financial management - session 5new1

8/13/2019 Financial Management - Session 5new1

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Sinking Fund is created to pay a liability.Eg.redemption of a debenture.

Sinking Fund is the reciprocal of Annuity.

A = Fn i

(1+i)n- 1


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Sinking Fund Formula using Table Method

SF = A = fn[ 1/cvfa ni]


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Class workA company has issued debentures of Rs. 50

lakhs to be repaid after 7 years. How muchshould a company invest in a sinking fund,earning 12% in order to pay debentures.


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Solution

A = 50,00,000 .12

(1+.12)7

-1

= 4,95,584/-


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Present value: The current worth of a future sum of money

or stream of cash flows given a specified rateof return.

Future cash flows are discounted at adiscount rate.

Present Value


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Class Work

1. What is the Present Value of a FD that will

pay Rs.1000 in 3 years if the prevailinginterest rate is 5% compounded annually?How much do I need to deposit now.


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Solution

pv = Fn PVF i n

= 1000 (.864 )

= 864


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Present Value of an AnnuityFormulaPV of an annuity = Annuity 1 - 1i 1+i)nPv of an annuity table methodPv = A * pvfa n i)


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Class WorkWhat amount you must invest today at 6%compounded annually so that you canwithdraw Rs.5000 at the end of each year forthe next 5 years.


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Present Value of an AnnuitySolutionPV of an annuity = 5000 1 - 11+.06)5.06

=Rs. 21,058

solution


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Present value of uneven cash FlowsConsider that an investor has an opportunity

of receiving Rs.1000, Rs.1,500,Rs.800,Rs.1100 and Rs. 400 respectively atthe end of one through five years. Find thepresent value of the stream of uneven cashflows . The required rate of return is 8%

Class Work


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Solution

No ofYears Amount PresentValue TotalValue1 1000 .926 926

2 1500 .857 1286

3 800 .794 635

4 1100 .735 809

5 400 .681 272

Total 3928


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Present value of a growing annuity In this case each cash flow grows by a factor

of (1+g). Similar to the formula for anannuity, the present value of a growingannuity (PVGA) uses the same variables with

the addition of gas the rate of growth of theannuity (A is the annuity payment in the firstperiod)


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A 1+g n

p= 1 -

i-g 1+i

Present value of a growing annuity


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Problem

A company pays a dividend of Rs.66/- . Thedividend stream is expected to grow at 10%per annum for 15 years. If the discount rate is21 %, what is the present value of theexpected series?

Pv of a growing annuity


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66 1.10 15

p= 1 -

.21 -.10 1.21

= Rs. 456.36/-

Present value of a growing annuity


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The present value of a fund which issegregated for perpetuity is calculated bydividing the amount with the interest rate.

Class work:

An asset is expected to fetch Rs.1000 forperpetuity @ 10% interest. what is the presentvalue of the asset or what compensation

would an investor accept today instead ofhaving it for perpetuity.

Perpetuity


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Present value of a perpetuity

Present value = PerpetuityInterest rate

= 1000.1

= Rs.10.000/-


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Loan Amortization using Table method

Installment Amount = P 1

PVFA ni


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Amortize a 6% loan of Rs.25,000 paid back in4 annual end of the period installments.

Class Work


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Solution:

= 25000 1

3.465

= 7215


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Year Beg. Amt Annualinstalment Interest Principalrepayment Remainingbalance1 25000 7214 1500 5714 19285

2 19285 7214 1157 6057 13227

3 13227 7214 793 6421 6806

4 6806 7214 408 6806.40 0

Loan Amortization repaymentschedule.


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Present Value of an Annuity Due:= Present value of an Annuity (1+i)


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ProblemExactly 10 years from now Mr. Nitin will startreceiving a pension of Rs.3,000 a year. Thepayment will continue for 16 years. Howmuch is the pension worth now. If Nitinsinterest rate is 10%

Broken period calculations


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Solution

Years 1 25 years

Years 1 9 = no pension

Total pv of an annuity for 25 years @ 10% =9.077

Total pv of an annuity for first 9 years @ 10% =

5.759

Present value of the pension= 3000 (9.077 5.759)

= 9954


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ProblemA bank has offered to you an annuity ofRs.1,800 for 10 years if you invest Rs.12,000today. What rate of return would you earn/

Implicit interest rate or rate ofreturn


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Solution:

12,000 = 1800 (pvfa r, 10)

pvfa r, 10= 12000/1800pvfa r, 10 = 6.667

Refer table for present value factor of an annuity ofRe.1 equal to 6.667

@ 8% = 6.710@ 9% = 6.418

So it lies between 8 and 9 %

Implicit interest rate or rate ofreturn


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Using method of linear interpolation

lower discount Value Required value

8% + Higher discount value lower discount value

6.710 - 6.667

6.418 - 6.710=.15

= 8.15%


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ProblemHow long will it take to double your money if it

grows at 12 % annually?

Solution:

Fn = p * cvf ni2 = 1 * cvf n12From the table of compoud value factor the

factor nearest to 2 @ 12% is 1.974 therefore n= 6 years

Double the amount

financial management - session 5new1

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