finance

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FinanceFinance School of Management School of Management

FINANCEFINANCE

Review of Questions and Problems

Part II: Chapter 4-6

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Understand the concept of the time value of money and discounted cash flow （ DCF ） techniques to make decisions

Complete calculatioins by Excel!

Ensure that the meanings and some key components of titles are understand

Complete your homework independently!

Main ContentsMain Contents

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Chapter 4: Time Value of Money and Chapter 4: Time Value of Money and Discounted Cash Flow AnalysisDiscounted Cash Flow Analysis

Problems of homework:4.20.a –discount rate used to determine the PV of

the cash flows of the project the opportunity cost of capital 4%:P112

market capitalization rate/risk-adjusted

rate/hurdle rate IRR/yield to maturity

-- cash inflows: positive /cash outflows: negative

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4.25.c – explain why we would reject a project

that has an IRR greater than its cost of

capital IRR rule: P116

Investment: IRR> cost of capital

Borrowing: IRR< cost of capital IRR rule can give bad or wrong decisions

under some cases:

multiple cash flows: not be unique or not exist

different investment scale: unsatisfying choice

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4.31.c--SOLUTION:Step 1: Find the monthly payments on alternative 1:

Step 2: Find the present value of the above payments at

a 9% APR to see how much lower it is:

n i PV FV PMT Result

3*12 2.9%/12 23,000 0 ? 667.85


3*12 9%/12 ? 0 667.85 21,001.75

(1,998.10)

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Chapter 5 Life-Cycle Financial PlanningChapter 5 Life-Cycle Financial Planning

Problems of homework: grasp the meanings of title complete calculations by Excel familiarity with the book

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Saving for Retirement-5.4Saving for Retirement-5.4

Key Components:Taxes equal to 7.5% of salary must be deducted12,000 social security benefit after age 65 must be

considered

Solutions:4.b


65-85 3% ? 0 28,000 416,569.3

45-65 3% 0 416,569.3 ? 15,502.92

The same date

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4.c-calculate PV/FV/PMT of different cash flows

on corresponding date （ starting or ending of

the year/month ） .


45-65 3% ? 0 50,000*(1-7.5%)

688,083.21

65-85 3% ? 0 12,000178,529.70

45-65 3% ? 178,529.70 0 98,847.57

45-85 3% 98,847.57+ 688,083.21

0 ? 34,044.50

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养老金计划（ Pension Plans ） -5.5

养老保险金制度的三大支柱，即退休人员的三种收入来源：

社会保险养老金（国家基本养老保险）企业年金（企业补充养老保险）个人商业养老保险

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相关概念：缴费率：职工在工作期间的缴费比率，一般为工资的一定比例退休给付：职工退休后可得的养老金数额替换率：个人进入退休期所领取的养老金与进入退休期上一年度工资的比例，或者是，进入退休期社会平均养老金与进入退休期上一年度社会平均工资的比例。该比例一般为 70 ％左右。工资增长率和利率税收优惠

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养老金计划的基本模式

从退休职工享受养老金的来源来看，分为：现收现付制：以同时期正在工作的一代人的缴费或税收支付已经退休一代人的养老金。换言之，以当年缴费或税收支付当年养老金，对融资不做任何积累。通常通过税收、雇主和雇员以工资为基础的缴费等方式为养老金养老金融资基金制：雇主或雇员以工作期间劳动收入的一部分缴费以形成某项投资基金，并由缴费及其投资收益为基础支付养老金的制度

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按养老基金的运作方式，分为：固定给付型（ Defined-Benefit ）：事先确定职工退休后每月可享受的退休金，再根据基金的运营情况、职工年龄、服务年限等逐年计算雇主或雇员的缴费额；多数情况下，雇员不缴费，养老费用全部由雇主负担，雇主缴费额取决于经办机构的投资收益状况

基数替代率养老金给付＝若干年的平均工资 *系数 *工作年限

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固定缴费型（ Defined-Contribution ）：雇主或雇员按规定比例出资，记入个人账户，其中雇主的缴费是固定的，并不承担风险，但必须提供一系列投资选择供雇员投资时参考，雇员自行决策、自担风险，养老金给付取决于缴费额和投资收益的高低

货币购买计划（ Money Purchase Plan ）：利用公式提前定义雇主的缴费额，如，支付雇员工资的 6% ，或支付与雇员相同的缴费利润分享计划（ Profit Sharing Plan ）：在利润基础上以现金或股利形式向雇员直接支付，如，缴纳税前利润的 10%

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Defined-benefit Pension Plan-5.5Defined-benefit Pension Plan-5.5Revised Questions:

Assume that the salaries in later years remain 50,000 in real terms until retirement and the expected rate of inflation is 4%

Annual pension benefit will be equal to 1% * (50,000* 1.0425) * 40 = $53,316.73


65-80 0.08 ? 0 -53,317 $456,363.39

40-65 0.08 ? -456,363 0 $66,637.23

The inflation rate is 4%

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Investing in Human Capital-5.7Investing in Human Capital-5.7Solutions:

Step 1: First find the FV of tuition and forgone salary at end of 2 years:

Step 2: Find the increase in salary which has this amount as its PV:


30-32 3% 0 ? 45000 91,350.00

32-65 3% 91,350 0 ? 4,399.06

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Buy or Lease a Car-5.9Buy or Lease a Car-5.9

Key Components:Ordinary wrong calculation: 400*12*3

values on different date cann’t be operated

directly, you must discount or compound them 400 lease fee is paid monthly starting immediately

immediate annuity / ordinary annuity Methods used to make decision:

discount or compound cash flows of alternatives to compare the investment cost

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Solutions:Compare the PVs of investment cost of

alternatives:

Compare the FVs: n i PV FV PMT Result

36 3%/12 0 ? 400 16,214.22(16,322.32)

36 3%/12 30,000 ? 0 38,107.11 (18,107.11)


36 3%/12 ? 0 400 12,764.72(12,850)

36 3%/12 ? 20,000 0 15,745 (14,255)

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Compare the PMTs


36 3%/12 -30,000 0 ? -940.09

36 3%/12 0 20,000 ? 493.39(-446.70)

1 3%/12 400 ? 0 -402.67

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Analysis the News-5.11Analysis the News-5.11

Key components: Ignorance of the time value of moneyAssume an interest rate, say 5%Analysis require that you should point out the errors

and give the right calculations

So, after 250 month, i.e. at age 85 and 10 months, Mary will eventually pull ahead.


(65-62)*3 5%/12 0 ? 800 31,002.67

? 5%/12 31,002.67 0 200 250

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Chapter 6 Analyze Investment ProjectsChapter 6 Analyze Investment Projects

Key components: net income / incremental cash flows. understand correctly working capital when you

calculate cash flows. deal with salvage value correctly when calculate

the deprecation. annualized capital cost method to compare

projects with different lives/decision horizons.

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Net Income/Incremental Cash FlowsNet Income/Incremental Cash Flows

NPV is the difference between the PVs of all future cash inflows minus the PVs of all current and future cash outflows

To find the incremental cash flows resulting from investment—Depreciation belongs to non-cash expense

Net Income=(1-tax rate)*(revenues-cash expenses-Dep) Incremental Cash Flow =Net Income +Depreciation =(1-tax rate)*(revenues-cash expenses-Dep) +Dep =(1-tax rate)*(revenues-cash expenses) +tax rate*Dep

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An Example: 6.7

to calculate the incremental cash flow

Sale 30,000

-Variable cost -3,000

-Fixed expenses -2,000

-depreciation -20,000

-Tax -2,000

Net income 3,000

+depreciation 20,000

Incremental cash flow 23,000

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Working Capital-6.13Working Capital-6.13 Working capital (=current asset-current liability) is

investment capital to cover expenses before any cash is collected from sale

That is to say, Case 1: you pay the amount equal to net working capital at the

beginning of operation and you will receive it at the end of operation

Case 2: you needn’t spend money at the beginning because current liability is enough to met the investment capital of current asset. However, at the end of operation, you must pay the difference in amount between current liability and current asset to liquidate your liability

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Solution: to calculate the incremental cash flows in each year.

Year 0 -80,000+7,000

Year 1 (1-0.35)*(35000-20000)+20000

Year 2 (1-0.35)*(35000*(1-0.05)-20000)+20000

Year 3 (1-0.35)*(35000*(1-0.05)^2-20000)+20000

Year 4 (1-0.35)*(35000*(1-0.05)^3-20000)+20000-7000

According to case 2, 7,000 net working capital which is saved because of purchasing of computer

is a cash inflow at the beginning of decision horizonis a cash outflow at the end of decision horizon

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to calculate PVs of each cash flows and then get NPV.

Cash flows PVs

-73,000 -73,000

29,750 26,096

28,613 22,016

27,532 18,583

19,505 11549

NPV=5245

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Annualized Capital Cost-6.23Annualized Capital Cost-6.23To compare the alternatives with different

decision horizonsSteps:

Forecast the cash flows in each yearCalculate the NPV of alternativesObtain the annualized capital cost-annualized NPV

n i PV FV PMT ACC

5 10% NPV 0 ? PMT

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Salvage Value/Depreciation in 6.23Salvage Value/Depreciation in 6.23 Forecast correctly the annual cash flows of

alternatives:

Income (cost saving) 50,000 70,000

-Maintenance cost -20,000 -15,000

-depreciation -60,000 -85,714

-Tax 10,500 10,750

Net income -19,500 -30,714

+depreciation 60,000 85,714

Incremental cash flow 40,500 65,750

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Salvage value is the resale value of the machine at the end of life of machine, so the salvage value is a cash inflow when we calculate the NPV of the alternative two


7 10% ? 60,000*0.65 65,750 340,112

(NPV=259,888)

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