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Fundamentals of Coporate Finance Ch4~5 Ross

By Sarah Riley,2014-07-02 05:53
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Fundamentals of Coporate Finance Ch4~5 Ross

CHAPTER 4

    DISCOUNTED CASH FLOW VALUATION

Answers to Concepts Review and Critical Thinking Questions

    1. Assuming positive cash flows and interest rates, the future value increases and the present value

    decreases.

    2. Assuming positive cash flows and interest rates, the present value will fall and the future value will

    rise.

3. The better deal is the one with equal installments.

    4. 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. A freshman does. The reason is that the freshman gets to use the money for much longer before

    interest starts to accrue.

6. It’s a reflection of the time value of money. GMAC gets to use the $500 immediately. If GMAC uses

    it wisely, it will be worth more than $10,000 in thirty years.

    7. Oddly enough, it actually makes it more desirable since GMAC only has the right to pay the full

    $10,000 before it is due. This is an example of a “call” feature. Such features are discussed at length

    in a later chapter.

    8. The key considerations would be: (1) Is the rate of return implicit in the offer attractive relative to

    other, similar risk investments? and (2) How risky is the investment; i.e., how certain are we that we

    will actually get the ?10,000? Thus, our answer does depend on who is making the promise to repay.

    9. The Treasury security would have a somewhat higher price because the Treasury is the strongest of

    all borrowers.

    10. The price would be higher because, as time passes, the price of the security will tend to rise toward

    $10,000. This rise is just a reflection of the time value of money. As time passes, the time until

    receipt of the $10,000 grows shorter, and the present value rises. In 2010, the price will probably be

    higher for the same reason. We cannot be sure, however, because interest rates could be much higher,

    or GMAC’s financial position could deteriorate. Either event would tend to depress the security’s

    price.

     CHAPTER 4 B- 2

    Solutions to Questions and Problems

NOTE: All-end-of chapter problems were solved using a spreadsheet. Many problems require multiple

    steps. Due to space and readability constraints, when these intermediate steps are included in this

    solutions manual, rounding may appear to have occurred. However, the final answer for each problem is

    found without rounding during any step in the problem.

     Basic

1. The simple interest per year is:

     $5,000 × .07 = $350

     So, after 5 years, you will have:

     $350 × 5 = $1,750 in interest.

     The total balance will be $5,000 + 1,750 = $6,750

     With compound interest, we use the future value formula:

     t FV = PV(1 +r) 5 FV = $5,000(1.07) = $7,012.76

     The difference is:

     $7,012.76 6,750 = $262.76

. To find the FV of a lump sum, we use: 2

     t FV = PV(1 + r)

     10 a. FV = ?1,000(1.06) = ?1,790.85 10 b. FV = ?1,000(1.07) = ?1,967.15 20 c. FV = ?1,000(1.06) = ?3,207.14

     d. Because interest compounds on the interest already earned, the future value in part c is more

    than twice the future value in part a. With compound interest, future values grow exponentially.

3. To find the PV of a lump sum, we use:

     t PV = FV / (1 + r)

     6 PV = ?15,451 / (1.05) = ?11,529.77 9 PV = ?51,557 / (1.11) = ?20,154.91 18 PV = ?886,073 / (1.16) = ?61,266.87 23 PV = ?550,164 / (1.19)= ?10,067.28

     CHAPTER 4 B- 3

    4. To answer this question, we can use either the FV or the PV formula. Both will give the same answer

    since they are the inverse of each other. We will use the FV formula, that is:

     t FV = PV(1 + r)

     Solving for r, we get:

     1 / t r = (FV / PV) 1

     21/2 FV = $307 = $265(1 + r); r = ($307 / $265) 1 = 7.63% 91/9 FV = $896 = $360(1 + r); r = ($896 / $360) 1 = 10.66% 151/15 FV = $162,181 = $39,000(1 + r); r = ($162,181 / $39,000) 1 = 9.97% 301/30 FV = $483,500 = $46,523(1 + r); r = ($483,500 / $46,523) 1 = 8.12%

    5. To answer this question, we can use either the FV or the PV formula. Both will give the same answer

    since they are the inverse of each other. We will use the FV formula, that is:

     t FV = PV(1 + r)

     Solving for t, we get:

     t = ln(FV / PV) / ln(1 + r)

     t FV = ?1,284,000 = ?625,000 (1.09); t = ln(?1,284,000/ ?625,000) / ln 1.09 = 8.35 yrs t FV = ?4,341,000 = ?810,000 (1.07); t = ln(?4,341,000/ ?810,000) / ln 1.07 = 24.81 yrs t FV = ?402,662,000 = ?18,400,000 (1.21); t = ln(?402,662,000 / ?18,400,000) / ln 1.21 = 16.19 yrs t FV = ?173,439,000 = ?21,500,000 (1.29); t = ln(?173,439,000 / ?21,500,000) / ln 1.29 = 8.20 yrs

    6. To find the length of time for money to double, triple, etc., the present value and future value are

    irrelevant as long as the future value is twice the present value for doubling, three times as large for

    tripling, etc. To answer this question, we can use either the FV or the PV formula. Both will give the

    same answer since they are the inverse of each other. We will use the FV formula, that is:

     t FV = PV(1 + r)

     Solving for t, we get:

     t = ln(FV / PV) / ln(1 + r)

     The length of time to double your money is:

     t FV = $2 = $1(1.06)

     t = ln 2 / ln 1.06 = 11.90 years

     The length of time to quadruple your money is:

     t FV = $4 = $1(1.06)

     t = ln 4 / ln 1.06 = 23.79 years

     CHAPTER 4 B- 4

     Notice that the length of time to quadruple your money is twice as long as the time needed to double

    your money (the difference in these answers is due to rounding). This is an important concept of time

    value of money.

7. To find the PV of a lump sum, we use:

     t PV = FV / (1 + r)20 PV = $800,000,000 / (1.095) = $130,258,959.12

    8. To answer this question, we can use either the FV or the PV formula. Both will give the same answer

    since they are the inverse of each other. We will use the FV formula, that is:

     t FV = PV(1 + r)

     Solving for r, we get:

     1 / t r = (FV / PV) 1 1/4 r = ($10,311,500 / $12,377,500) 1 = 4.46%

     Notice that the interest rate is negative. This occurs when the FV is less than the PV.

9. A consol is a perpetuity.