
3. The investor buys a new 12 – month T-bill at a discount rate of 7½ percent. Sixty days later, the bill is sold at a price that results in a discount rate of 7 percent.
4. A large manufacturing corporation acquired a T-bill in the secondary market 30 days from its maturity but is forced to sell the bill 15 days later. At time of purchase, the bill carried a discount rate of 8 percent, but was sold at Discount Rate of 7¾ percent.

Answer 1

Answer a

i)Determination of Bank discount rate for 3 months T Bill

T bill is $98.25 and Face value $100

Discount is $100 - $98.25 = $1.75

The discount to be divided by face value i.e. $1.75/$100 = .0175 i.e. 1.75%

Since this is three month T Bill

So 360/90 = 4 i.e. there are four three months period in a year

Therefore, 1.75% to be multiplied by 4 = 7%

Calculation of Investment yield

Yield = Interest Current price ˣ100

          = 7 98.25ˣ100

        

          = 7.12%

ii)Determination of Bank discount rate for 3 months T Bill

T Bill is $96 and Face value is $100

Discount is $100 - $96= $4

Since it is 12 month T bill so the rate of discount is ($4/100) ˣ1 = 4%

Calculation of Investment yield

Yield = Interest Current price ˣ100

          = 4 96ˣ100

        

          = 4.16%

iii)When T Bill is 1 month period the bank discount rate is the following

T Bill is $97.50 and Face value is $100

Discount is $100 - $97.50 = $2.5

The discount to be divided by face value i.e. $2.50/$100 = .025 = 2.5%

Since this is one month T Bill

So 360/30 = 12 i.e. there are 12 one month period in a year

Therefore, 2.5% ˣ12 = 30%

Calculation of Investment yield

Yield = Interest Current price ˣ100

          = 30 97.50ˣ100

        

          = 30.76%

Answer b

Calculation of holding period yield

Holding period yield = Money Market yield360Time to maturity ˣ100

Situation c) Duration 360 days sold after 60 days

Holding period yield = .0736060 ˣ100

                                   = .0116 ˣ100

                               =1.16%

Situation d) Duration 30 days for maturity and sold after 15 days

Holding period yield = .0433015 ˣ100

                                  = 2.15%