QUIZ

问答

1. At an interest rate of 12 percent, the six-year discount factor is .507. How many dollars is $.507 worth in six years if invested at 12 percent?

$1.00.

1.在利率是12%的条件下，六年期的贴现因数是.507。那么如果以12%投资$.507，则在六年价值多少？

$1.00.

2. If the PV of $139 is $125, what is the discount factor?

125/139 = .899

2.如果$139的PV是$125，贴现因数是什么？

125/139 = .899

3. If the eight-year discount factor is .285, what is the PV of $596 received in eight years?

596 × .285 = $170

3.如果八年期的贴现因数是.285，在八年收到的$596的PV是什么？

596 × .285 = $170

4. If the cost of capital is 9 percent, what is the PV of $374 paid in year 9?

374/(1.09)⁹ = $172

4.如果资本成本为9%，$374在9年的PV是什么？

374/(1.09)⁹ = $172

5. A project produces the following cash flows:

Year	Flow
1	432
2	137
3	797

If the cost of capital is 15 percent, what is the project’s PV?

5.一项目产生如下现金流：

Year	Flow
1	432
2	137
3	797

如果资本成本为15%，项目的PV是什么？

6. If you invest $100 at an interest rate of 15 percent, how much will you have at the end of eight years?

100 × (1.15)⁸ = $305.90

6.如果你以15%的利率投资$100，在八年末你会得到多少？

100 × (1.15)⁸ = $305.90

7. An investment costs $1,548 and pays $138 in perpetuity. If the interest rate is 9 percent, what is the NPV?

NPV = -1548 + 138/.09 = -$14.67

7.一项投资花费$1,548，支付$138到永久。如果利率为9%，NPV是什么？

NPV = -1548 + 138/.09 = -$14.67

8. A common stock will pay a cash dividend of $4 next year. After that, the dividends are expected to increase indefinitely at 4 percent per year. If the discount rate is 14 percent, what is the PV of the stream of dividend payments?

PV = 4/(.14 - .04) = $40

8.一普通股将在下一年支付现金股利$4。之后，股利期望可以无限期每年增长4%。如果贴现率为14%，股利支付流的PV是什么？

PV = 4/(.14 - .04) = $40

9. You win a lottery with a prize of $1.5 million. Unfortunately the prize is paid in 10 annual installments. The first payment is next year. How much is the prize really worth? The discount rate is 8 percent.

9.你彩票中奖赢了$1,500,000。不幸的是，奖金被分成10年按年支付。首次支付在下一年。这份奖金的实际价值是多少？贴现率8%。

10. Do not use the Appendix tables for these questions. The interest rate is 10 percent.

a. What is the PV of an asset that pays $1 a year in perpetuity?

b. The value of an asset that appreciates at 10 percent per annum approximately doubles in seven years. What is the approximate PV of an asset that pays $1 a year in perpetuity beginning in year 8?

c. What is the approximate PV of an asset that pays $1 a year for each of the next seven years?

d. A piece of land produces an income that grows by 5 percent per annum. If the first year’s flow is $10,000, what is the value of the land?

(a) PV =1/.10 =$10

(b) PV =(1/.10)/(1.10)⁷=10/2 = $5 (approximately)

(c) PV = 10 - 5 = $5 (approximately)

(d) PV = C/(r - g) = 10,000/(.10 - .05)= $200,000

10. 不使用附表来回答这些问题。利率为10%

a.一项一年支付$1到永久的资产的PV是什么？

b.一项每年增值10%的资产的价值在七年中接近翻倍。一项在8年开始一年支付$1到永久的资产的PV的近似值是什么？

c.一项在接下来七年的每一年支付$1的资产的PV的近似值是什么？

d.一块土地产生一个每年增长5%的收益。如果第一年的现金流是$10,000,土地的价值是什么？

(a) PV =1/.10 =$10

(b) PV =(1/.10)/(1.10)⁷=10/2 = $5 (近似值)

(c) PV = 10 - 5 = $5 (近似值)

(d) PV = C/(r - g) = 10,000/(.10 - .05)= $200,000

11. Use the Appendix tables at the end of the book for each of the following calculations:

a. The cost of a new automobile is $10,000. If the interest rate is 5 percent, how much would you have to set aside now to provide this sum in five years?

b. You have to pay $12,000 a year in school fees at the end of each of the next six   years. If the interest rate is 8 percent, how much do you need to set aside today to cover these bills?

c. You have invested $60,476 at 8 percent. After paying the above school fees, how much would remain at the end of the six years?

a. From Appendix Table 1, 1/(1.05)⁵ = .784. You therefore need to set aside 10,000 × .784 = $7,840.

b. From Appendix Table 3, the present value of $1 a year for 6 years at 8% is $4.623. Therefore you need to set aside 12,000 × 4.623 = $55,476.

c. From Appendix Table 2, 1.08⁶=1.587. Therefore, at the end of 6 years you would have 1.587 × (60,476 - 55,476) = $7,935

11.使用书末的附表来计算下列问题：

a.一辆新汽车的花费是$10,000。如果利率为5%，为在五年可以提供这个数额，你现在需要留出多少？

b.你在接下来的六年中的每一年末都必须支付一年$12,000的学费。如果利率为8%，你现在需要留出多少来负担这些帐单？

c.你已经以8%投资了$60,476。在支付了上述学费之后，在六年末将剩余多少？

a. 查附表1, 1/(1.05)⁵ = .78。所以你需要留出10,000 × .784 = $7,840。

b. 查附表3, 8%利率下一年$1持续六年的现值是$4.623。所以你需要留出12,000 × 4.623 = $55,476.

c. 查附表2, 1.08⁶=1.587。所以, 在六年末你将会有1.587 × (60,476 - 55,476) = $7,935

12. You have the opportunity to invest in the Belgravian Republic at 25 percent interest. The inflation rate is 21 percent. What is the real rate of interest?

(1.25)/(1.21) - 1 = .033, or 3.3%

12.你有投资Belgravian共和国的机会，25%的利息。通货膨胀率是21%。真实利率是什么？

(1.25)/(1.21) - 1 = .033, or 3.3%

13. The continuously compounded interest rate is 12 percent.

a. You invest $1,000 at this rate. What is the investment worth after five years?

b. What is the PV of $5 million to be received in eight years?

c. What is the PV of a continuous stream of cash flows, amounting to $2,000      per year, starting immediately and continuing for 15 years?

(a) 1,000e^{.12 ×5} =1,000e^.6 =$1,822

(b) PV =5e^{-.12 ×8}= 5e^-.96 = $1.915 million

(c) PV = C/r(1 – e^-rt)= 2,000/.12(1 – e^{-.12 × 15}) = $13,912

13.连续复利利率12%

a.你以这个利率投资$1,000。五年之后投资价值多少？

b.在八年收到的$5,000,000的PV是多少？

c.金额一年$2,000，立即开始并且连续15年的一个连续现金流的PV是多少？

(a) 1,000e^{.12 ×5} =1,000e^.6 =$1,822

(b) PV =5e^{-.12 ×8}= 5e^-.96 = $1.915 million

(c) PV = C/r(1 – e^-rt)= 2,000/.12(1 – e^{-.12 × 15}) = $13,912

14. You are quoted an interest rate of 6 percent on an investment of $10 million. What is the value of your investment after four years if the interest rate is compounded:

a. Annually, b. monthly, or c. continuously?

(a) $12.625 million; (b) $12.705 million; (c) $12.712 million

14.你被报价利率6%，对于一项$10,000,000的投资。四年之后你的投资的价值是多少如果利率的复利形式是：

a.按年, b.按月, 或者c.连续?

(a) $12.625 million; (b) $12.705 million; (c) $12.712 million

15. Suppose the interest rate on five-year U.S. government bonds falls to 4.0 percent. Recalculate the value of the 7 percent bond maturing in 2006. (See Section 3.5.)

$1,133.55. This calculation assumes annual coupon payments and compounding.

15.假设五年期美国政府债券的利率跌至4.0%。重新计算2006年到期7%债券的价值。（参见Section 3.5）

$1,133.55. 计算假设利息按年支付和复利。

16. What is meant by a bond’s yield to maturity and how is it calculated?

The yield to maturity is the (single) discount rate that gives a present value equal to a bond’s price. It is calculated by trial and error, by computer or calculator, or from bond tables.

16.债券的到期收益率意味着什么以及如何它是如何计算的？

到期收益率是使现值等于债券价格的（单一）贴现率。它可以通过试误法、计算机或计算器、债券表来计算。