Problem Set 2 Due 1.19.24的副本

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Feb 20, 2024

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Corporate Finance PBPL 28683/PPHA 34410 Problem Set 2 Due January 19, 2024 11:59PM CST Submit via Gradescope 90 Points Show your work (either as a spreadsheet or by showing the formula you used.) 1. Calculate how much money you will have if you invest $100,000: (5 pts.) a. at 7.2% annually for 10 years b. at 9.0% annually for 8 years c. at 8.0% annually for 9 years d. at 16% annually for 4.5 years e. These are examples of “the rule of 72”. Why do you think that name was given to these examples? 2. Calculate the future value of $50,000 invested today, given the following rates and time periods. (5 pts.) a. r=4%, t= 10 years b. r=8%, t=10 years c. r=10%, t=20 years d. r=15%, t =20 years 3. Calculate the present value of $50,000 received in t number of years, given the rates and time periods shown in question 2. (5 pts.) 4. You are building a new office headquarters that is estimated to create efficiencies, saving your company $9,000,000 annually for ten years. You will move in immediately upon completion. The building cost, which you will pay upon completion, is estimated at $55,000,000. If this estimated saving is correct and your company’s cost of capital is 12% annually, does this appear to be a good investment? What is the name of the rule you used to make this decision? (10 pts.) 5. (5 pts. each) a. You have the opportunity to invest in a growing perpetuity paying $100,000 per annum in year 1. The rate of growth is expected to be 4% annually. If the market rate of interest is 6% annually, how much should you be willing to pay for this perpetuity? b. You have the opportunity to invest in a growing 10 year annuity paying $100,000 per annum in year 1. The growth rate is expected to be 6% annually. If the market rate of interest is 7% annually, how much should you be willing to pay for this annuity? What would you pay for the annuity if instead of 10 years, the annuity’s term is 20 years?
6. You won your state lottery and the prize is available in several alternative payments: (15 pts.) a. $100,000,000 today b. $18,000,000 per annum for 8 years c. $6,000,000 per annum in perpetuity d. $10,000,000 per annum for 20 years e. $1,500,000 in year one, growing at 3.5% per annum in perpetuity Which would you choose if the available market interest rate is 4% annually? Which, if the rate were 8%? 7. Recall the OAT bond we looked at in class. Using the cash flows below, answer the following questions: 2021 2022 2023 2024 2025 2026 3.50 3.50 3.50 3.50 3.50 103.50 Cash Flows (€) a. What would be the price of the 3.50% OAT’s on April 30, 2020 if annual interest rates for newly issued six year French government bonds were: (5 pts.) i. 3.5%? ii. 1.0%? b. What is the yield to maturity for the 3.50% OAT bond on April 30, 2020 when the annual interest rates for newly issued six year French government bonds were: (5 pts.) i. 3.5%? ii. 1.0%? 8. All of the bonds below are mispriced to some degree in the spreadsheet below given the market interest rate assumptions. If you have the choice of buying any of these bonds at the stated price, which would you choose if the market rate of interest were 4%? What would you choice be if the market rate of interest were 8%? Assume all bonds have a face amount of $100 at maturity. (10 pts.). Hint: Think about which bonds are the best value for each dollar you have to spend (or to borrow to sell short, see question 9). Coupon Maturity 4% 8% Bond A 5% 7 99 81 Bond B 3% 10 89 66 Bond C 0% 5 78 64 Bond D 0% 2 91 86 Bond E 8% 6 122 101 Bond F 4% 4 98 83 Market Price at
9. Using the information above which bond would you sell short at a 4% market rate of interest? At an 8% market rate of interest? (10 pts.) 10. Use the Bond Price Duration Calculator (the “Calculator”) spreadsheet I provided to compare the following two bonds, assuming the market discount rate is 5% annually: A six-year maturity zero coupon note with a face value of $1,000. A seven-year maturity note paying 12% annually with a face value of $1,000. (You need to think carefully about the adjustments you need to make to the Calculator to get this to work.) (10 pts.) a. Which note is riskier according to their duration? b. Does this result surprise you? Give a common-sense explanation of this result.
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