FINAL EXAM REVIEW

Fall 2014

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

Incremental ROR Analysis

Bond Yields

True Cost of a Loan

Benefit/Cost Ratio

Incremental B/C Analysis

Breakeven Analysis

Depreciation

Nominal & Effective Interest

Nominal Interest RateExample = APR

r = i × m

Effective Interest RateExample = APY

ie = (1+ i)n – 1

PP CP

When using (P|A,i%,n), etc.i and n must agree w.r.t. time

ie = (1+ i)n – 1

Mortgages and Car Loans

Monthly payment amount isB0 (A|P,i%,n)

Remaining balance at any time(including Time 0) is equal to thePW of the remaining payments.

Capitalized Cost

Present worth when n =

(P|A,i%,) = 1/i

(A|P,i%,) = i

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

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:

F = P (1 + ERR)n

Incremental ROR Analysis

Start with lowest-cost project (which is“do nothing” for revenue projects) andaccept a more expensive project only if

i* or EROR > MARR

Bond Yields

Yield to MaturityPurchase price depends on market

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

Zero-Coupon BondsBond purchased at a deep discount

Bond redeemed for face value at maturity

True Cost of a Loan

Calculate the IRR of the cash flows

Benefit/Cost Ratio

𝐵/𝐶=𝑃𝑊𝑃𝑊

=𝐴𝑊𝐴𝑊

=𝐶𝐶𝐶𝐶

≥1

Benefit/Cost Ratio

𝐶𝑜𝑛𝑣𝑒𝑛𝑡𝑖𝑜𝑛𝑎𝑙 𝐵/𝐶=𝐵𝑒𝑛𝑒𝑓𝑖𝑡𝑠−𝐷𝑖𝑠𝑏𝑒𝑛𝑒𝑓𝑖𝑡𝑠  

𝐶𝑎𝑝𝑖𝑡𝑎𝑙𝐶𝑜𝑠𝑡𝑠−𝑂∧𝑀𝐶𝑜𝑠𝑡𝑠

𝑀𝑜𝑑𝑖𝑓𝑖𝑒𝑑 𝐵/𝐶=𝐵𝑒𝑛𝑒𝑓𝑖𝑡𝑠−𝐷𝑖𝑠𝑏𝑒𝑛𝑒𝑓𝑖𝑡𝑠−𝑂∧𝑀𝐶𝑜𝑠𝑡𝑠

𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝐶𝑜𝑠𝑡𝑠

Incremental B/C Analysis

Start with lowest-cost project (based onthe denominator of the B/C formula) andaccept a more expensive project only if

B/C 1

Breakeven Analysis

One Project

Set PW = 0 and solve for x

Two Projects

Set PWA = PWB and solve for x

Straight-Line Depreciation

𝐵𝑉=𝐵−∑ 𝐷 𝑗=𝐵−𝑡 𝐷 𝑗

𝐷 𝑗=𝐵−𝑆𝑛