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!)
Figure 1 : Cash flows for Vito’s Deli
0
$ 1100
$ 1210
1
2
- $ 2100
© K. Cuthbertson and D. Nitzsche
Time
Figure 2 : NPV and the discount rate
NPV
Internal rate
of return
0
8% 10%
12%
© K. Cuthbertson and D. Nitzsche
Discount (loan) rate
Table 2 : Different cash flow profiles
Projects
Cash flows
Project A (normal)
(-100, 150)
Project B (Rolling Stones
concert)
Project C (Open Cast Mining)
(100, -150)
(-100, 245, -150)
© K. Cuthbertson and D. Nitzsche
Figure 3 : Project A, normal cash flows
Cash flows = { -, -, -, … +, +, …, +}
NPV
Invest if IRR > cost of borrowing , r
0
r
Loan rate or
discount rate, r
IRR= 50%
© K. Cuthbertson and D. Nitzsche
Figure 4 : Project B, Rolling Stones concert
Cash flows = { +, +, …, -, - , - }
NPV
Invest if IRR < cost of borrowing , r
IRR=50%
0
r
Loan rate or
discount rate, r
© K. Cuthbertson and D. Nitzsche
Figure 5 : Project C, open-cast mining
Cash flows = { -,-,-, …+,+, +, …,-,-, -}
NPV
Multiple IRR = 20% and 25%
r = loan rate
0
20%
25%
© K. Cuthbertson and D. Nitzsche
Loan rate or
discount rate, r
Table 3 : Scale problem
Cash flow Cash flow
at t=0 ($) at t+1 ($)
Project A
-10
15
NPV ($)
(r = 10%)
3.64
Project B
-80
110
20
© K. Cuthbertson and D. Nitzsche
IRR (%)
37.5
50
Figure 6 : Mutually exclusive projects
NPV
NPVL > NPVE
Switching point
NPVL < NPVE
0
8.71%
33.15%
18.36%
Discount (loan) rate
Project E
Project L
© K. Cuthbertson and D. Nitzsche
Figure 7 : Decision tree
Abandon
AV1 = 50
pu = 0.75
U
Do not abandon
NPV1U = 150
pu|u
pd|u
S
pd = 0.25
D
UU
UD
Abandon
AV1 = 50
pu|d
DU
Do not abandon
NPV1D = 40
pd|d
We have the choice to abandon the project at ‘U’ or ‘D’.
© K. Cuthbertson and D. Nitzsche
DD
Table 6 : Investment appraisal – other methods
Year 0 Year 1 Year 2 Year 3 Year 4
Cash flow, CF
Discount factor,
d
PV
-1000
500
500
700
0
1
0.869
6
435
0.756
1
378
0.497
2
348
-
-1000
NPV = 161
Payback period = 2 years
Discounted payback = 2 – 3 years
© K. Cuthbertson and D. Nitzsche
-