Unformatted text preview: IE 343 Midterm 1 Review Chapter 2: Cost concepts and Design Economics Types of costs Fixed Variable Total cost = Total Fixed cost + Total Variable cost Recurring Non-recurring Direct Indirect Sunk (Ignore all sunk costs) Opportunity (Don't ignore) Costs (cont.) Cash Book Investment Incremental Marginal Price demand relaSonship: p = a - bD Total revenue: T R = aD - bD 2 Total cost: T C = f + vD Total profit: = aD - bD2 - f - vD
a-v OpSmal demand: D = 2b OpSmal price: P = a+v 2 Example: A company has determined that the price and the monthly demand of one of its products are related by the equaSon D = (400 - p) . The associated fixed costs are $1,125/month, and the variable costs are $100/unit. a. What is the opSmal number of units that should be produced and sold each month? b. What is the breakeven point? Chapter 4: The Time Value of Money Money has Sme value: Prefer money now to money later Why have interest at all? Simple interest Interest is earned only on the principal I = (P)(N)(i) Compound interest Interest is earned on both the principal and the interest accrued Economic equivalence Cash flows with the same economic effect Compare cash flows at the same point in Sme Willing to trade one cash flow for another that is economically equivalent Cash flow diagrams can be used to visualize cash flows Down arrows: Cash oualows Up arrows: Cash inflows Single payments with compound interest Find F given P F = P (1 + i)N = P (F/P, i%, N ) Single payment compound amount factor Find P given F: Reciprocal of F given P Single payment present worth factor P = F = F (P/F, i%, N ) (1 + i)N We also have find N and find i i= F P
1 N -1 F log P N= log 1 + i Uniform series (AnnuiSes) Cash flows occurring at fixed Sme intervals By convenSon, we use end of year for payments Find given A F (1 + i)N - 1 = A(F/A, i%, N ) F =A i Find given A P Find given F A (1 + i)N - 1 = A(P/A, i%, N ) P =A i(1 + i)N i = F (A/F, i%, N ) A=F (1 + i)N - 1 Find A given P A=P N i(1 + i) = P (A/P, i%, N ) N -1 (1 + i) Understand the derivaSons With just knowledge of F given P and F given A, can derive all the formulas Can even derive F given P and F given A from scratch Finding i and N best done using spreadsheet Deferred annuiSes are annuiSes where payments are not at the end of the first year, but at the end of year J The present equivalent value of a deferred annuity at Sme 0 is given by P0 = A(P/A, i%, N - J)(P/F, i%, J) Remember, can combine mulSple interest formulas in the same quesSon You might have a quesSon that has both single payments and annuiSes, or one with 2 annuiSes Uniform (ArithmeSc) Gradient of cash flows Unlike annuiSes, cash flows increase (or decrease) by a constant amount G DerivaSon of present value by considering all cash flows at Sme 0 N N 1 (1 + i) - 1 - P =G N i i(1 + i) (1 + i)N Can find values for (P/G, i%, N) in Appendix C Finding uniform annuity amount given G 1 N A=G - i (1 + i)N - 1 Also found in Appendix C F given G not given in Appendix 1 (1 + i)N - 1 F =G -N i i Remember payments start at end of year 1, so might have to use an annuity and uniform gradient series Geometric sequence of cash flows, where cash flows increase (or decrease) at a rate rather than by an amount " "N A1 1- 1+f 1+i A1 N
1+i i-f P = f = i, f = i. With P, can then find A or F using previous relaSonships Unlike uniform gradient series, payments start at end of first year, like normal annuiSes Nominal rates list annual rate, followed by compounding informaSon EffecSve rates reflect actual interest earned over the period Conversion: r M i= 1+ -1 M Can either have single payments, or mulSple payments where cash flow period coincides with compounding period If have mulSple payments with cash flows less frequently than compounding, find effecSve rate per cash flow period r k i= 1+ -1 M Example: Kris buys a car for $24,000. The dealership lets her defer payments for 12 months. If she makes 36 end-of-month payments, and interest is % per month, how much will Kris' payments be? ...
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- Spring '08
- payments, SME