19 现值问题 5年后得到的10000元，相当于现在得到多少钱？ 现值：将来（n年后）的一笔资金，它现在的 价值，我们称为复利现值或折现值 P V 公式:PV = FVn / (1+i)nPV = FVn (PVIFi,n) -- 见表 IIPVIFi,n—Present value interest factor of $1 at i% for n periods
20 在《投资价值理论》（The Theory of Investment Value）一书中，威廉斯提出了一套以股利收入为计算基础，来计算股票真实价值的确切公式。这里，他首次引进折现（discounting）的观念。把收入的观念倒过来想，由后往前推，不考虑你明年有多少钱、赚多少利息，而是看看把未来收入换算成現值之后，会比现在少了多少价值他主张股票的真实价值等于其未来所有股利的现值由于折现的观念过去少有人懂，它就流行起来，为投资人所爱用
48 Should you get your master degree? Two years of work experience after college, you have to decide whether to get a master degree or not. Suppose you are earning $80,000/year before entering a business school and assume that the tuition costs are $20,000/year. Expected salary upon graduation is $ 100,000 and assume that you will receive your salary at the beginning of the year. You can invest money at 2%. Further assume that the first payment of $ 20,000 has to be made at the start of the program, the second payment one year later. Assume that you will work 20 years after graduation, and that the salary differential ($20,000) will continue through this period.
49 Time line of Cash Flow for getting your master degree Year 2Year 1Year 3Year 222000010000080000Time line of Cash Flow for getting your master degreeTime line of Cash Flow for NOT getting a master degree
57 10%简单年利率下计息次数与EAR之间的关系 连续复利： EAR = er-1 where e is
58 需要记住的：You ALWAYS need to make sure that the interest rate and the time period match.If you are looking at annual periods, you need an annual rate.If you are looking at monthly periods, you need a monthly rate.If you have an APR based on monthly compounding, you have to use monthly periods for lump sums, or adjust the interest rate appropriately if you have payments other than monthly
59 Pure Discount Loans Interest-Only Loans Amortized Loans 贷款类型和分期贷款 Three basic types of loansPure Discount LoansInterest-Only LoansAmortized Loans
60 贷款类型和分期贷款Pure Discount Loans: The borrower receives money today and repays a single lump sum at some time in the future.e.g. a Treasury Bill (or T-Bill for short) is a promise by the government to repay a fixed amount at some time in the future, generally short term 3 to 12 months. Treasury Bills are pure discount loans.If a T-Bill promises to repay $1,000 in 3 months and the market interest rate is 10% EAR, then what should be the market price for this T-Bill?
61 贷款类型和分期贷款Interest-Only Loans: Borrow money today and pay interest only for a certain period of time and at the end of that period pay the original loan amount.Note that if there is only one period a pure discount loan and interest only loan are the same.Most government bonds are interest-only bonds.Amortized Loans: The borrower is required to repay parts of the principal amount over time. The process of making regular payments to reduce the principle is called amortizing the loan.
62 贷款类型和分期贷款 There are two special cases of loan amortization: Equal payments of the principalBy making equal payments of the principal, the principal is reduced by the same amount every period.However, the total payments per period change as the interest payments on the unpaid principal change.One needs to calculate the payment each period separately.Equal paymentsBoth the principal and the interest payment change every period.However, the total payment per period is constant.One needs to calculate the payment once.
63 分期偿还贷款例 Julie Miller 向银行借 $10,000， 年利率 12%. 5年等额偿还. Step 1: 每年偿还额 PV0 = R (PVIFA i%,n)$10,000 = R (PVIFA 12%,5)$10,000 = R (3.605)R = $10,000 / = $2,774
64 分期偿还贷款例[Last Payment Slightly Higher Due to Rounding]
66 买房子！你准备好了吗？You are ready to buy a house which costs &900,000 and you have $180,000 for a down payment. You need to borrow $ 720,000 from the bank and promise to pay back the money on monthly mortgage payments. The interest rate on the loan is 6% per year with monthly compounding for a 20-year fixed rate loan. How much will you offer for the payment each month?