### Numerical asked in RBI GRADE B Phase II 2016 2017 and 2018

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**Numerical asked in RBI GRADE B Phase II Finance and Management Paper in 2016, 2017 and 2018 (Memory based)**

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**Q.1 A bank has CRAR of 11.5% for capital of 230,000 crores. Calculate the CRAR as per BASEL II and RBI requirement for in line with BASEL II norms.**

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**Solution: **

The Capital to Risk weighted Asset Ratio (CRAR) as per Basel II norms: 8% of Rs. 230,000 = 18400

The Capital to Risk weighted Asset Ratio (CRAR) as per RBI norms: 9% of Rs. 230,000 = 20700

**Q.2 A person pruchase a share at a price of Rs. 400 and after one month sold at Rs 440. If he invests in future of the same share, price of the future is same of the share price and he has to pay 20% margin money for buying the future and sells the same after one month at Rs. 440, what will be the % return for both.**

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**Solution:**

Percentage return by selling of share: {(Selling price- buying price) / Buying Price} *100

= (440-400)/400 = (40/400)*100 =10%

Future price = 400

Total Investment in future = 20% of 400 = 80

Total gain = Selling price of future – Buying price = 440-400 = 40

Percentage return by selling of Future = (40/80)*100 =50%

**Q.3 250 is converted into 1000 in 16 years, identify the interest rate.**

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**Solution:**

**As per rule 144 money will be quadruple in years = 144/ Interest rate**

16 = 144/ Interest rate

Interest Rate = 144/16 = 9%

**Q.4 Rs. 400 will be converted into Rs. 800 at the rate of 9% in how many years.**

**Solution:**

As per rule 72 money will be doubled in years = 72/ Interest rate = 72/9 = 8 years

**Q.5 ABC Ltd issued `Rs. 2,00,000, 9% debentures at a discount of 10%. The tax rate is 50%. Compute the after tax cost of debt.**

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**Solution:**

Kd (after-tax) = I/P(1-t)

Kd = Cost of debt; I= interest; P= net proceeds, Where T = tax rate

Interest, I = 200000*9/100= 18000

Net proceed = 200000 – 200000*10/100 = 180000

T = 0.50

Kd (after tax) = I/P(1-t) = 18000/180000(1-0.5) = 0.05 or 5%

**Q.6 ABC Ltd. is engaged in sale of footballs. Its cost per order is Rs. 400 and its carrying cost unit is Rs. 10 per unit per annum. The company has a demand for 20,000 units per year. What is the economic order quantity**

**Solution:**

Where:

S is the cost of placing one order

D is the annual demand

H is the annual cost of holding one unit of inventory

S= 400

D=20000

H=10

Economic Order Quantity | = | √2 x 400 x 20000 | |

10 |

**= 1265 units**

**Q.7 Determine the present value of an annuity of Rs.700 each paid at the end of each of the next six years. Assume an 8 per cent of interest per annum.**

**Solution:**

Present value of an annuity** = C {1 – 1/ (1+i) ^{n}} / i **

Here C = 700, n = 6, i = 0.08

Present value = 700{1 – 1/ (1+0.08)^{6}} / 0.08 = 700X4.623 = 3236.10

**Q.8 Mr. X purchased a bond of face value Rs.1,000 at a price of Rs. 1005 bearing a coupon rate of 12% is redeemable at par in 10 years. Find out the value of the bond if required rate of return is 10%.**

Face Value of the Bond = Rs.1000

Purchase price rs 1005 indicates that Bond is purchased at premium

Coupon Rate, C = 12%

Interest P.a. = Face Value of the Bond*Coupon Rate = Rs.1000*12% = Rs.120 p.a.

Maturity Period = 10 yrs

M = Rs.1000

Present Value of Bond =PV

i= 10%=0.10

PV = C x PVIFA(10 years, 10%) + RV x PVIF(10th years, 10%)

PV = **C*{1 – 1/ (1+i) ^{n}} / i + M / (1+ i)^{n}**

PV = **120*{1 – 1/ (1+0.10) ^{10}} / 0.10 + 1000 / (1+ 0.10)^{10}**

PV = 120*6.144 + 1000*0.386 = Rs.1123

Present Value of bond= 1123

**Q.9 The share price and earning per share for 5 different bank as follows, which bank has the highest P/E ratio:**

Name of the bank | Share price per share | Earnings per share |

AXIS Bank | 1020 | 60 |

ICICI Bank | 1240 | 52 |

HDFC Bank | 2060 | 67 |

CITI Bank | 830 | 44 |

YES Bank | 1450 | 70 |

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- YES Bank
- CITI Bank
**HDFC Bank**- ICICI Bank
- AXIS Bank

**Solution: P/E ratio = **Price per Share / Earnings per share

**Q.10 Total cost on 1000 units is Rs. 12000 and total cost on 1200 units is Rs. 12800. Find out the break even point sales for 2200 units.**

**Solutions:**

Suppose Fixed Cost = X

Variable cost per unit = Y

Fixed cost = FC

Variable Cost= VC

Total cost =FC+VC

X+1000 Y = 12000

X+1200 Y = 12800

Solving the above two equation you will get Y=4 and X= 8000

So Variable cost per unit = Rs. 4

And Fixed cost =Rs. 8000

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**At Break even Point**

Sales value – Fixed cost – Variable cost = 0

Sales value = FC + VC

S_{BE} = FC + VC

S_{BE} = 8000 + 2200 x 4

S_{BE} = 8000 + 8800 = 16800

Sales value at break even point for Total 2200 Quantity = Rs. 16800

**Q.11 XYZ company has sales of Rs. 25,00,000. Variable cost of Rs. 15,00,000 and fixed cost of Rs. 500,000 and debt of Rs. 12,50,000 at 8% rate of interest. Find out operating and financial leverages.**

**Solutions:**

Statement of Profit

Sales =Rs. 25,00,000

Variable cost = Rs. 15,00,000

Contribution = Rs. 25,00,000 – Rs. 15,00,000 = Rs. 10,00,000

Fixed cost = Rs. 5,00,000

Operating Profit = Rs. 10,00,000 – Rs. 5,00,000 = Rs. 5,00,000

**Calculation of Operating leverage**

Operating leverage = Contribution / Operating Profit = 10,00,000 / 5,00,000 =2

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**Calculation of financial leverage**

Earnings before Interest and Tax (EBIT) = 5,00,000

Interest on Debenture (8% of 12,50,000) = 1,00,000

Earnings before Tax =5,00,000-1, 00,000= Rs.4,00,000

Operating leverage = Operating Profit (EBIT) / Earning Before Tax (EBT)

= 5,00,000 / 4,00,000 =1.25

**A firm purchased a share of another firm’s common stock exactly one year ago for Rs 45. During the past year, common stock paid an annual dividend of Rs. 5. The firm sold the stock today at Rs. 85, the rate of return the firm has earned:**- 50%
- 70%
- 85%
**100%**

Investment by firm= 45

Profit/gain by selling stock = 85-45= 40

Dividend received = 5

Total return/gain = 40+5 =45

% return = (Total return / investment) *100 = (45/45)*100 =100%

**Calculate WACC if a firm has 20 million in long term debt, rs 4 million preferred stock, rs 16 million of common equity, all at market value , the before tax cost for debt , preferred stock and common equity form of capital are 8%, 9% and 15% respectively. Assume 40% tax rate:**- 7%
- 9%
- 5%
**3%**

**WACC = [(D/V x Rd) x (1 – T)] + (E/V x Re) + (P/V x Rp) **

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(0.5) (8%) (1-.40) + (0.10) (9%) +(0.40) (15%) = 2.4% +0 .9% + 6% = 9.3%.

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E = market value of the firm’s equity (market cap) = 16 Mn

D = market value of the firm’s debt = 20 Mn

P= market value of the firm’s Preferred stock = 4Mn

V = total value of capital (equity + debt +preferred stock) = 40Mn

E/V = percentage of capital that is equity

D/V = percentage of capital that is debt

Re = cost of equity = 15% = 0.15

Rd = cost of debt (yield to maturity on existing debt) =8%= 0.08

Rp = cost of preferred stock = 9% = 0.09

T = tax rate = 40% = 0.40

- How much will receive Rs 1 lakh at the end of each of next 6 year, If interest rate to is 8%:
- 17685
**21631**- 23904
- 26098

Present value of an annuity** (PV) = C { 1 – 1/ (1+i) ^{n}} / i **

Here C = ? n = 5 i = 0.05 PV= 100000

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