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The ask discount rate on a particular money market instrument is 3.75%. The face...
Mar 16, 2024
The ask discount rate on a particular money market instrument is 3.75%. The face value is 200,000anditmaturesin51days.Whatisitscurrentprice?Whatwouldbethecurrentpriceifithad71daystomaturity?(b)Whatwouldbeyouraskdiscountrate162−dayTreasurybillfor200,000 and it matures in 51 days. What is its current price? What would be the current price if it had 71 days to maturity? (b) What would be your ask discount rate % and bond equivalent rate % on the purchase of a 162-day Treasury bill for 4,875 that pays $5,000 at maturity?
Answer
The current price of the money market instrument with 51 days to maturity is 198,537.50,andwith71daystomaturity,itis198,537.50, and with 71 days to maturity, it is 198,212.50. The ask discount rate on the purchase of a 162-day Treasury bill is 3.07%, and the bond equivalent rate is 6.23%.
Solution
a
Current Price Calculation for 51 days: The current price is calculated using the formula P=FV×(1−d×t360) P = FV \times \left(1 - \frac{d \times t}{360} \right) where P P is the current price, FV FV is the face value, d d is the discount rate, and t t is the time to maturity in days
b
Current Price for 51 days: Using the formula, P=200,000×(1−0.0375×51360)=200,000×(1−0.00520833)=200,000×0.99479167=$198,537.50 P = 200,000 \times \left(1 - \frac{0.0375 \times 51}{360} \right) = 200,000 \times (1 - 0.00520833) = 200,000 \times 0.99479167 = \$198,537.50
c
Current Price Calculation for 71 days: Using the same formula with t=71 t = 71 days, P=200,000×(1−0.0375×71360)=200,000×(1−0.00739583)=200,000×0.99260417=$198,212.50 P = 200,000 \times \left(1 - \frac{0.0375 \times 71}{360} \right) = 200,000 \times (1 - 0.00739583) = 200,000 \times 0.99260417 = \$198,212.50
d
Ask Discount Rate Calculation: The ask discount rate is calculated using the formula d=FV−PFV×360t d = \frac{FV - P}{FV} \times \frac{360}{t} where P P is the purchase price of the Treasury bill
e
Ask Discount Rate for Treasury bill: Using the formula, d=5,000−4,8755,000×360162=0.025×2.22222222=0.0307 or 3.07% d = \frac{5,000 - 4,875}{5,000} \times \frac{360}{162} = 0.025 \times 2.22222222 = 0.0307 \text{ or } 3.07\%
f
Bond Equivalent Rate Calculation: The bond equivalent rate (BER) is calculated using the formula BER=FV−PP×365t BER = \frac{FV - P}{P} \times \frac{365}{t}
g
Bond Equivalent Rate for Treasury bill: Using the formula, BER=5,000−4,8754,875×365162=0.02564103×2.25308642=0.0623 or 6.23% BER = \frac{5,000 - 4,875}{4,875} \times \frac{365}{162} = 0.02564103 \times 2.25308642 = 0.0623 \text{ or } 6.23\%
Key Concept
Discount Rate and Bond Equivalent Rate
Explanation
The discount rate is the percentage reduction from the face value of a bill, reflecting the interest cost to the purchaser. The bond equivalent rate is an annualized version of the discount rate, adjusted for a 365-day year, providing a comparable rate to bonds with semiannual interest payments.
Key Concept
Current Price of Money Market Instruments
Explanation
The current price of a money market instrument is calculated by discounting its face value by the discount rate over the period until maturity, adjusted for a 360-day year, which is a banking convention.
You borrowed $10,000,000 in the commercial paper market. The rate on 60-day commercial paper is 6.58 percent. (a) If you issued 60-day commercial paper through a dealer, how much must you repay at the end of the 60-day period? (5 marks) (b) Assume that, 60 days from now, CP rates have not changed. Instead of repaying your borrowings, you want to roll them over for another 60 days. How much must you repay at the end of the second 60 days?
Answer
For part (a), you must repay 10,329,000attheendofthe60−dayperiod.Forpart(b),youmustrepay10,329,000 at the end of the 60-day period. For part (b), you must repay 10,662,842 at the end of the second 60-day period.
Solution
a
Calculation of Repayment Amount for the First 60-Day Period:
The amount to be repaid can be calculated using the formula for the future value of a present amount at simple interest: $FV = PV(1 + rt)$, where $PV$ is the present value, $r$ is the rate, and $t$ is the time in years. Given that $PV = $10,000,000, $r = 6.58\% = 0.0658$, and $t = \frac{60}{365}$ years, we can calculate the future value as follows: $FV = $10,000,000 \times (1 + 0.0658 \times \frac{60}{365}) = $10,329,000.
b
Calculation of Repayment Amount for the Second 60-Day Period:
Assuming the rate has not changed, we use the future value from part (a) as the new present value and apply the same formula: $FV_{\text{new}} = FV_{\text{old}}(1 + rt)$. With $FV_{\text{old}} = $10,329,000, $r = 0.0658$, and $t = \frac{60}{365}$ years, the new future value is $FV_{\text{new}} = $10,329,000 \times (1 + 0.0658 \times \frac{60}{365}) = $10,662,842.
Key Concept
Simple Interest Calculation
Explanation
The repayment amount for commercial paper is calculated using the simple interest formula, which takes into account the principal amount, the interest rate, and the time period of the loan.
Key Concept
Rollover of Commercial Paper
Explanation
When commercial paper is rolled over, the future value of the initial borrowing becomes the present value for the next borrowing period, and the same interest calculation is applied again to determine the new repayment amount.
You borrowed $10,000,000 in the commercial paper market. The rate on 60-day commercial paper is 6.58 percent. (a) If you issued 60-day commercial paper through a dealer, how much must you repay at the end of the 60-day period? (5 marks) (b) Assume that, 60 days from now, CP rates have not changed. Instead of repaying your borrowings, you want to roll them over for another 60 days. How much must you repay at the end of the second 60 days?
Answer
For part (a), you must repay 10,165,333.33attheendofthe60−dayperiod.Forpart(b),youmustrepay10,165,333.33 at the end of the 60-day period. For part (b), you must repay 10,334,444.44 at the end of the second 60-day period.
Solution
a
Calculation of Repayment Amount for the First 60-day Period: The repayment amount is calculated using the formula for the future value of a present amount at simple interest: FV=PV(1+rt) FV = PV(1 + rt) where FV FV is the future value, PV PV is the present value, r r is the rate of interest (expressed as a decimal), and t t is the time period in years
b
Applying the Formula for the First 60-day Period: Given that PV=$10,000,000 PV = \$10,000,000 , r=6.58%=0.0658 r = 6.58\% = 0.0658 , and t=60360 t = \frac{60}{360} (since commercial paper rates are annualized and there are 360 days in the commercial paper market year), we get: FV=$10,000,000(1+0.0658×60360)=$10,165,333.33 FV = \$10,000,000(1 + 0.0658 \times \frac{60}{360}) = \$10,165,333.33
c
Calculation of Repayment Amount for the Second 60-day Period: To find the repayment amount for the second 60-day period, we use the future value from the first period as the present value for the second period
d
Applying the Formula for the Second 60-day Period: Using the future value from part (a) as the new present value, we get: FVsecond period=$10,165,333.33(1+0.0658×60360)=$10,334,444.44 FV_{\text{second period}} = \$10,165,333.33(1 + 0.0658 \times \frac{60}{360}) = \$10,334,444.44
Key Concept
The future value of a present amount at simple interest is used to calculate the repayment amount for commercial paper.
Explanation
The repayment amount includes the principal plus the interest accrued over the 60-day period, calculated at an annualized interest rate. When rolling over the debt for another 60 days, the future value at the end of the first period becomes the present value for the second period's calculation.
On June 15, 2018, you purchase a $100,000 T-note that matures on Nov 15, 2024 (settlement occurs two days after purchase, so you receive actual ownership of the bond on June 17, 2018). The coupon rate on the T-note is 5.4% and the current price quoted on the bond is 108:08. The last coupon payment occurred on May 15, 2018, and the next coupon payment will be paid on Nov 15, 2018. a. Calculate the accrued interest due to the seller from the buyer at settlement. b. Calculate the dirty price of this transaction.
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