Formulas

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School
The University of Hong Kong **We aren't endorsed by this school
Course
FINA 1310
Subject
Finance
Date
Oct 12, 2023
Pages
1
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Formulas 1. Present and future values of a cash flow stream ( C 1 , C 2 , ..., C T ) PV = C 1 1 + r + C 2 (1 + r ) 2 + ... C T (1 + r ) T = T X t =1 C t (1 + r ) t FV = PV (1 + r ) T 2. Geometric series: ( a p, a p 2 , a p 3 , ... ): sum of first N terms: S N = a p 1 - p N 1 - p . If p < 1 then sum of the whole series is S 1 = a p 1 - p 3. Annuity present value: PV = C 1 - 1 (1+ r ) T r 4. Annuity due present value: PV = C 1 - 1 (1+ r ) T r (1 + r ) 5. Perpetuity present value: PV = C r 6. Growing annuity present value: PV = C 1 - ( 1+ g 1+ r ) T r - g 7. Growing perpetuity present value ( r > g ): PV = C r - g 8. EAR and APR: EAR = 1 + APR m m - 1 m !1 ! exp( APR ) - 1 9. Bond value: P = C 1 - 1 (1+ r ) T r + Par (1 + r ) T 10. Stock value after current dividends: P 0 = 1 X t =1 D t (1 + r ) t (a) Constant dividends: P 0 = D 1 r (b) Growing dividends: P 0 = D 1 r - g 11. Nominal rate, real rate and inflation: (1 + r nom. ) = (1 + r real )(1 + ) 12. NPV=PV of benefits - PV of costs 13. Internal rate of return: discount rate that makes NPV = 0 14. (Discounted) payback period = Number of years that pass before the sum of (discounted) invest- ment's cash flows equals the cost of the investment 15. Profitability index: PV of future cash flows divided by initial investment 1
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