M.I.T. Sloan School of Management

Spring 1999 15.415

First Half Summary
Present Values • Basic Idea: We should discount future cash flows. The appropriate discount rate is the opportunity cost of capital. • Net Present Value: The net present value of a stream of yearly cash flows is N P V = C0 + C1 C2 Cn + + ··· + , 2 1 + r1 (1 + r2 ) (1 + rn )n

where rn is the n year discount rate. • Monthly Rate: The monthly rate, x, is x = (1 + EAR) 12 − 1, where EAR is the effective annual rate. The EAR is EAR = (1 + x)12 − 1. • APR: Rates are quoted as annual percentage rates (APR’s) and not as EAR’s. If the APR is monthly compounded, the monthly rate is x= AP R . 12
1

• Perpetuities: The present value of a perpetuity is PV = C1 , r

where C1 is the cash flow and r the discount rate. This formula assumes that the first payment is after one period. 1

• Annuities: The present value of an annuity is P V = C1 1 1 − r r(1 + r)t ,

where C1 is the cash flow, r the discount rate, and t the number of periods. This formula assumes that the first payment is after one period. Capital Budgeting Under Certainty • The NPV Rule: We should accept a project if its NPV is positive. If there are many mutually exclusive projects with positive NPV, we should accept the project with highest NPV. The NPV rule is the right rule to use. • The Payback Rule: We should accept a project if its payback period is below a given cutoff. If there are many mutually exclusive projects below the cutoff, we should accept the project with shortest payback period. There are two problems with the payback rule. First, it does not take into account cash flows after the cutoff. Second, it does not discount cash flows. Discounted payback fixes the second problem but not the first. • The Internal Rate of Return (IRR): The IRR of a project is the discount rate in the NPV calculation that makes the NPV equal to zero.