Time Value of Money Formulae pdf Financial Management notes with solved problems pdf Financial Management tuition TVM formulae RBL Academy http://rblacademy.com

Time Value of Money Formula

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1. Future value (FV) of asingle cash flow = PV × (1+r) ⁿ = PV × FVF _{r, n}

2. Future value of Annuity = Annuity amount × [(1+r) ⁿ + 1] ÷ r

                                            = Annuity amount × FVAF _{r, n}

3. Future value of Annuity due = [Annuity amount × [(1+r) ⁿ + 1] ÷ r] × (1+r)

                                                   = Annuity amount × FVAF _{r, n} × (1+r)

4. Present value (PV) of asingle cash flow = FV ÷ (1+r) ⁿ = FV × PVF _{r, n}

5. Present value (PV) ofAnnuity = Annuity amount × [1 – {1 ÷ (1 + r) ⁿ}] ÷ r

                                                     = Annuity amount × PVAF _{r, n}

6. Present value (PV) of Annuity due = [Annuity amount × [1 – {1 ÷ (1 + r) ⁿ}] ÷ r] × (1+r)

                                                              = Annuity amount × PVAF _{r, n} × (1+r)

7. Present value of perpetuity = Cash flow ÷ r

8. Present value of growing perpetuity = Cash flow ÷ (r – g)

9. Present value of growing annuity = [Cash flow ₁ ÷ (r-g) ] × [ 1- { (1+g) ÷(1+r)}ⁿ ]

10. Present value of growing annuity due = [Cash flow ₁ ÷ (r-g) ] × [ 1- { (1+g) ÷ (1+r)}ⁿ ] × (1 + r)

11. Future value of growing annuity = Present value of growing annuity × (1+r) ⁿ  

                                                           = [Cash flow ₁ ÷ (r-g) ] × [ (1+r)ⁿ – (1+g)ⁿ]

12. Future value of growing annuity due = Present value of growing annuity × (1+r) ⁿ × (1 +r)

                                                                  = [Cash flow ₁ ÷ (r-g) ] × [ (1+r)ⁿ – (1+g)ⁿ] × (1 +r)

In case, r = g

13. Present value of growingannuity = CF₁ × [n ÷ (1 + r)]

14. Present value of growingannuity due = CF₁ × [n ÷ (1 + r)] ×(1 + r)

15. Future value of growingannuity = CF₁ × n × (1+r) ⁿ⁻¹

16. Future value of growingannuity due = CF₁ × n × (1+r) ⁿ⁻¹ × (1 + r)

Finding growth rates

FV = PV (1 +g) ⁿ

g (growth rate) = _(FV/PV) _ ₁

PVF_{r, n} = PVIF_{r, n} = Present value interest factor at rate of interest r after n periods.

PVFA_{r, n} = PVIFA_{r, n} = Present value interest factor for an annuity at rate of interest r after nperiods.

FVF_{r, n} = FVIF_r,n =  CVIP_r,n = CVP_r,n  = Future or compound value interestfactor at rate of interest r after n periods.

FVFA_{r, n} = FVIFA_{r, n} = CVIPAr, n = CVPA_{r, n} = Future or compound value interestfactor for an annuity at rate of interest r after n periods.

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