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 Rate
Example = APR
r=i×m
Effective Interest Rate
Example = 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 is
B0 (A|P,i%,n)
Remaining balance at any time
(including Time 0) is equal to the
PW 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.
2.
3.
4.
Draw the net cash flow diagram
Compound all positive cash flows to Time n
Discount all negative cash flows to Time 0
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) and
accept a more expensive project only if
i* or EROR > MARR
Bond Yields
Yield to Maturity
Purchase 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 Bonds
Bond 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
𝑃𝑊 𝐴𝑊 𝐶𝐶
𝐵/𝐶 =
=
=
≥1
𝑃𝑊 𝐴𝑊 𝐶𝐶
Benefit/Cost Ratio
𝐵𝑒𝑛𝑒𝑓𝑖𝑡𝑠 − 𝐷𝑖𝑠𝑏𝑒𝑛𝑒𝑓𝑖𝑡𝑠
𝐶𝑜𝑛𝑣𝑒𝑛𝑡𝑖𝑜𝑛𝑎𝑙 𝐵/𝐶 =
𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝐶𝑜𝑠𝑡𝑠 − 𝑂&𝑀 𝐶𝑜𝑠𝑡𝑠
𝐵𝑒𝑛𝑒𝑓𝑖𝑡𝑠 − 𝐷𝑖𝑠𝑏𝑒𝑛𝑒𝑓𝑖𝑡𝑠 − 𝑂&𝑀 𝐶𝑜𝑠𝑡𝑠
𝑀𝑜𝑑𝑖𝑓𝑖𝑒𝑑 𝐵/𝐶 =
𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝐶𝑜𝑠𝑡𝑠
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 PWA = PWB and solve for x
Straight-Line Depreciation
𝐵𝑉 = 𝐵 −
𝐷𝑗 = 𝐵 − 𝑡 𝐷𝑗
𝐵−𝑆
𝐷𝑗 =
𝑛