# 第5章 资金的时间价值.

## Presentation on theme: "第5章 资金的时间价值."— Presentation transcript:

Cash flow-in (现金流入) 1 2 3 4 5 Time periods Cash flow-out (现金流出)

Interest on Interest Interest Earned Total Interest Earned 1 \$100.00 \$5.00 \$0.00 2 \$10.00 3 \$15.00 4 \$20.00 5 \$25.00

Principal Simple Interest Interest on Interest Interest Earned Total Interest Earned 1 \$100.00 \$5.00 \$0.00 2 \$105.00 \$0.25 \$5.25 \$10.25 3 \$110.25 \$0.51 \$5.51 \$15.76 4 \$115.76 \$0.79 \$5.79 \$21.55 5 \$121.55 \$1.08 \$6.08 \$27.63

FVn = P0 (FVIFi,n) -- 见表 I FVIFi,n—Future value interest factor of \$1 at i% at the end of n periods

10% \$10,000 FV5

Excel function FV

P V 公式: PV = FVn / (1+i)n PV = FVn (PVIFi,n) -- 见表 II PVIFi,n—Present value interest factor of \$1 at i% for n periods

10% \$10,000 PV

Parts of an Annuity (普通年金第1年年末） \$ \$ \$100 现在 相等现金流

1. 全面阅读问题 2. 决定是PV 还是FV 3. 画一条时间轴 4. 将现金流的箭头标示在时间轴上 5. 决定问题是单个的现金流、年金或混合现金流 6. 年金的现值不等于项目的现值（记不变的东西） 7. 解决问题

10% \$ \$600 \$400 \$400 \$100 PV0

\$ \$ \$ \$400 \$1,268.00 PV0 = \$ + \$ \$200 \$347.20 + \$100 \$62.10

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.

Time line of Cash Flow for getting your master degree
Year 2 Year 1 Year 3 Year 22 20000 100000 80000 Time line of Cash Flow for getting your master degree Time line of Cash Flow for NOT getting a master degree

10%简单年利率下计息次数与EAR之间的关系

Pure Discount Loans Interest-Only Loans Amortized Loans 贷款类型和分期贷款
Three basic types of loans Pure Discount Loans Interest-Only Loans Amortized Loans

Equal payments of the principal By 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 payments Both the principal and the interest payment change every period. However, the total payment per period is constant. One needs to calculate the payment once.

PV0 = R (PVIFA i%,n) \$10,000 = R (PVIFA 12%,5) \$10,000 = R (3.605) R = \$10,000 / = \$2,774

1. 计算 每期偿还额. 2. 计算第t期偿还的 利息. (第t-1 期的贷款余额) x (i% / m) 3. 计算第t期偿还的 本金. (每期偿还额 - 第2 步的利息) 4. 计算第t 期的贷款余额. (第t-1期的贷款余额- 第 3 步的本金偿还) 5. 从第2步起循环.

The difference between simple interest and compound interest. The present value formula

Amortized Loans