# Principles Finance Essay

2013 Words9 Pages
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.