Payback period = number of years prior to full recovery +
𝑢𝑛𝑐𝑜𝑣𝑒𝑟𝑒𝑑 𝑐𝑜𝑠𝑡 𝑎𝑡 𝑡ℎ𝑒 𝑠𝑡𝑎𝑟𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑙𝑎𝑠𝑡 𝑦𝑒𝑎𝑟
𝑐𝑎𝑠ℎ 𝑓𝑙𝑜𝑤 𝑖𝑛 𝑡ℎ𝑒 𝑙𝑎𝑠𝑡 𝑦𝑒𝑎𝑟
Calculate IRR, let IRR = 𝑥
500
400
300
100
+
+
+
(1 + 𝑥) (1 + 𝑥)2 (1 + 𝑥)3 (1 + 𝑥)4
1000 (1 + 𝑥)4 = 500(1 + 𝑥)3 + 400(1 + 𝑥)2 + 300(1 + 𝑥) + 100
4
3
1000 (𝑥 + 4𝑥 + 6𝑥 2 + 4𝑥 + 1) = 500(𝑥 3 + 3𝑥 2 + 3𝑥 + 1) + 400(𝑥 2 + 2𝑥 + 1) + 300(1 + 𝑥) + 100
Accept project if IRR > required return
When IRR and NPV contradict, always follow NPV. (when project has unconventional cash flows (not all negative cash flows precede positive
cash flows )
1000 =
PV (growing perpetuity) 
Profitability Index 
C
r  g
C = cash flow for that year, r = cost of capital rate, g = growth rate
Value Created
NPV

Resource Consumed
Resource Consumed
Include opp cost, externalities
Changes in Net Working Capital = Current Assets –Current Liabilities
Net Working Capital  Current Assets  Current Liabilities
 Cash  Inventory  Receivables  Payables
 FV 
YTM n  

 P 
1
n
 1
For single projects
R 
1
T
 R1
Var (R) 
Expected Return  E  R  

2
Var (R)  E  R  E  R   


R
PR  R

R
PR 
1
T  1
1 T
 Rt
T t 1
 RT  
 R2 
T
 R
t 1
t
 R
2
Sum of probability*rate of return
R
 E  R 
2
SD( R) 
Var ( R)
Workings in decimal and answers in percentage.
Equity cost of capital
Debt cost