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Problem Set 1: Solutions UCLA MQE Core Finance Prof. Pierre-Olivier Weill 1. Exercise 1 (a) What should be, at time t = 0, the price of a security that pays 100 each year t ∈ { 1 , 2 , 3 , 4 , 5 } ? The price of this security is given by P 1 = 100 1 . 03 + 100 1 . 03 2 + 100 1 . 03 3 + 100 1 . 03 4 + 100 1 . 03 5 = 457 . 97 (b) What should be, at time t = 0, the price of a security that pays 100 in all year t ≥ 6? To answer this question, we use the annuity formula with T = ∞ (what is called the “perpetuity” formula). It implies that, at t = 5, the price of the security that pays 100 in all years t ≥ 6 is 100 / 0 . 03. To obtain the price at time t = 0, we apply the present value factor 1 / (1 . 03) 5 . In sum, we obtain P 2 = 100 0 . 03(1 . 03) 5 = 2875 . 36 (c) What should be, at time t = 0, the price of a perpetuity that pays 100 every year? Using again the annuity formula with T = ∞ we obtain: P 3 = 100 0 . 03 = 3333 . 33 (d) Explain the relationship between the security prices you calculated in questions (a), (b), and (c). One can verify that the relationship is P 1 + P 2 = P 3 . This is so because the payoff of security 3 is the sum of the payoff of security 1 and security 2. 2. Exercise 2: please see Python code. 3. Problem 8 in Chapter 2 of Luenberger, on sunk cost. A young couple has made a nonrefundable deposit equal to a month’s rent ( $ 1,000) on a 6-month apartment lease 2 days ago. Yesterday, the last day of the last month, they found a different apartment (near the aforementioned one) that they like just as well, but its monthly rate is just $ 900. They would need to pay the initial $ 1,000 nonrefundable deposit

with the first monthly rent payment for this new apartment. Rent is paid at the beginning of the month. They plan to be in the apartment only 6 months. It’s 7:00 am of the first day of the month and they have to move today to their preferred apartment at 11:00 am after making the corresponding payment. Should they switch to the new apartment? What if they plan to stay 1 year? Assume a monthly interest rate of 1%. To answer this question we first construct a table to summarize the required payments for both apartments for the first 6 months: Month 1 Month 2 Month 3 Month 4 Month 5 Month 6 Current Apartment $ 1,000 $ 1,000 $ 1,000 $ 1,000 $ 1,000 $ 1,000 New Apartment $ 1,900 $ 900 $ 900 $ 900 $ 900 $ 900 If they plan to stay for 6 months, the present value of the remaining payments for the current apartment 1: PV(Current Apt, 6 months) = $1 , 000 + $1 , 000 0 . 01 × " 1 - 1 (1 + 0 . 01) 5 # = $5 , 853 . 43 If they plan to stay for 6 months, the present value of the remaining payments for the new apartment is: PV(New Apt, 6 months) = $1 , 900 + $900 0 . 01 × " 1 - 1 (1 + 0 . 01) 5 # = $6 , 268 . 09 Since the second PV is larger that the first, we conclude that, if they plan to stay for 6 months only, the young couple should not switch to the new apartment. If they plan to stay for one year, the present value of the remaining payments for the current apartment is: PV(Current Apt, 12 months) = $1 , 000 + $1 , 000 0 . 01 × " 1 - 1 (1 + 0 . 01) 11 # = $11 , 367 . 62 If they plan to stay for one year, the present value of the remaining payments for the new apartment is: PV(Current Apt, 12 months) = $1 , 900 + $900 0 . 01 × " 1 - 1 (1 + 0 . 01) 11 # = $11 , 230 . 87

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Question 11

ques 11

We have purchased a security with the following payment schedule: Year 1 2 3 Payment $100 S150 S400 If the present value of this investment is $580.59, what is the rate of return (or interest rate) ?

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Hi could you please help solve this? Thanks

Q. 16 Consider a security with a duration of 7 years. The current interest rate level is 10% p.a. How does the price of the security change if interest rates increase by 1.5% (round your answer to two decimals) ? Choose the correct option The price of the security will decrease by 1.5%. The price of the security will increase by 1.5%. The price of the security will decrease by 8.5%. The price of the security will increase by 9.55%. The price of the security will decrease by 9.55%.

hi could you please help solve questions 5.2?

If Po is the initial price of the security, P₁ is the price after you hold it for a year, and X represents a direct payment, an asset's rate of return is equal to: rate of return = (P₁ - Po) rate of return = (P₁ - Po) + X rate of return = (P₁-Po) / Po + XPo rate of return = (P₁ - Po)/Po + X

plz solve the question with explanation get upvotes

Question 5.A bank has borrowing needs at timeT >0. Show that by combining an FRAtrade today with a libor loan at timeT, the bank can today lock in its interest cost forthe periodTtoT+α. Does the borrowing bank need to buy or sell the FRA to do this?What is the fixed rate that the bank locks in?

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Q24

4. Finding the interest rate and the number of years The future value and present value equations also help in finding the interest rate and the number of years that correspond to present and future value calculations. If a security currently worth $5,600 will be worth $12,379.82 seven years in the future, what is the implied interest rate the investor will earn on the security—assuming that no additional deposits or withdrawals are made? 12.00% 4.52% 9.60% 0.32% If an investment of $35,000 is earning an interest rate of 4.00%, compounded annually, then it will take for this investment to reach a value of $44,286.17—assuming that no additional deposits or withdrawals are made during this time. Which of the following statements is true—assuming that no additional deposits or withdrawals are made? If you invest $1 today at 15% annual compound interest for 82.3753 years, you’ll end up with $100,000. If you invest $5 today at…

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Attempts 4. Finding the interest rate and the number of years The future value and present value equations also help in finding the interest rate and the number of years that correspond to present and future value calculations. If a security currently worth $2,000 will be worth $2,809.86 three years in the future, what is the implied interest rate the investor will earn on the security-assuming that no additional deposits or withdrawals are made? O9.60% Keep the Highest / 10 O 0.47% O 12.00% O 7.12% If an investment of $30,000 is earning an interest rate of 8.00%, compounded annually, then it will take a value of $37,791.36-assuming that no additional deposits or withdrawals are made during this time. for this investment to reach Which of the following statements is true-assuming that no additional deposits or withdrawals are made? O An investment of $25 at an annual rate of 10% will return a higher value in five years than $50 invested at an annual rate of 5% in the same time. O An…

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6. Finding the interest rate and the number of years The future value and present value equations also help in finding the interest rate and the number of years that correspond to present and future value calculations. If a security currently worth $9,200 will be worth $15,767.18 seven years in the future, what is the implied interest rate the investor will earn on the security-assuming that no additional deposits or withdrawals are made? 5.83% O6.40% 8.00% O 1.71 % If an investment of $50,000 is earning an interest rate of 8.00%, compounded annually, then it will take a value of $89,052.92-assuming that no additional deposits or withdrawals are made during this time. for this investment to reach Which of the following statements is true-assuming that no additional deposits or withdrawals are made? An investment of $25 at an annual rate of 10% will return a higher value in five years than $50 invested at an annual rate of 5% in the same time. An investment of $50 at an annual rate of…

5. Finding the interest rate and the number of years The future value and present value equations also help in finding the interest rate and the number of years that correspond to present and future value calculations. If a security currently worth $9,200 will be worth $15,767.18 seven years in the future, what is the implied interest rate the investor will earn on the security-assuming that no additional deposits or withdrawals are made? O 8.00% O 5.83% 1.71% O 0.24% If an investment of $50,000 is earning an interest rate of 8.00%, compounded annually, then it will take a value of $89,052.92-assuming that no additional deposits or withdrawals are made during this time. Which of the following statements is true-assuming that no additional deposits or withdrawals are made? O If you invest $1 today at 15% annual compound interest for 82.3753 years, you'll end up with $100,000. O If you invest $5 today at 15% annual compound interest for 82.3753 years, you'll end up with $100,000. for…

Assume that you are given the following historical returns for the Market and Security J. Also assume that the expected risk-free rate for the coming year is 4.0 percent, while the expected market risk premium is 15.0 percent. Given this information, determine the required rate of return for Security J for the coming year, using CAPM. Year 1 2 O21.20% 3 4 5 6 O22.34% O 23.49% O24.63% O24.10% Market 10.00% 12.00% 16.00% 14.00% 12.00% 10.00% Security J 12.00% 14.00% 18.00% 22.00% 18.00% 14.00%

hi could you please help solve exercise 5.24?

5. Finding the interest rate and the number of years The future value and present value equations also help in finding the interest rate and the number of years that correspond to present and future value calculations. If a security currently worth $12,800 will be worth $16,843.93 seven years in the future, what is the implied interest rate the investor will earn on the security—assuming that no additional deposits or withdrawals are made? 7.60% 0.19% 4.00% 1.32% If an investment of $40,000 is earning an interest rate of 4.00%, compounded annually, then it will take for this investment to reach a value of $53,679.69—assuming that no additional deposits or withdrawals are made during this time. Which of the following statements is true—assuming that no additional deposits or withdrawals are made? It takes 14.21 years for $500 to double if invested at an annual rate of 5%. It takes 10.50 years for $500 to double if invested…

3. Finding the interest rate and the number of years Aa Aa E The future value and present value equations also help in finding the interest rate and the number of years that correspond to present and future value calculations If a security currently worth $9,200 will be worth $12,106.57 seven years in the future, what is the implied interest rate the investor will earn on the security-assuming that no additional deposits or withdrawals are made? 7.60% 0 0.19% О 4.00% О 1.32% If an investment of $35,000 is earning an interest rate of 4.00%, compounded annually, then it will take for this investment to reach a value of $41,755.92-assuming that no additional deposits or withdrawals are made during this time. Which of the following statements is true-assuming that no additional deposits or withdrawals are made? It takes 10.50 years for $500 to double if invested at an annual rate of 5%. 0 It takes 14.21 years for $500 to double if invested at an annual rate of 5%.

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