资产评估理论基础1007

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?
20
620000
3.25% 20150 1023000 1138420.84 36998.68 1175419.51 152419.5129
30
620000
3.25% 20150 1224500 1567485.16 50943.27 1618428.43 393928.4319
40
620000
3.25% 20150 1426000 2158261.39 70143.50 2228404.89 802404.8891
利率
利息 本息和 本金
利息
本息和
息差
Year Principal Interests Rates Interests Sum Principal Interests
Sum
1
620000
3.25%
20150 640150 620000.00 20150.00 640150.00
0
10
620000
3.25% 20150 821500 826803.36 26871.11 853674.47 32174.46839
2 The Interest Rate and the Growth Rate
3 The Timing Assumption
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.
项目 一、城乡居民及单位存款
（一）活期 （二）定期 1.整存整取 三个月 半年 一年 二年 三年 五年 2.零存整取、整存零取、存本取息 一年 三年 五年 3.定活两便 二、协定存款 三、通知存款 一天 七天
年利率（%） 0.35
2.85 3.05 3.25 3.75 4.25 4.75 2.85 2.9
80
620000
3.25% 20150 2232000 7757226.20 252109.85 8009336.05 5777336.048
90
620000
3.25% 20150 2433500 10680880.56 347128.62 11028009.18 8594509.183
100 620000
(1.06×1.06)−1=❑
450×[
1 0.1236
−
1 0.1236×0.123610
]=❑
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.
2845.63 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%.
[
1 r
×
r
1 ×(1+r
)T
]
Growing
Annuity
:
C
[
r
1 −g
−
1 r−g
×
(
1+ g 1+r
T
)
]
ATr ,T indicate number of periods , r indicate interest rate.
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?
3.25% 20150 2635000 14706443.61 477959.42 15184403.03 12549403
700000 600000 500000 400000 300000 200000 100000
0 1 2 3 4 5 6 7 8 9 10 11
图 1 复利本金利息和
年度 Year 本金 Principal 利息 Interests 利息 Interests
$ 66.60 = $ 3.00
+
$ 3.18 0.11−0.06
$ 3.00 Imminent Divedend $ 3.18($3.00x1.06) Present Value of all dividends beginning a year ¿ now
Annuity 年金 例子 Example
3 按一年以内定期整存整取同档次利率打6折执行
1.15 .
0.8 1.35
Example
图 2 中国经济赶上美国需要多少时间 US =1.015x China=1.08x
US ' GDP is 3 ,China ' s GDP 1 ;
Example
图 3 两百年以后
(1.1135)74 = ? ;
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])}
2−
Consol
1=
C r
−
C r
×[
1 (1+r
)T
]
Consol 2 − Consol 1 = The present value of cash flows for T years
Perpetuity
:
PV
=
C r
Growing
Perpetuity
:
PV
=
(
r
C −g
)
Annuity : PV =C
50
620000
3.25% 20150 1627500 2971697.82 96580.18 3068278.00 1440778
60
620000
3.25% 20150 1829000 4091713.80 132980.70 4224694.50 2395694.499
70
620000
3.25% 20150 2030500 5633857.42 183100.37 5816957.79 3786457.791
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%。
Present
Value
=
C 1+
r
+
C (1+r
)2
+