Chapter 6 Valuation Techniques MGT 3412 Fall 2013 University of Lethbridge

Learning outcomes Understand compounding and discounting Capital Investment Project Decision NPV(DPV) and IRR criteria Decision trees and Scenario Analysis Practical issues (mutually exclusive, capital rationing, real vs. nominal cash flows DPV technique for bonds and stocks

Compounding and discounting Simple vs compounded interest - Future Value Mathematics of compounding Multiple period compounding Discounting and Present Value Formulas and Financial Calculator

Investment Valuation NPV – discounted cash flow valuation – Estimate cash flows – Estimate discount rate (depends on risk!)

© K. Cuthbertson and D. Nitzsche Figure 1 : Cash flows for Vito’s Deli 0 12 Time $ 1210$ $ 2100

© K. Cuthbertson and D. Nitzsche Discount (loan) rate NPV 0 8%10%12% Internal rate of return Figure 2 : NPV and the discount rate

© K. Cuthbertson and D. Nitzsche Table 2 : Different cash flow profiles ProjectsCash flows Project A (normal)(-100, 150) Project B (Rolling Stones concert) (100, -150) Project C (Open Cast Mining)(-100, 245, -150)

© K. Cuthbertson and D. Nitzsche Loan rate or discount rate, r NPV 0 r IRR= 50% Invest if IRR > cost of borrowing, r Cash flows = { -, -, -, … +, +, …, +} Figure 3 : Project A, normal cash flows

© K. Cuthbertson and D. Nitzsche Loan rate or discount rate, r NPV 0 r IRR=50% Cash flows = { +, +, …, -, -, - } Invest if IRR < cost of borrowing, r Figure 4 : Project B, Rolling Stones concert

© K. Cuthbertson and D. Nitzsche Loan rate or discount rate, r NPV 0 20% Multiple IRR = 20% and 25% r = loan rate 25% Cash flows = { -,-,-, …+,+, +, …,-,-, -} Figure 5 : Project C, open-cast mining

© K. Cuthbertson and D. Nitzsche Table 3 : Scale problem Cash flow at t=0 ($) Cash flow at t+1 ($) NPV ($) (r = 10%) IRR (%) Project A Project B

© K. Cuthbertson and D. Nitzsche Discount (loan) rate NPV % 18.36% 33.15% NPV L > NPV E Project L Project E Switching point NPV L < NPV E Figure 6 : Mutually exclusive projects

© K. Cuthbertson and D. Nitzsche We have the choice to abandon the project at ‘U’ or ‘D’. S D U Abandon AV 1 = 50 Do not abandon NPV 1 U = 150 UU UD Abandon AV 1 = 50 Do not abandon NPV 1 D = 40 p d = 0.25 p u = 0.75 p u|u p d|u DU DD p u|d p d|d Figure 7 : Decision tree

© K. Cuthbertson and D. Nitzsche Table 6 : Investment appraisal – other methods Year 0Year 1Year 2Year 3Year 4 Cash flow, CF Discount factor, d PV NPV = 161 Payback period = 2 years Discounted payback = 2 – 3 years