Day 45 in MIT Sloan Fellows Class 2023, Managerial Finance2, NPV & Some terminologies

Time Value of Money(TVM)

This is about the time value of money.

• To compute the present value of a future cashflow, we have to discount it.
• To compute the future value of a present cashflow, we have to compound it.

Discount rate(r)

Discount rate is the "exchange rate" over time like we exhange different currency across countries.

Net Present Value(PV)

• PV (CF t) = CFt/(1+r)^t
• NPV(CF t) : cumulative value of PV

Future Value(FV)

• FV t = CF0 * (1+r)^t

Perpetuity and Annuity

Constant recurring cash flow(A), forever, starting 1-period from now

• PV(perpetuity) = A/r
• PV(perpetuity with growth) = A/(r-g) g is growth rate
• PV(Annuity) = A/r * (1- 1/(1+r)^t)

APR/EAR

• Annual Percentage rate(APR)
• Effective annual rate(EAR)

If k is the number of periods per year and r is the "per-period" interest rate, 

1+EAR = (1+(APR/k))^k=(1+r)^k

For example, k = 12(monthly) and APR is 1.2%, then r = 0.1 %, EAR = 1.21%

Inflation nominal and real

Inflation ii measures the changes in the Consumer Price Index (also known as CPI), which reflects the changes in prices on a benchmark consumer basket.

Real rate of return are the inflation-adjusted rates.

r(real) = (1+r(nominal))/(1+i) - 1

Terminologies

• Collateral: 担保
• Principal: 元本
• Pay down: 頭金