Financial Management Homework #5

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New York University *

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Finance

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Feb 20, 2024

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Financial Management Homework #5 Critical Thinking & Critical Review: 5.1 As you increase the length of time involved, what happens to the present value of an annuity? What happens to the future value? Assuming positive cash flows and a positive interest rate, both the present and the future value will rise. 5.2 What happens to the future value of an annuity if you increase the rate, r? What happens to the present value? Assuming positive cash flows and a positive interest rate, the present value will fall, and the future value will rise. 5.3 Tri-State Megabucks Lottery advertises a $10 million grand prize. The winner receives $500,000 today and 19 annual payments of $500,000. A lump sum option of $5 million payable immediately is also available. Is this deceptive advertising? It’s deceptive, but very common. The deception is particularly irritating given that such lotteries are usually government sponsored! 5.4 Suppose you won the Tri-State Megabucks Lottery in the previous question. What factors should you take into account in deciding whether you should take the annuity option or the lump sum option? The most important consideration is the interest rate the lottery uses to calculate the lump sum option. If you can earn an interest rate that is higher than you are being offered, you can create larger annuity payments. Of course, taxes are also a consideration, as well as how badly you really need $5 million today. 5.5 If you were an athlete negotiating a contract, would you want a big signing bonus payable immediately and smaller payments in the future, or vice versa? How about looking at it from the team’s perspective? If the total amount of money is fixed, you want as much as possible as soon as possible. The team (or, more accurately, the team owner) wants just the opposite. 5.6 Suppose two athletes sign 10-year contracts for $80 million. In one case, we’re told that the $80 million will be paid in 10 equal installments. In the other case, we’re told that the $80 million will be paid in 10 installments, but the installments will increase by 5 percent per year. Who got the better deal? The better deal is the one with equal installments.

5.7 Should lending laws be changed to require lenders to report EARs instead of APRs? Why or why not? Yes, they should. APRs generally don’t provide the relevant rate. The only advantage is that they are easier to compute, but, with modern computing equipment, that advantage is not very important. 5.8 On subsidized Stafford loans, a common source of financial aid for college students, interest does not begin to accrue until repayment begins. Who receives a bigger subsidy, a freshman or a senior? Explain. A freshman does. The reason is that the freshman gets to use the money for much longer before interest starts to accrue. 5.9 In words, how would you go about valuing the subsidy on a subsidized Stafford loan? The subsidy is the present value (on the day the loan is made) of the interest that would have accrued up until the time it begins to accrue. 5.10 Eligibility for a subsidized Stafford loan is based on current financial need. However, both subsidized and unsubsidized Stafford loans are repaid out of future income. Given this, do you see a possible objection to having two types? The problem is that the subsidy makes it easier to repay the loan, not obtain it. However, the ability to repay the loan depends on future employment, not current need. For example, consider a student who is currently needy, but is preparing for a career in a high-paying area (such as corporate finance!). Should this student receive the subsidy? How about a student who is currently not needy, but is preparing for a relatively low-paying job (such as becoming a college professor)?

Questions and Problems: 1. Eulis Co. has identified an investment project with the following cash flows. If the discount rate is 10 percent, what is the present value of these cash flows? What is the present value at 18 percent? At 24 percent? Year Cash Flow 1 $680 2 490 3 975 4 1,160 PV = FV / (1 + r)t PV@10% = $680/(1.10) + $490/(1.10)^2 + $975/(1.10)^3 + $1,160/(1.10)^4 = $2,547.97 PV@18% = $680/(1.18) + $490/(1.18)^2 + $975/(1.18)^3 + $1,160/(1.18)^4 = $2,119.91 PV@24% = $680/(1.24) + $490/(1.24)^2 + $975/(1.24)^3 + $1,160/(1.24)^4 = $1,869.09 2. Investment X offers to pay you $3,400 per year for nine years, whereas Investment Y offers to pay you $5,200 per year for five years. Which of these cash flow streams has the higher present value if the discount rate is 6 percent? If the discount rate is 22 percent? PVA = C({1 – [1/(1 + r)t]} / r) At an interest rate of 6 percent: X@6%: PVA = $3,400{[1 – (1/1.06)^9 ] / .06 } = $23,125.75 Y@6%: PVA = $5,200{[1 – (1/1.06)^5 ] / .06 } = $21,904.29 And at an interest rate of 22 percent: X@22%: PVA = $3,400{[1 – (1/1.22)^9 ] / .22 } = $12,873.37 Y@22%: PVA = $5,200{[1 – (1/1.22)^5 ] / .22 } = $14,890.93 Investment X has greater PV at 6% but a lower PV at 22% interest rate. 3. Booker, Inc., has identified an investment project with the following cash flows. If the discount rate is 8 percent, what is the future value of these cash flows in Year 4? What is the future value at an interest rate of 11 percent? At 24 percent? Year Cash Flow 1 $985 2 1,160 3 1,325 4 1,495 FV = PV(1 + r)t FV@8% = $985(1.08)^3 + $1,160(1.08)^2 + $1,325(1.08) + $1,495 = $5,519.84 FV@11% = $985(1.11)^3 + $1,160(1.11)^2 + $1,325(1.11) + $1,495 = $5,742.10

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