Week 2
Time Value of Money
& Capital Budgeting

Time Value of Money

Capital Budgeting principles:

Calculation of
Present Value : PV= FVn / (1 + i)n
Future Value (FVn =PV x (1 + i)n

Cost of Capital

when they raise financing by selling securities like Debt, Preferred Stock and Equity.

pricing of ownership claims

identifying the optimal Capital Structure.

Net Present Value: marginal benefit versus marginal cost comparison
NPV = -(Initial Investment) + the PV of Cash Flow for each Period(NPV): 


   NPV=−C0*C1/(1+r)+C2/(1+r)2+...+CT/(1+r)T

Internal Rate of Return (IRR)

Payback Period

Perpetuities & Annuities

Perpetuities :a never-ending, constant stream of cash flows

PV of a perpetuity: PV = C/r Growing perpetuity PV = C/(r-g)

Growing Annuities PV of Growing Annuity Equation

Payback Period: a measure of how long it takes to recover the amount of the investment. Initial investment/Cash Savings or Increase of Cash Flow. Ignores Time value of Money

Discounted Payback Period: Time to recover cost of investment using discounted future Cash Flow

  • Considers Time value of Money

Accounting Rate of Return:

  • Average Net Income/ Average Investment
  • Indicator of Profitability
  • Ignores Time value of Money
  • Interest Rate to cause NPV=0
  • compared to management’s required rate of return
  • cannot be used to compare, or rank, mutually exclusive projects or to compare projects of different durations
  • When the “normal case” (an initial negative outflow, followed by positive inflows) of cash flows is reversed, , the IRR decision rule must be reversed
  • Scale problems exist with IRR. Often, small projects will show a higher IRR over large projects, even though the latter will have a higher NPV. In these cases incremental IRR analysis must be employed

Profitability Index

  • PV Cash Flows/ Investment
  • Consider Time Value of Money

it measures the magnitude, timing, and risk associated with future cash flows, which further illustrates its link to the firm’s stock price.

Types of Projects

Independent projects

Mutually exclusive investment decisions

One method for eliminating multiple IRRs is to use the Modified Internal Rate of Return (MIRR). Discount all cash outflows to the present, and compound all cash inflows to the last period of the project. Then, find the rate that equates the values. The discounting and compounding can be done at borrowing and investment rates, respectively.

Capital Rationing
:when a firm must choose between projects due to restrictions on the number of new projects that can be undertaken
However, while other measures (profitability index, IRR, etc.) provide helpful information to capital budgeting decision-making, NPV remains an all-purpose measure to evaluate projects.