公司理财笔记整理

5 Time value of money

Compinding future value FV

Discounting present value PV

Interest rate exchange rate between earlier and later money

❖FV = PV(1 + r)t

❖PV = FV / (1 + r)t

▪r = period interest rate, expressed as a decimal

▪t = number of periods

▪Future value interest factor = (1 + r)t复利终值系数

▪1/(1+r) t present value factor 现值系数

For a given interest rate – the longer the time period, the lower the present value

For a given time period – the higher the interest rate, the smaller the present value

❖r = (FV / PV)1/t– 1

❖t = ln(FV / PV) / ln(1 + r)

6 Discounted Cash Flow Valuation

❖Future and Present Values of Multiple Cash Flows

You think you will be able to deposit $4,000 at the end of each of the next three years in a bank account paying 8 percent interest、You currently have $7,000 in the account、How much will you have in three years? In four years?

Today (year 0 CF): 3 N; 8 I/Y; -7,000 PV; CPT FV = 8,817、98 FV = 7000(1、08)3 = 8,817、98 Year 1 CF: 2 N; 8 I/Y; -4000 PV; CPT FV = 4,665、60 FV = 4,000(1、08)2 = 4,665、60

Year 2 CF: 1 N; 8 I/Y; -4000 PV; CPT FV = 4,320 FV = 4,000(1、08) = 4,320

Year 3 CF: value = 4,000

Total value in 3 years = 8817、98 + 4665、60 + 4320 + 4000 = 21,803、58

Value at year 4: 1 N; 8 I/Y; -21803、58 PV; CPT FV = 23,547、87

You are offered an investment that will pay you $200 in one year, $400 the next year, $600 the next year and $800 at the end of the next year、You can earn 12 percent on very similar investments、What is the most you should pay for this one?

Point out that the question could also be phrased as “How much is this investment worth?”Calculator:

Year 1 CF: N = 1; I/Y = 12; FV = 200; CPT PV = -178、57Year 2 CF: N = 2; I/Y = 12; FV = 400; CPT PV = -318、88Year 3 CF: N = 3; I/Y = 12; FV = 600; CPT PV = -427、07Year 4 CF: N = 4; I/Y = 12; FV = 800; CPT PV = - 508、41Total PV = 178、57 + 318、88 + 427、07 + 508、41 = 1,432、93

现金流都发生在年末 e/g 后付变先付 相当于原来得数据*（1+r ）

Valuing Level Cash Flows: Annuities and Perpetuities Annuity 年金连续相同得现金流 – finite series of equal payments that occur at

regular intervals 曠緩颟鎵叶洼颁。If the first payment occurs at the end of the period, it is called an ordinary

annuity 普通年金If the first payment occurs at the beginning of the period, it is called an annuity

due 先付年金Perpetuity – infinite series of equal payments 永续年金只有现值没有终值 期数

无限❖ Perpetuity: PV = C / r ❖ Annuities 优先股有永续年金得特征

杠杆：自由资金撬动借有资产 美国杠杆高借贷方便

FVDN 先付 FVIFA 普通 Growing Perpetuity 增长年金A growing stream of cash flows with a fixed maturity 增长率一定

A growing stream of cash flows that lasts forever 用来计算股票得价格 产品未来所有得价值现在得现值 相当于股票现在得价格不就是交易价格

The expected dividend next year is $1、30, and dividends are expected to grow at 5% forever 、 If the discount rate is 10%, what is the value of this promised dividend stream?如果现在卖价小于26即可买入

❖ Comparing Rates: The Effect of Compounding

Effective Annual Rate (EAR)

This is the actual rate paid (or received) after accounting for compounding that occurs during the t r t t

r t

FVIFA C r r C FV PVIFA C r r C PV ,,1)1()1(11⨯=⎥⎦

⎤⎢⎣⎡-+=⨯=⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡+-=)

1(,r FVIFA C FVD n i N +⨯⨯=)

1(,r PVIFA C PVD n i +⨯⨯=t t r g C r g C r C PV )1()1()1()1()1(12++⨯++++⨯++=

-Λ⎥

⎥⎦⎤⎢⎢⎣⎡⎪⎪⎭⎫ ⎝⎛++--=t r g g r C PV )1()1(1Λ+++⨯+++⨯++=3

2

2)1()1()1()1()1(r g C r g C r C PV g r C PV -=00.26$05.10.30.1$=-=PV