FINAL EXAM REVIEW Spring 2015

Nominal and Effective Interest Rates Payment Period  Compounding Period Mortgages and Car Loans MARR and WACC Present Worth and Annual Worth Capitalized Cost Cost Projects with Unequal Lives Revenue Projects with Unequal Lives Internal Rate of Return Modified Internal Rate of Return Bond Prices and Yields True Cost of a Loan Benefit/Cost Ratio Breakeven Analysis Depreciation

Nominal & Effective Interest Nominal Interest Rate Example = APR r = i × m (no compounding) Effective Interest Rate Example = APY i e = (1+ i) n – 1 (interest compounds)

PP  CP When using (P|A,i%,n), etc. interest period must match payment period so adjust the interest rate to match i e = (1+ i) n – 1

Mortgages and Car Loans Monthly payment amount is Remaining balance at any time (including Time 0) is equal to the PW of the remaining payments.

Loans Loan Payments Payment = AW of Original Loan Amount Loan Balance Balance = PW of remaining payments True Cost of a Loan Calculate IRR of cash flows

MARR & WACC MARR Based on Cost of Capital MARR = WACC + Desired Profit MARR Based on Opportunity Cost Use IRR of most attractive unfunded project

Revenue Projects w/ Equal Lives “Do Nothing” is an Option Total Investment Analysis Choose Highest PW, FW or AW > 0 Incremental Investment Analysis Start with lowest cost project (“do nothing”) Accept a more expensive project only if  i* or  i′ > MARR  B/C > 1

Cost Projects w/ Equal Lives “Do Nothing” is NOT an Option Total Investment Analysis Choose least negative PW, FW or AW or lowest EUAC Incremental Investment Analysis Start with lowest cost option (not “do nothing”) Accept a more expensive option only if  i* or  i′ > MARR  B/C > 1

Capitalized Cost

Revenue Projects “Do Nothing” is an Option “Implicit Reinvestment Assumption” Study Period = Longest Project Life Choose project with highest PW Implicitly assumes profits reinvested at MARR

Cost Projects “Do Nothing” is NOT an Option “Repeatability Assumption” Study Period = LCM of Project Lives Choose option with least negative AW or lowest EUAC Implicitly assumes cash flows are repeated to LCM

Internal Rate of Return The interest rate that makes the PW = 0 If PW(i*) > 0, choose a higher i* If PW(i*) < 0, choose a lower i* Bracket the solution and interpolate

Modified Internal Rate of Return 1.Draw the net cash flow diagram 2.Compound all positive cash flows to Time n 3.Discount all negative cash flows to Time 0 4.Solve for the external rate of return (EROR): F = P (1 + EROR) n

Incremental ROR Analysis Start with lowest-cost project (which is “do nothing” for revenue projects) and accept a more expensive project only if  i* or  EROR > MARR

Bond Prices and Yields Yield to Maturity Coupon rate and YTM are both APRs Coupons paid twice a year (usually) Bond redeemed for face value at maturity Calculate the IRR of the cash flows Bond Price Calculate PW of remaining coupons plus face value at maturity

True Cost of a Loan Calculate the IRR that makes the borrowed amount economically equivalent to the payments

Benefit/Cost Ratio

Incremental B/C Analysis Start with lowest-cost project (based on the denominator of the B/C formula) and accept a more expensive project only if  B/C  1

Breakeven Analysis One Project Set PW = 0 and solve for x Two Projects Set PW A = PW B and solve for x

Breakeven Analysis No Time Value of Money

Straight-Line Depreciation

Declining Balance Depreciation

MACRS Depreciation