#2 Time Value of Money solved problems pdf time value of money notes with solved illustrations pdf time value of money numerical with solutions pdf Financial management notes with solved illustrations pdf

 

TimeValue of Money Part 2 solved questions with solutions

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7. Mr. Ajai will receive Rs. 30,000 after 3 years. How much he has invested now if rate of interest is 10%.

Solution:

Money invested today = Present value = FV × PVF _{.1, 3} = Rs. 30,000 × 0.751 = 22,530

                                                                       = FV / (1+r)ⁿ = Rs. 30000/ (1.1)³ = 22530

8. Shyam will receive Rs. 6,000, Rs. 4,000 and Rs. 2,000 at the end of 1st, 2nd and 3rd year. Find present value of these cash flows considering discounting rate be 15 %.

Solution:

	A	B	C= A×B
Year	FV	PVFr,n	PV = FV × PVFr,n
1	Rs. 6,000	PVF.15, 1 = 0.870	Rs. 5,220
2	Rs. 4,000	PVF.15, 2 = 0.756	Rs. 3,024
3	Rs. 2,000	PVF.15, 3 = 0.658	Rs. 1,316
Present value of future cash flows			=5220+3024+1316 = Rs. 9560

 

9. Find the present value of the annuity consisting of a cash inflow of 17,000 per year for 3 years discounting rate being 18 %

Solution:

Present value of annuity = Annuity × PVAF _{.18, 3} = Rs. 17,000 × 2.174 = Rs. 36, 958

10. How much Rina has to invest to yield Rs. 10,000 p.a. in perpetuity if opportunity cost of capital (r) is 11 %.

Solution:

Amount to be invested by Rina = Present value of perpetuity = Cash flow ÷ r = Rs. 10,000 ÷.11

= Rs. 90,909

11. Rajni makes recurring deposit of Rs. 13,000 in the beginning of each of 5 years starting now at 12% p.a. how much she will get after 5 years?

Solution:

Future value of Annuity due = Annuity × FVAF_{0.12, 5} × (1+.12) = Rs. 13,000 × 6.353 × 1.12

= Rs. 92,500

12. What amount should be invested now to get an amount of Rs. 25,000 in the beginning of next 5 years at 8 % p.a. rate of interest?

Solution:

Present value of Annuity due = Annuity × PVAF_{0.09, 5} × (1+.09) = 25000 × 3.890 × 1.09

 = Rs. 1,06, 002.5

13. TCS wants to offer scholarship of Rs. 35,000 per year to 100 disabled sports persons  starting from one year now and it will increase at a constant rate of 5% every year Find the present value ofthis scholarship if rate of interest is 7%.

Solution:

Present value of perpetuity with constant growth rate = CF ÷ (r-g) = Rs. 35,000 ÷ (0.07-0.05)

= Rs. 17, 50, 000

Present value of scholarship given to 100 disabled sportspersons = Rs. 17,50, 000 × 100

= Rs. 17, 50, 00, 000

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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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