资产评估理论基础(2)

基础概念

1 现值 （Present Value）

2 复利（Compound Interests）

利息的计算方式

(1+i)=1+2×i+i

22221Principal;2×isimpleinterest;iinterestoninterest;

复利的力量

单利利率

Interests Rates

3.25%

3.25%

3.25%

3.25%

3.25%

3.25%

3.25%

3.25%

3.25%

3.25%

3.25%复利利息Interests20150.0026871.1136998.6850943.2770143.5096580.18132980.70183100.37252109.85347128.62477959.42年度Year1102030405060708090100本金Principal620000620000620000620000620000620000620000620000620000620000620000利息Interests2015020150201502015020150201502015020150201502015020150本息和本金SumPrincipal640150620000.00821500826803.3610230001138420.8412245001567485.1614260002158261.3916275002971697.8218290004091713.8020305005633857.4222320007757226.20243350010680880.56263500014706443.61本息和Sum640150.00853674.471175419.511618428.432228404.893068278.004224694.505816957.798009336.0511028009.1815184403.03息差032174.46839152419.5129393928.4319802404.889114407782395694.4993786457.7915777336.0488594509.18312549403

Example

图2 中国经济赶上美国需要多少时间

xUS=1.015

China=1.08x

US'GDPis3,China'sGDP1

;

图3 两百年以后

Example

(1.1135)=?

;74

Ibbotson {and} Sinquefield calculated what the stock market returned as a whole from 1926 to 1999. They find that one dollar placed in these stocks at the beginning of 1926 would have been worth $2845.63. Annual return is 11.346%.

Example:

Peter Minuit,director-general of New Netherlands, the Dutch west India Company's Colony in North America. In 1626， 60 Dutch Guilders(10.61g Sliver Coin)

图4 Dutch Guilders

native Americans, In 1667,Ducth were forced to exchange it for Suriname with the British.

图 6 曼哈顿岛（Manhattan Island）

Where is the island?

Where is 自由女神？

Suriname

163821 square km

Justice – Duty – Loyalty

公平 责任 忠诚

24×(1+0.05)=?387

Question.

一家餐馆的合理利润应该在多少？

3 永续年金（Perpetuity）

CCCC++++ 1+r(1+r)2(1+r)3(1+r)4

PresentValue=C

rPresentValue=

CInterest=×r=Cr

4 增长永续 （Growing Perpetuity）

Example

1 Numerator

Rothstein Corporation is just about to pay a dividend of $3.00 per share. Investors anticipate that the annual dividend will rise by 6 percent a year forever. The applicable interest rate is 11 percent.What is the price of the stock today.

$66.60=$3.00+$3.18

0.11 0.06

$3.00ImminentDivedend

$3.18($3.00x1.06)PresentValueofalldividendsbeginningayear¿now

2 The Interest Rate and the Growth Rate

3 The Timing Assumption

Annuity 年金

例子 Example

PresentValue=C

r

Consol2:PresentValue=C1

r×[(1+r)T]

Consol2 Consol1=C

C1

×[(1+r)T]

Consol2 Consol1=ThepresentvalueofcashflowsforTyears

Perpetuity:PV=C

r

GrowingPerpetuity:PV=C

(r g)

Annuity:PV=C[1

r×1

r×(1+r)T]

GrowingAnnuity:C[111+

r g gT

r g×(1+r)]

AT

r,Tindicatenumberofperiods,rindicateinterestrate.

Mark Young has just won the state lottery, paying $50000 a year for 20 years.He is to receive this first payment a year form now. The state advertises this as the Million Dollar Lottery because $ 1000000= $50000 x 20. If the interest rate is 8 percent, what is the true value of the lottery?

马克赢得了一笔州彩票，金额为1000000美元，但要20年分期，每期5万美元，第一笔奖金一年后收到。

解答：

Million Dollar Lottery = 50000 x{1/0.08 – 1/[0.08(1.08)20])}

Million Dollar Lottery = 50000 x{1/0.08 – 1/[0.08(1.08)19])}

变形1 后付年金

Trick 1: Delayed Annuity

Danielle Caravello will receive a four-year annuity of 500 per year, beginning at data 6.If the interest rate is 10 percent, what is the present value of her annuity?

0 1 2 3 4 5 6 7 8 9 10

500 500 500 500 500

Trick 2: Annuity in Advance 先付年金

In a previous example, mark Young received 50000 a year for 20 years.In that example, he was to receive the first payment a year from the winning data. Let us now assume that the first payment occurs immediately. The total number of payments remains 20.

接Mark Young例子，如果第一期奖金立即收到，而不是一年后才能收到，维持20期的奖金，那么又如何计算呢？

Trick 3： The Infrequent Annuity 不规则年金

Miss Ann Chen receive an annuity of 450, payable once every two years. The annuity stretches out over 20 years. The first payment occurs at date 2, that is, two years from today. The annual interest rate is 6 percent.

Ann Chen小计每次收到450，每两年一次，期限20年，第一次收到付款是在第二期，每年利息率是6%。

(1.06×1.06) 1=

11 ]= 0.12360.1236×0.123610450×[

Trick 4: Equating Present Value of Two Annuities

Harold and Helen Nash are saving for the college education of their newborn daughter, Susan. The Nashes estimate that college expenses will run 30000 per year when their daughter reaches college in 18 years. The annual interest rate over the next few decades will be 14 percent. How much money must they deposit in the bank each year so that their daughter will be completely supported through four years of college.

Nash夫妇为刚出生的女儿存款。......

0 1 17 18 19 20 21

Birth 2 Deposit tution 1 tution 3

1 Deposit last deposit tution 2 tution 4

Step 1: 计算学费

Step 2: 学费折现 9422.91

C×A17=9422.910.14Step 3:

A17=

6.37290.14

Growing Annuity

111+gGrowingAnnuity:C[ ×()]T

Stuart Gabriel, a second-year MBA student, has just been offered a job at $80000 a year, He anticipates his salary increasing by 9 percent a year until his retirement in 40 years. Given an interest rate of 20 percent, what is the PV of his lifetime salary?

For pervious example, Harold and Helen Nash planned to make 17 identical payments in order to fund the college education of their daughter, Susan. Alternatively, imagine that they planned to increase their payments at 4 percent per year. What would their first payment be?

What Is a Firm Worth?

Suppose you are in the business of trying to determine the value of small companies.

Let's consider the example of a firm that is expected to generate net cash flows 5000 in the first year and 2000 for each of next five years. The firm can be sold for 10000 seven years from now. The owner would like to be able to make 10 percent on their investment in the firm.

The present value of the firm

End of Year

1

2

3

4

5

6

7Net Cash FlowPV Factor 10%0.910.830.750.680.620.560.51

Present Value of FirmPV

本文来源：https://www.bwwdw.com/article/oqge.html