Bank Management and Finance 5

BankManagement and Finance

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ASSIGNMENTTASK 2

QUESTION1

Money – weighted rate of return

Themoney-weighted rate of return refers to the discounting rate thatrelates the present value of cash inflows to the present value ofoutflows. It is calculated by applying a present value interestfactor (PVIF) which is computed as follows.

PVIF where r is the cash flow discounting rate and n is the number ofperiods the cash is being discounted.

Fora series of discounting

Ifthe portfolio returns are expressed in logarithmic, the logarithmicreturn during the entire period can be expressed as follows

Bysimplifying the arithmeticaverage money weighted rate of returnfor n periods will be equal to

Fora portfolio, the money – weighted rate of return can be computedfrom the formula below

PV(Cash Outflows) = PV (Cash Inflows)

PV(CashOutflows)= V(Cash inflows)

WhereA is the amount of proceedings from the shares the amount ifnegative for cash outflow and positive for cash inflow.

Calculatingthe money-weighted rate of return for the bank using the detailsprovided for buy and sell of shares CashoutflowsAttime t = 0(1January2012):

150shares purchased @ $156.30 per share = $23,445Andthe cash Inflows (from the dividends and the sale of shares)Attime t = 1

(1January2013):150 shares @ $10 dividend per share = $1,500

Onsale of shares

100shares sold @ $165per share = $16,500

Attime t = 2 (in year 2014)

(1January2014)50 shares @ $15 dividend per share = $750

Onsale of the remaining shares

50shares sold @ $170 per share = $8,500

Therefore,the above equation of calculating the money weighted rate of returnsof the bank’s portfolio can now be applied.PV(Cash Outflows) = PV (Cash Inflows)

Thatis

23,445= 1,500 + 16,500)+ 750 + [8,500=18,000(1+r) + [9,250]

Letting(1 + r)^{-1}to be x

18,000x+ 9,250x^{2}− 23,445 = 0

Solvingthe quadratic equations

We’ver = r = 0.120017 which is approximately 12%.

Partb)

Time-weightedrate of return TWROR

Thetime-weighted rate of return of the bank can be computed as follows

(1+ TWROR)^{ 2}= (1 + r_{1})(1+ r_{2})

Whereby,r_{1}and r_{2}represents the holding period returns in year 1 and 2 respectively.

Attime t = 0, The value of the portfolio is $23,445.

Andat time t = 1, There is cash inflow from sale of share worth $16,500and $1,500 in dividends. The valuation of the remaining 50 shares areworth worth $8,250 (50 × $165).

Therefore,the total valuation of the portfolio at time t = 1 is 16,500 + 1500 +8250 = $26,250

Theholding period returns in year 1is calculated as followsr1= 0.1196 for the first year

Theamount invested at year t = 1, is $8,250Attime t = 2, divindends worth $750 are received. Also there is a saleof shares worth of $8,500 (50 × $170). Therefore, the value of theportifolio at t = 2 is $9,250 + $750 = $8,500

r2= 0.121212 for the second year

applyingthe formula for time weighted rate of return

(1+ TWROR)^{ 2}= (1 + r_{1})(1+ r_{2})

√(0.1212× 0.1196) = 1 + TWROR

TWROR= 0.1204 = 12%

Question2)

Loaninterest: 10% $100,000,000 = 10,000,000

Applyingthe duration model, the basis point interest rate increased to 11.5%

Themarket value of Loan, MV_{A}= $10,000,000(PVIFA_{n=2, i = 11.5%})+ $100,000,000

(PVIFA_{n=2, i = 11.5%})= -0.25518 (from the PVIFA table)

(PVIF_{n=2},_{i = 11.5%})= $97,448,169.

Therefore,the change in the value of the loan is 97,448,169 – 100,000,000 =-$2,551,831 (which shows a decrease).

Calculating the market value

Interest8% => 0.08*90,000,000

Marketvalue = (0.08*90,000,000) + 90,000,000 = 97,200,000

Marketvalue of the note, MV_{N}= PVIF_{i= 9.5%}× $97,200,000 = $88,767,123

Thereforethere in a decrease in the market value of the note from 100,000,000to $88,767,123. ∆L = 88,767,123 – 100,000,000 = -$1,232,877

Comparing the results obtained in a and b above

Theabove results can be compared by examining the change in equity inrelation to the value of assets and debt.

Thechange in equity is equal to the change in assets minus the change inliabilities.

Thatis ∆E = ∆A – ∆L where ∆A= -$2,551,831 and ∆L= -$1,232,877

∆E= ∆A – ∆L

-$2,551,831 – (-$1,232,877) = -$1,318,954.

Therise in the interest rate resulted to a decrease in the assets valuewith a higher value than the decrease in the value of the liability.This caused the market value of the equity to decrease by $1,318,954.

Question3)

Cost of Car = $45,000.Hire Purchase interest rate 10.25% = 0.85417% per month

Numberof periods = 5 *12 = 60 moths

LoanInterest = 10.25%Balloon Payment ($45,000*20%)=$9,000Application fee = $125

Totalcash required = (45,000 + 9,000 + 125) = $54,125

Annualpayment of the loan = = $1156.67 per month

Thereforethe monthly instalment will be $1,156.67

See the amortization schedule in the excel spreadsheet attached. The loan balance as at 30 period is $31,384.99

The loan interest payable at 40

^{th}period is $189.1949 (loan balance * the interest rate). See the workings on the amortization table.Future value of annuity (FVA)

== = $49,236.38

Net financing cost

Thisis the cost of hire purchase = 10.25%

Financing cost under the hire purchase

i*(1-T)= 10.25%(1-0.3) = 7.175%

Question4)

A loss of $1 million shifts the distribution from 94 percentile to 96 percentile point. Hence, at 95% confidence level, the VaR is $1 million.

The expected shortfall is equivalent to the expected conditional loss represented by the 5% tail in the normal distribution curve. The expected shortfall at 95% confidence level can be calculated as follows

Loss | Chance | Expected shortfall |

1 million | 20% | $0.2 million |

10 million | 80% | $8.0 million |

Total expected shortfall | 8.2 million |

For the two investments the chance of loss for $20 million is 0.04 x 0.04 = 0.0016

Andfor loss of $11 million is 2 x 0.04 x 0.02 = 0.0016

Chancefor $9 million loss 2 x 0.04 x 0.94 = 0.0752

Chancefor $2 million loss, 0.02 x 0.02 = 0.04

Chancefor no loss, 2 x 0.2 x 0.94 = 0.0376

Chancefor$2 million profit, 0.94 x 0.94 = 0.8836

Thisimplies that the 95% VaR is $9 million.

The expected shortfall at 5 percent tail

0.0016/0.05= 0.032

Chancefor $20 million loss, a 0.0016/0.05 = 0.032

Chancefor $11 million loss and a 0.936 chance of a loss of $9 million

Therefore,expected shortfall is 0.032*$20 + 0.032*$11 + 0.936*$9 = $9.416million.