### Quiz On Discounting:

__Question1:__Calculate present value factors at 12% p.a. for a period for 5 years?#### Solution:

**Example 1)**

__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

→=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

Alternatively using pv annuity table you can find the answer.

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. 70626Alternatively 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%

This means that the investor will be ready to pay Rs.125 to purchase a preference share and earn a dividend of 10 rupee

C=cash flow i.e. dividend per period-Rs.10 pa

→R=8%

**Ans:**Hence Market Value Per Share is 10/8% =125This 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%

→=Rs.75

→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

Amount to be invested in sinking fund is Rs.327595.

SFI * (1+0.1)5-1/0.1 = 2000000

→= 2000000/6.1051

→=327595

**Ans:-**Amount to be invested in sinking fund is Rs.327595.