# Time Value of Money: Part 3

### Quiz On Discounting:

Question1:Calculate present value factors at 12% p.a. for a period for 5 years?

#### Solution:

Example 1)
PV factor= 1/(1+r)n
→=1/(1+0.12)5
→=1/1/7623
Ans:→=0.567

Question2:Calculate the present Value of Rs.200000 to be received after 7 years at 10% compounded annually.

#### Solution:

Example 2)
PV=amount*1/(1+R)n
→=200000*1/(1+0.10)7
→=200000*1/1.9487
Ans:→=Rs.102633

### Present Value Of Annuity Due:

Question3:Mr.S expects to receive Rs.20000 at the beginning of each year for 4 years. Calculate the present value of the annuity due assuming interest rate is 9%.

#### Solution:

Example 3)
PV of Rs.20000 receivable at beginning of the 1 year = Rs.20000
PV of Rs.20000 receivable at the beginning of the 2nd year
→= 20000*1/1+0.09)1
→=20000*0.9174
→=18348
Similarly next year it will be = 20000*1/(1+0,09)2
→=16834
And for 4th year = 20000*1/(1+0.09)3
→= 20000*0.7722
→=Rs.15444
Ans:Totaling these you get Rs. 70626
Alternatively using pv annuity table you can find the answer.

### Present Value Of A Perpetuity:

Question4:A company has issued 10% preference shares of Rs.100each. what would be market price of the preference share if the rate of interest for the investor is 8% ?

#### Solution:

Example 4)
PV of a constant perpetuity = c/r
C=cash flow i.e. dividend per period-Rs.10 pa
→R=8%
Ans:Hence Market Value Per Share is 10/8% =125
This means that the investor will be ready to pay Rs.125 to purchase a preference share and earn a dividend of 10 rupee

Question5:A company has paid equity dividend of Rs.12 per share. Its profits and dividends are expected to grow at 6% calculate the market [rice of an equity share, if the rate of interest for the investor is 22%.

#### Solution:

Example 5)
PV of growing perpetuity= C/R-G
→C=cash flow i.e. dividend per period =rs 12
→R = rate of interest
→G=growth rate in cash flow
→PV=12/22%-6%
→=12/16%
Ans:-
→=Rs.75

### Sinking Fund:

Question6:Rane ltd. Has issued debentures of Rs.20 lakh to be repaid after 5 years. How much should the company invest insinking fund earning 105 in order to be able to repay debentures?

#### Solution:

Example 6)
sinking fund instalment* (1+R)n -1/R = Rs.2000000
SFI * (1+0.1)5-1/0.1 = 2000000
→= 2000000/6.1051
→=327595
Ans:-
Amount to be invested in sinking fund is Rs.327595.

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